SYSTEM OF LOGIC, 



RATIOCINATIVE AND INDUCTIVE; 



BEING A CONNECTED VIEW OP 



THE PRINCIPLES OF EVIDENCE AND THE METHODS 
OF SCIENTIFIC INVESTIGATION. 



BY JOHN STUART MILL 



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NEW-YORK: 

HARPER & BROTHERS, PUBLISHERS, 
82 CLIFF STREET. 

1848. 



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PREFACE. 



This book makes no pretence of giving to the world a new 
theory of our intellectual operations. Its claim to attention, if it 
possess any, is grounded on the fact that it is an attempt not to 
supersede, but to embody and systematize, the best ideas which 
have been either promulgated on its subject by speculative writers, 
or conformed to by accurate thinkers in their scientific inquiries. 

To cement together the detached fragments of a subject, never 
yet treated as a whole ; to harmonize the true portions of discordant 
theories, by supplying the hnks of thought necessary to connect 
them, and by disentangling them from the errors with which they 
are always more or less interwoven ; must necessarily require a 
considerable amount of original speculation. To other originality 
than this, the present work lays no claim. In the existing state of 
the cultivation of the sciences, there would be a very strong pre- 
sumption against any one who should imagine that he had effected 
a revolution in the theory of the investigation of truth, or added 
any fundamentally new process to the practice of it. The im- 
provement which remains to be effected in methods of philoso- 
phizing (and the author believes that they have much need of 
improvement) can only consist in performing, more systematically 
and accurately, operations with which, at least in their elementary 
form, the human intellect in some one or other of its employments 
is already familiar. 

In the portion of the work which treats of Ratiocination, the 
author has not deemed it necessary to enter into technical details 
■which may be obtained in so perfect a shape from the existing 
treatises on what is termed the Logic of the Schools. In the con- 
tempt entertained by many modern philosophers for the syllogistic 
art, it will be seen that he by no means participates ; although the 
scientific theory on v/hich its defence is usually rested appears to 
him erroneous : and the view which he has suggested of the nature 
and functions of the Syllogism may, perhaps, afford the means of 



IV PREFACE. 

conciliating the principles of the Art with as much as is well- 
grounded in the doctrines and objections of its assailants. 

The same abstinence from details could not be observed in the 
First Book, on Names and Propositions ; because many useful 
principles and distinctions which were contained in the old Logic, 
have been gradually omitted from the writings of its later teachers ; 
and it appeared desirable both to revive these, and to reform and 
rationalize the philosophical foundation on which they stood. The 
earher chapters of this preliminary Book will consequently appear, 
to some readers, needlessly elementary and scholastic. But those 
who know in what darkness the nature of our knowledge, and of 
the processes by which it is obtained, is often involved by a con- 
fused apprehension of the import of the different classes of Words 
and Assertions, will not regard these discussions as either frivolous, 
or irrelevant to the topics considered in the later Books. 

On the subject of Induction, the task to be performed was that 
of generalizing the modes of investigating truth and estimating 
evidence, by which so many important and recondite laws of 
nature have, in the various sciences, been aggregated to the stock 
of human knowledge. That this is not a task free from difficulty 
may be presumed from the fact, that even at a very recent period, 
eminent writers (among whom it is sufficient to name Archbishop 
Whately, and the author of a celebrated article on Bacon in the 
Edinhurgh Review), have not scrupled to pronounee it impossible. 
The author has endeavored to combat their theory in the manner 
in v^^hich Diogenes confuted the skeptical reasonings against the 
possibility of motion ; remembering that Diogenes' argument would 
have been equally conclusive, although his individual perambula- 
tions might not have extended beyond the circuit of his own tub. 

Whatever may be the value of what the author has succeeded 
in effecting on this branch of his subject, it is a duty to acknowledge 
that for much of it he has been indebted to several important trea- 
tises, partly historical and partly philosophical, on the generalities 
and processes of physical science, which have been published within 
the last few years. To these treatises, and to their authors, he has 
endeavored to do full justice in the body of the work. But as with 
one of these writers, Mr. Whewell, he has occasion frequently to 
express differences of opinion, it is more particularly incumbent on 
him in this place to declare, that without the aid derived from th(^ 
facts and ideas contained in that gentleman's History of the Induc- 
tive Sciences, the corresponding portion of this work would probably 
not have been written. 



PREFACE. V 

The concluding Book is an attempt to contribute towards the 
solution of a question, which the decay of old opinions, and the 
agitation that disturbs European society to its inmost depths, render 
as important in the present day to the practical interests of human 
life, as it must at all times be to the completeness of our speculative 
knowledge : viz., Whether moral and social phenomena are really 
exceptions to the general certainty and uniformity of the course of 
nature ; and how far the methods, by which so many of the laws 
of the physical world have been numbered among truths irrevo- 
cably acquired and universally assented to, can be made instru- 
mental to the gradual formation of a similar body of received 
doctrine in moral and political science. 

While the views promulgated in these volumes still await the 
verdict of competent judges, it would have been useless to attempt 
to make the exposition of them so elementary, as to be suited to 
readers wholly unacquainted with the subject. It can scarcely be 
hoped that the Second Book will be throughout intelligible to any 
one who has not gone carefully through some one of the common 
treatises on Logic ; among which that of Archbishop Whately is, 
on every account, to be preferred. And the Third Book presup- 
poses some degree of acquaintance with the most general truths 
of mathematics, as well as of the principal branches of physical 
science, and with the evidence on which those doctrines rest. 
Among books professedly treating of the mental phenomena, a 
previous familiarity with the earlier portion of Dr. Brown's Lec- 
tures, or with his treatise on Cause and Effect, would, though not 
indispensable, be advantageous ; that philosopher having, in the 
author's judgment, taken a more correct view than any other 
English writer on the subject of the ultimate intellectual laws of 
scientific inquiry; while his unusual powers of popularly stating and 
felicitously illustrating whatever he understood, render his works 
the best preparation which can be suggested, for speculations sim- 
ilar to those contained in this Treatise. 



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CONTENTS. 



INTRODUCTION. 



Page 



^ 1. A definition at the commencement 

of a subject must be provisional . 1 

2. Is logic the art and science of rea- 

soning? 2 

3. Or the art and science of the pursuit 

of truth? ib. 

4. Logic is concerned with inferences, 

not with intuitive truths . . 3 

5. Relation of logic to the other sci- 

ences 5 

6. Its utility, how shown ... 6 
' 7. Definition of logic stated and illus- 
trated ...... 7 

BOOK I. 

OF NAMES AND PROPOSITIONS. 

CHAPTER I. 

Of the necessity of commencing with an Anaylsis 

of Language. 
^ 1. Theory of names, why a necessary 

part of logic 11 

2. First step in the analysis of Propo- 

sitions .12 

3. Names must be studied before 

Things 13 

CHAPTER II. 

Of Names. 
^ 1. Names are names of things, not of 

our ideas 15 

2. Words which are not names, but 

parts of names . . . . ib. 

3. General and Singular names . .17 

4. Concrete and Abstract . . .18 

5. Connotative and Non-connotative . 20 

6. Positive and Negative . . .27 

7. Relative and Absolute , . .28 

8. Univocal and Equivocal . . 30 

CHAPTER III. 

Of the Things denoted by Names. 
i) 1. Necessity of an enumeration of 
Namable Things. The Categories 
of Aristotle 30 

2. Ambiguity of the most general 

names 32 

3. Feelings, or states of consciousness 34 

4. Feelings must be distinguished 

from their physical antecedents. 
Perceptions, what . . .35 

5. "Volitions, and Actions, what . .36 

6. Substance and Attribute . . 37 



^ 7. Body 38 

8. Mind 4^ 

9. Quahties ■....', 42 

10. Relations . . . ^ .* 44 

11. Resemblance ...*.. 46 

12. Quantity .....' 48 

13. All attributes of bodies are grounded 

upon states of consciousness . 49 

14. So also all attributes of mind . 50 

15. Recapitulation . . , .51 

CHAPTER IV. 

Of Propositions. 
§ 1. Nature and ofiSce of the copula . 52 

2. Affirmative and Negative proposi- 

tions 54 

3. Simple and Complex . . . 55 

4. Universal, Particular, and Sirigular 57 

CHAPTER V. 

Of the Import of Propositions. 
^ 1. Doctrine that a proposition is the 
expression of a relation between 
two ideas 59 

2. Doctrine that it is the expression of 

a relation between the meanings 
of two names . . . . 61 

3. Doctrine that it consists in referring 

something to, or excluding some- 
thing from, a class . . .63 

4. What it really is . , . .66 

5. It asserts (or denies) a sequence, a 

coexistence, a simple existence, a 
causation . . ... 67 

6. — or a resemblance . . . .69 

7. Propositions of which the terms are 

abstract 71 

CHAPTER VL 

Of Propositions merely Verbal. 
^ 1. Essential and Accidental proposi- 
tions . . •. • • .73 

2. All essential propositions are identi- 

cal propositions . . . .74 

3. Individuals have no essences . . 77 

4. Real propositions, how distinguished 

from verbal 78 

5. Two modes of representing the im- 

port of a Real proposition . . 79 

CHAPTER VII. 

Of the Nature of Classification, and the Five 

Predicables. 
^ 1. Classification, how connected with 

Naming BO 



VUl 



CONTENTS. 



Page 

§ 2. The Predicables, what ... 81 

3. Genus and Species .... ib. 

4. Kinds have a real existence in nature 83 

5. Differentia 86 

6. Ditferentise for general purposes, and 

differentiae for special or technical 
purposes 88 

7. Proprium . . . . . .89 

8. Accidens .90 

CHAPTER Via 

Of Definition. 
"5> 1. Definition, why treated of in this 

place 91 

2. A definition, what .... ib. 

3. Every name can be defined, whose 

meaning is susceptible of analysis 92 

4. Complete, how distinguished from ' 

incomplete definitions . . .94 

5. — and from descriptions . . .95 

6. What are called definitions of Things 

are definitions of Names with an 
implied assum ption of the existence 
of Things corresponding to them . 98 

7. — even when such things do not in 

reality exist . . . . . 101 

8. Definitions, though of \iames only, 

must be grounded on knowledge 
of the corresponding Things . 103 

BOOK II. 

OF REASONING. 

CHAPTER I. 

Of Inference, or Reasoning, in general. 
'5> 1. Retrospect of the preceding Book . 107 

2. Inferences improperly so called . 108 

3. Inferences proper, distinguished into 

inductions and ratiocinations . Ill 

CHAPTER II. 

Of Ratiocination, or Syllogism. 
■S 1. Analysis of the Syllogism .' .112 

2. The dictum de omni not the founda- 

tion of reasoning, but a mere iden- 
tical proposition . . . .116 

3. What is the really fundamental ax- 

iom of Ratiocination . . . 119 

4. The other form of the axiom . . 120 

CHAPTER III. 

Of the Functions, and Logical Value, of the 

Syllogism. 
^ 1. \s the SyV.ogism a petitio princivii ? . 122 

2. Insufficiencj of the common theory ib. 

3. All inference is from particulars to 

particulars 124 

4. General propositions are a record of 

such inferences, and the rules of 
the syllogism are rules for the in- 
terpretation of the record . . 129 
'). The syllogism not tho, type of rea- 
soning, but a test of it . ... 131 

6. The true type, what . . . 134 

7. Relation between Induction and De- 

duction 136 

CHAPTER IV. 

Of Trains of Reasoning, and Deductive Sciences. ! 
^ 1. For what purpose trains of reasoning 

exist 137 



Paga 

2. A train of reasoning is a series of 

inductive inferences . . . 138 

3. — from particulars to particulars 

through marks of marks . . 139 

4. Why there are deductive sciences . 141 

5. — and why other sciences still re- 

main experimental . . . 144 

6. Experimental sciences may become 

deductive by the progress of experi- 
ment 145 

7. In what manner this usually takes 

place 146 

CHAPTER V. 

Of Demonstration, and Necessary Truths. 

1. The theorems of geometry are only 

necessm-y truths in the sense of 
necessarily following from hypoth- 
eses 148 

2. Those hypotheses are real facts with 

some of their circumstances omit- 
ted 150 

3. Some of the first principles of geom- 

etry are axioms, and these are not 
hypothetical 151 

4. — but are experimental truths . . 152 

5. An objection answered . . .154 

6. Mr. Whewell's opinions on axioms 

examined 155 

CHAPTER VI. 

The same Subject continued. 

1. All deductive sciences are Inductive 162 

2. The propositions of the science of 

number are not verbal, but gener- 
alizations from experience , 

3. In what sense hypothetical 

4. The characteristic property of dem- 

onstrative science is to be hypo- 
thetical . . . . . 

5. Definition of demonstrative evidence 

and of logical necessity . . . 170 



164 

168 



169 



BOOK III. 

OF INDUCTION. 

CHAPTER I. 

Preliminary Observations on Induction in general. 
§ 1. Importance of an Inductive Logic . 171 
2. The logic of science is also that of 
business and life . . . . 172 

CHAPTER n. 

Of Inductions improperly so called. 
§ 1. Inductions distinguished from verbal 

transformations . . . . 174 

2. — from inductions, falsely so called, 

in mathematics 175 

3. —and from descriptions . . .177 

4. Examination of Mr. Whewell's the- 

ory of induction .... 178 

CHAPTER III. 

On the Ground of Induction. 
§ 1. Axiomofthe uniformity of the course 

of nature . . . . . 183 

2. Not true in every sense. Induction 

per enumerationem simplicem . . 186 

3. The question of Inductive Logic 

stated 187 



CONTENTS. 



IX 



Page 

CHAPTER IV. 
Of Laws of Nature. 
i) 1. The general regularity in nature is 
a tissue of partial regularities, call- 
ed laws 189 

2. Scientific induction must be ground- 

ed upon previous spontaneous in- 
ductions 191 

3. Are there any inductions fitted to be 

a test of all others ? . . .192 

CHAPTER V. 

Of the Law of Universal Causation. 

^ 1. Theuniversallawof successive phe- 
nomena is the Law of Causation . 194 

2. — i. e. the law that every consequent 

has an invariable antecedent . 196 

3. The cause of a phenomenon is the 

assemblage of its conditions . . 197 

4. The distinction of agent and patient 

illusory 201 

5. The cause is not the invariable ante- 

cedent, bni the unconditional invari- 
able antecedent . . . . 202 

6. Can a cause be simultaneous with 

its effect ? 204 

7. Idea of a Permanent Cause, or ori- 

ginal natural agent . . . 206 

8. Uniformities of coexistence between 

effects of different permanent 
causes, are not laws . . . 208 

9. M. Comte's objections to the word 

cause 209 

CHAPTER VI. 

Of the Composition of Causes. 

<j 1. Two modes of the conjunct action 
of causes, the mechanical and the 
chemical 210 

2. The composition of causes the gen- 

eral rule; the other case excep- 
tional 212 

3. Are effects proportional to their 

causes? 214 

CHAPTER VII. 

Of Observation and Experiment. 

'^) 1. The first step of inductive inquiry is 
a mental analysis of complex phe- 
nomena into their elements . . 216 

2. The next is an actual separation of 

those elements . . . . 217 

3. Advantages of experiment over ob- 

servation 218 

i. Advantages of observation over ex- 
periment 220 

CHAPTER VIII. 

Of the Four Methods of Experimental Inqiury. 

^ 1. Method of Agreement . . .222 

2. MethodofDiflerence . . .224 

3. Mutual relation of these two meth- 

ods 225 

4. Joint Method of Agreement and Dif- 

ference 227 

5. Method of Residues . . .229 

6. Method of Concomitant Variations . 230 

7. Limitations of this last method . 234 



Page 

CHAPTER IX. 

Miscellaneous Examples of the Four Methods, 
ij 1. Liebig's theory of metallic poisons . 237 

2. — how far a perfect example . . 239 

3. Theory of induced electricity . . 240 

4. Dr. Wells' theory of dew. . . 242 

5. Examples ofthe Method of Residues 247 

CHAPTER X. 

Of Plurality of Causes ; and of the Intermixture 

of Effects. 
{) 1. One effect may have several causes 250 

2. — which is the source of a character- 

istic imperfection of the Method of 
Agreement 251 

3. Plurahty of Causes, how ascertained 253 

4. Concurrence of causes which do not 

compound their effects . . . 254 

5. Difficulties of the investigation, 

when causes compound their ef- 
fects 256 

6. Three modes of investigating the 

laws of complex effects . . 259 

7. The method of simple observation 

inapplicable 260 

8. The purely experimental method in- 

applicable 261 

CHAPTER XI. 

Of the Deductive Method, 
(j 1. First stage ; ascertainment of the 
laws of the separate causes by di- 
rect induction .... 264 

2. Second stage ; ratiocination from 

the simple laws to the complex 
cases 267 

3. Third stage ; verification by specific 

experience 208 

CHAPTER XII 

Of the Explanation of Laws of Nature. 
^ 1. Explanation defined . . . 271 

2. First mode of explanation, by resolv- 

ing the law of a complex effect into 
the laws of the concurrent causes 
and the fact of their coexistence . ib. 

3. Second m^xle ; by the detection of an 

intermediate link in the sequence . 272 

4. Laws are always resolved into laws 

more general than themselves . ih. 

5. Third mode ; the subsumption of 

less general laws under a more 
g'eneral one . . . . 274 

6. What the explanation of a law of 

nature amounts to . . . . 270 

CHAPTER Xni. 
Miscellaneous Examples of the Explanatum of 

Laws of Nature. 
(J 1. Liebig's theory of the contagious- 
ness of chemical action . . 277 

2. His theory of respiration . . . 280 

3. Other speculations of Liebig . • 282 

4. Examples of following newly-dis- 

covered laws into their complex 
manifestations .... 283 

5. Examples of empirical generaliza- 

tions, afterwards confirmed and 
explained deductively . . . 284 

6. Example from mental science . . 285 



CONTENTS. 



§ 7. 



The deductive method henceforth 
the main instrument of scientific 
inquiry .... 



Page 



286 



CHAPTER XIV. 
Of the Limits to the Explanation of Laws of 

Nature ; and of Hypotheses. 
% 1. Can all the sequences in nature be 

resolvable into one law ? . . 286 

2. Ultimate laws cannot be less numer 

ous than the distinguishable feel 
ings of our nature . 

3. In what sense ultimate facts can be 

explained .... 

4. The proper use of scientific hypoth 

eses 

5. Their indispensableness . 

6. Legitimate, how distinguished from 

illegitimate hypotheses 

7. Some inquiries apparently i'lypothet 

ical are really inductive 



287 
289 



296 



297 



CHAPTER XV. 

Of Progressive Effects ; and of the Continued 

Action of Causes. 

How a progressive effect results 

from the simple continuance of 

the cause . . . . . 300 

— and from the progressiveness of 



^ 1. 



the cause 
Derivative laws generated from 
single ultimate law 



302 



304 



CHAPTER XVI. 

Of Empirical Laws. 
i 1. Definition of an empirical Idiw . 305 

2. Derivative laws commonly depend 

upon collocations . . . .306 

3. The collocations of the permanent 

causes are not reducible to any law 307 

4. And hence -empirical laws cannot be 

relied upon beyond the limits of 
actual experience .... ib. 

5. Generalizations which rest only on 

the Method of Agreement can only 

be received as empirical laws . 308 

6. Signs from whicti an observed uni- 

formity of sequence may be pre- 
sumed to be resolvable . . . 309 

7. Most, if not all, cases of sequence 

from very complex antecedents, 
are resolvable . . . .311 

8. Two kinds of empirical laws . , 312 

CHAPTER XVII. 

Of Chance, and its Elimination. 

% 1. Theproof of empirical laws depends 

on the theory of chance . . 312 

2. Chance defined and characterized .313 

3. The elimination of chance . .316 

4. Discovery of a residual phenomena 

by eliminating chance . . ,317 

5. The doctrine of chances . . . 318 

CHAPTER XVIII. 

Of the Calculation of Chances. 
^ 1. The foundation of the <loctrine of 
chances, as taught by Laplace, de- 
fective 319 

2. The real foundation, what . . 320 



Pago 

§ 3. Theorem of the doctrine of chances, 
which relates to the cause of a 
given event ..... 322 

4. In what cases the doctrine is practi- 

cally apphcable .... 325 

5. How applicable to the elimination 

of chance ib. 

CHAPTER XIX. 

Of the Extension of Derivative Laws to adjacent 
Ca^es. 

<5> 1. Derivative laws, when not causal, 
are almost always contingent upon 
collocations 327 

2. On what grounds they can be ex- 

tended to cases beyond the bounds 

of actual experience . . . 328 

3. Those cases must be adjacent cases 329 

CHAPTER XX. 

Of Analogy. 

§ 1. Various senses of the word analogy 332 

2. Nature of analogical evidence . ib. 

3. On what circumstances its value 

depends . . . . . . 335 

CHAPTER XXI. 

Of the Evidence of the Law of Universal 
Causation. 
<^ 1. The law of causality rests upon an 

induction by simple enumeration . 337 

2. In what cases such induction is 
allowable 339 

3. The universal prevalence of the law 
of causality may once have been 
doubtful . ■ . . . . . 340 

4. Grouna of its present certainty . 341 

5. Limits of the reliance due to it . 342 



CHAPTER XXII. 

Of Uniformities of Coexistence not dependent 
upoji Causation. 
The uniformities of coexistence 
which result from laws of se- 
quence 343 

2. The properties of Kinds are unifor- 

mities of coexistence . . . 344 

3. Some are derivative, others ultimate 345 

4. No universal axiom of coexistence . 346 

5. The evidence of uniformities of co- 

existence, how measured . . 347 

6. When derivative, their evidence is 

that ot empirical laws . . . 348 

7. So also when ultimate , . . 349 

8. The evidence stronger in proportion 

as the law is more general . . ib. 

9. Eveiy distmct Kind must be ex- 

aimned 350 



§ 1. 



CHAPTER XXIII. 

Of Approximate Gcncralizatioyis, and Prohable 

Evidence. 
% 1. The inferences called probable, rest 

upon approximate generalizations 351 

2. Approximate generalizations less 

useful m science than in life . 352 

3. In vvliat cases they must be re- 

sorted to 353 

4. In what manner proved . . . 354 

5. With what precautions employed . 358 



CONTENTS. 



XI 



Page 

^ 6. The two modes of combining proba- 
bilities . . . . . . 35G 

7. How approximate generalizations 
may be converted into accurate 
generalizations equivalent to them 358 

CHAPTER XXIV. 
Of the Remaining Laws of Nature. 
(Ji 1. Propositions which assert mere ex- 
istence 360 

2. Resemblance, considered as a sub- 

ject of science .... 361 

3. The axioms and theorems of mathe- 

matics comprise the principal laws 
of resemblance .... 363 

4. — and those of order in place, and 

rest upon induction by simple 
enumeration 36-1 

5. The propositions of arithmetic affirm 

the modes of formation of some 
given number .... ib. 

6. Those of algebra affirm the equiva- 

lence of different modes of forma- 
tion of numbers generally . . 367 

7. The propositions of geometry are 

laws of outward nature . . 369 

8. Why geometry is almost entirely 

deductive . . . . .371 

9. Function of mathematical truths in 

the other sciences, and limits of 
that function 372 

CHAPTER XXV. 

Of the Grounds of Disbelief. 
<J 1. Improbability and impossibility . 374 

2. Examination of Hume's doctrine of 

miracles ib.. 

3. The degrees of improbability cor- 

respond to differences in the na- 
ture of the generalization with 
which an assertion coiiliicts . . 377 

4. A fact is not incredible because the 

chances are against it . . . 379 

5. An opinion of Laplace examined . 380 

BOOK IV. 

OF OPERATIONS SUBSIDIARY TO 
LNDUCTION. 

CHAPTER I. 
Of Observation and Description. 
^ 1. Observation, how far a subject of 

logic 383 

2. A great part of what seems observa- 

tion is really inference . . . 384 

3. The description of an observation 

affirms more than is contained in 
the observation ... . . 386 

4. — namely, an agreement among phe- 

nomena ; and the comparison of 
phenomena to ascertain such 
agreements is a preliminary to in- 
duction .387 

CHAPTER II. 

Of Abstraction, or the Formation of Conceptions. 

ij 1. The comparison which is a pre- 
liminary to induction implies 
general conceptions . . . 389 | 
2. — but these need not be preexistent 390 j 



Page 

§ 3 A general conception, originally the 
result of a comparison, becomes 
itself the type of comparison .392 

4. What is meant by appropriate con- 

ceptions 394 

5. — and by clear conceptions . . 395 

6. Cases in which the conception must 

preexist 396 

CHAPTER III. 

Of N.aming, as subsidiary to Induction. 

<5) 1. The fundamental property of names 

as an instrument of thought . . 397 

2. Names are not indispensable to in- 

duction 398 

3. In what manner subservient to it . 399 

4. General names not a mere contriv- 

ance to economize the use of lan- 
guage 400 

CHAPTER IV. 

Of the Requisites of a Philosophical Language ; 
and the Principles of Definition. 

^ 1. First requisite of philosophical lan- 
guage, a steady and determinate 
meaning for every general name . 400 

2. Names in common use have often a 

loose connotation .... 401 

3. — which the logician should fix, with 

as little alteration as possible . 402 

4. Why definition is often a question 

not of words but of things . . 404 

5. How the logician should deal with 

the transitive applications of words 406 

6. Evil consequences of casting off any 

portion of the customary connota- 
tion of words 409 

CHAPTER V. 

Of the Natural History of the Variations in the 
Meaning of Terms. 

(J 1. How circumstances originally acci- 
dental become incorporated into 
the meaning of words , . . 414 

2. — and sometimes become the whole . 

meaning 415 

3. Tendency of words to become gen- 

eralized 416 

4. — and to become specialized . . 418 

CHAPTER VI. 

The Principles of a Philosophical Language 
further considered. 

() 1. Second requisite of philosophical 
language, a name for every im- 
portant meaning .... 421 

2. — viz., first, an accurate descriptive 

terminology ib. 

3. — secondly, a name for each of the 

more important results of scientific 
abstraction 424 

4. — thirdly, a nomenclature, or system 

of the names of kinds . . . 426 

5. Peculiar nature of the connotation 

of names which belong to a no- 
menclature 427 

6. In what cases language may, and 

may not, be used mechanically . 428 



Xll 



CONTENTS. 



CHAPTER VII. 



Page 



Of Classification, as subsidiary to Induction. 

(^ 1. Classification, as here treated of, 
wherein different from the classi- 
fication implied in naming . . 432 

2. Theory of natural groups . . 433 

3. Are natural groups given by type, or 

by definition ? . . . . 436 

4. Kinds are natural groups . . 438 

5. How the names of Kinds should be 

constructed 441 

CHAPTER VIII. 

Of Classification by Series. 

(^ 1, Natural groups should be arranged 

in a natural series .... 443 

2. The arrangement should follow the 

degrees of the main phenomenon . 444 

3. — which implies the assumption of 

a type-species .... 445 

4. How the divisions of the series 

should be determined . . . 446 

5. Zoology affords the completest type 

of scientific classification . . 447 



BOOK V. 

ON FALLACIES. 

CHAPTER I. 

Of Fallacies in general. 

^ 1. Theoiy of fallacies a necessary part 

of logic ...... 448 

2. Casual mistakes are not fallacies . 449 

3. The moral sources of erroneous 

opinion, how related to the intel- 
lectual 450 

CHAPTER II. 

Classification of Fallacies. 

i} 1. On what criteria a classification of 

fallacies should be grounded . 451 

2. The five classes of fallacies . . 452 

3. The reference of a fallacy to one or 

■ other class is sometimes arbitrary 454 

CHAPTER m. 

Fallacies of Simple Inspection, or a priori 
Fallacies. 

i) 1. Character of this class of fallacies . 456 

2. Natural prejudice of mistaking sub- 

jective laws for objective, exempli- 
fied in popular superstitions . . 457 

3. Natural prejudices, that things 

which we think of together must 
exist together, and that what is 
inconceivable must be false . . 459 

4. Natural prejudice of ascribing ob- 

jective existence to abstractions . 463 

5. Fallacy of the Sufficient Reason . 464 

6. Natural prejudice, that the ditfer- 

ences In nature correspond to the 
distinctions ia language . . 466 

7. Prejudice, that a phenomenon can- 

not have more than one cause . 468 

8. Prejudice, that the conditions of a 

phenomenon must resemble the 
phenomenon 470 



Page 
CHAPTER IV. ' 

Fallacies of Observation.. 
% 1. Non-observation, and Mahobserva- 

tion 475 

2. Non-observation of instances, and 

non-observation of circumstances . ib 

3. Examples of the former . . , 476 

4. — and of the latter .... 479 

5. Mal-observation characterized and 

exemplified 482 

CHAPTER V. 

Fallacies of Generalization. 
% 1. Character of the class . . . 485 

2. Certain kinds of generalization must 

always be groundless . . . ih. 

3. Attempts to resolve radically differ- 

ent phenomena into the same . 486 

4. Fallacy of mistaking empirical for 

causal laws 487 

5. Post hoc, ergo propter hoc ; and the 

deductive fallacy corresponding 
to it 490 

6. Fallacy of False Analogies . . 491 

7. Function of metaphors in reasoning 495 

8. How fallacies of generalization grow 

out of bad classification . . 497 

CHAPTER VL 

Fallacies of Ratiocination. 
% 1. Introductory remarks . , . 498 

2. Fallacies in the conversion and asqui- 

poUency of propositions . . ib. 

3. Fallacies in the syllogistic process . 499 

4. Fallacy of changing the premisses . ib. 

CHAPTER VII. 

Fallacies of Confusion. 
§ 1. Fallacy of Ambiguous Terms . . 502 

2. Fallacy of Petitio Principii . . 510 

3. Fallacy of Ignoratio Elenchi . . 515 



BOOK VI. 

ON THE LOGIC OF THE MORAL SCIENCES. 

CHAPTER I. 

Tntroductory Remarks. 
§ 1. The backward state of the Moral 
Sciences can only be remedied by- 
applying to them the methods of 
Physical Science, duly extended 
and generalized .... 519 
2. How far this can be attempted in 

the present work . • . . 520 ' 

CHAPTER II. 

Of Liberty arid Necessity. 

^ 1. Are human actions subject to the 

law of causality ? . . . .521 

2. The doctrine commonly called Phil- 

osophical Necessity, in what sense 
true . . . . . . 522 

3. Inappropriateness and pernicious 

effect of the term Necessity . . 523 

4. A motive not always the anticipa- 

tion of a pleasure or a pain . . 526 



CONTENTS. 



xm 



CHAPTER III. 



Page 



That there is, or may be, a Science of Human 
Nature. 
§ 1. There may be sciences which are 

not exact sciences , . . 527 

2. To what scientific type the Science 
of Human Nature corresponds . 528 

CHAPTER IV. 

Of the Laws of Mind 

^ 1. What is meant by Laws of Mind? . 530 

2. Is there a science of Psychology ? , ib. 

3. The principal investigations of Psy- 

chology characterized . . . 532 

4. Relation of mental facts to physical 

conditions 534 

CHAPTER V. 

Of Ethology, or the Science of the Formation of 
Character. 

§ 1. The Empirical Laws of Human 

Nature 537 

2. — are merely approximate generali- 

zations. The universal laws are 
those of the formation of char- 
acter 538 

3. The laws of the formation of char- 

acter cannot be ascertained by 
observation and experiment . . 540 

4. — but must be studied deduc- 

tively .542 

5. The Principles of Ethology are 

the axiomata media of mental 
science 544 

6. Ethology characterized . . .545 



CHAPTER VL 

General considerations on the Social Science. 

j 1. Are Social Phenomena a subject of 

Science ? 547 

2. Of what nature the Social Science 
must be 548 

CHAPTER VJ 

Of the Chemical, or Experimental Method in 

the Social Science. 
5> 1. Characters of the mode of thinking 
which deduces political doctrines 
from specific experience . , 550 

2. In the Social Science experiments 

are impossible .... 551 

3. — the Method of Diflference 'inap- 

plicable 552 

4. — and the Methods of Agreement, 

and of Concomitant Variations, 
inconclusive 553 

5. The Method of Residues presup- 

poses Deduction ..... 554 



Pace 

CHAPTER Vm. 

Of the Geometrical, or Abstract Method. 
^ 1. Characters of this mode of thinking 555 

2. Examples of the Geometrical 

Method 557 

3. The interest-philosophy of the Ben- 

tham School ib. 

CHAPTER IX. 
Of the Physical, or Concrete Deductive Method. 
'^ 1. The Direct and Inverse Deductive 

Methods 561 

2. Difficulties of the Direct Deductive 

Method in the Social Science . 563 

3. To what extent the different 

branches of sociological specula- 
tion can be studied apart. Po- 
litical Economy characterized . 565 

4. Political Ethology, or the science 

of national character . . . 569 

5. The Empirical Laws of the Social 

Science 570 

6. The Verification of the Social 

Science 572 

CHAPTER X. 

Of the Inverse Deductive, or Historical Method. 

^ 1. Distinction between the general 
Science of Society, and special 
sociological inquiries . . . 574 

2. What is meant by a State of Society ib. 

3. The Progressiveness of Man and 

Society 575 

4. The laws of the succession of states 

of society can only be ascertained 
by the Inverse Deductive Method 577 

5. Social Statics, or the science of the 

Coexistences of Social Phe- 
nomena 578 

6. Social Dynamics, or the science of 

the Successions of Social Phe- 
nomena 583 

7. Outlines of the Historical Metlwd . 584 

8. Future prospects of Sociological 

inquiry 586 

CHAPTER XL 

Of the Logic of Practice, or Art ; including 
Morality and Policy. 
^ 1. Morality not a Science, but an Art . 588 

2. Relation between rules of art and 

the theorems of the corresponding 
science ib. 

3. What is the proper function of rules 

of art? 589 

4. Art cannot be Deductive . . . 590 

5. Art consists of the truths of Science, 

arranged in the order suitable for 
practical use . . . . .591 

6. Application of the preceding princi- 

ples to Morahty .... 592 

7. Conclusion 593 



A SYSTEM OF LOGIC. 



INTRODUCTION. 



§ 1. There is as great diversity among authors in the modes which 
they have adopted of defining logic, as 'in their treatment of the details 
of it. This is v^^hat might naturally be expected on any subject oil 
w'hich writers have availed themselves of the same language, as a means 
of delivering different ideas. Ethics and jurisprudence are liable to 
the remark in common with logic. Almost every philosopher having 
taken a different view of some of the particulars which these branches 
of knowledge are usually understood to include ; each has so framed 
his definition as to indicate beforehand his own peculiar tenets, and 
sometimes to beg the question in their favor. 

This diversity is not so much an evil to be complained of, as an in- 
evitable and in some degree a proper result of the imperfect state of 
those sciences. There cannot be agreement about the definition of a 
thing, until there is agreement about the thing itself. To define a 
" thing, is to select from among the whole of its properties those which 
shall be understood to be designated and declared by its name; and 
the properties must be very well knoTvn to us before we can be com- 
petent to determine which of them are fittest to be chosen for this pur- 
pose. Accordingly, in the case of so complex an aggregation of par- 
ticulars as are comprehended in anything which can be called a science, 
the definition we set out with is seldom that which a more extensive 
knowledge of the subject shows to be the most appropriate. Until 
we know the particulars themselves, we cannot fix upon the most correct 
and compact mode of circumscribing them by a general description. 
It was not till after an extensive and accurate acquaintance with the 
details of chemical phenomena, that it was found possible to frame a 
rational definition of chemistry ; and the definition of the science of life 
and organization is still a matter of dispute. So long as the sciences 
are imperfect, the definitions must partake of their imperfections; and 
if the former are progressive, the latter ought to be so too. As much, 
therefore, as is to be expected from a definition placed at the com- 
mencement of a subject, is that it should define the scope of our in- 
quiries: and the definition which I am about to offer of the science of 
logic, pretends to nothing more, than to be a statement of the question 
which I have put to myself, and which this book is an attempt to re- 
solve. The reader is at liberty to object to it as a definition of logic; 
but it is at all events a correct definition of the subject of this 
volume. 

A ■ . - 



'2 INTRODUCTION. 

§ 2. Logic has often been called the Art of Reasoning. A writer* 
who has done more than any other living person to restore this study 
to the rank from which it had fallen iii the estimation of the cultivated 
classes in our own country, has adopted the above definition with an 
amendment; he has defined logic to be the Science, as well as the Art, 
of reasoning ; meaning, by the former term, the analysis of the mental 
process which takes place when&ver we reason, and by the latter, the 
rules, grounded upon that analysis, for conducting the process correctly. 
There can be no doubt as to the propriety of the emendation, A right 
understanding of the mental process itself, of the conditions it depends 
upon, and the steps of which it consists, is the only basis on which a 
system of rules, fitted for the direction of the process, can possibly be, 
founded. Art necessarily presupposes knowledge ; art, in any but its 
infant state, presupposes scientific knowledge ; and if every art does 
not bear the name of the science upon which it rests, it is only because 
several sciences are often necessary to form the groundwork of a single 
art. Such is the complication of human affairs, that to enable one thing 
to be done, it is often requisite to know the nature and properties of 
many things. 

Logic, then, comprises the science of reasoning, as well as an art, 
founded on that science. But the word Reasoning, again, like most 
other scientific terms in popular use, abounds in ambiguities. In one 
of its acceptations, it means syllogizing ; or the mode of inference 
which may be called (with sufficient accuracy for the present purpose) 
concluding from generals to particulars. In another of its senses, to 
reason, is simply to infer any assertion, from assertions already admitted : 
and in this sense, induction is as much entitled to be called reasoning 
as the demonstrations of geometry. 

Writers on logic have generally preferred the former acceptation of 
the term; the latter, and more extensive signification, is that in which 
I mean to use it. I do this by virtue of the right I claim for every 
author, to give whatever provisional definition he pleases of his own 
subject. But sufficient reasons will, I believe, unfold themselves as 
we advance, why this should be not only the provisional but the final 
definition. It involves, at all events, no arbitrary change in the mean- 
ing of the word; for, with the general usage of the English language, 
the wider signification, I believe, accords better than the more re- 
stricted one. 

§ 3. But reasoning, even in the widest sense of which the word is 
susceptible, does not seem to include all that is included, either in the 
best, or even in the most current, conception of the scope and province 
of our science. The employment of the word Logic to denote the 
theory of argumentation, is derived from the Aristotelion, or, as they 
are commonly termed, the scholastic logicians. Yet even with them, 
in their systematic treatises, argumentation was the. subject only of the 
third part : the two former treated of terms, and of propositions ; under 
one or other of which heads were, moreover, included. Definition and 
Division. Professedly, indeed, these previous topics were introduced 
only on account of their connexion with reasoning, and as a prepara- 
tion for the doctrine and rules of syllogism. Yet they were treated 
with greater minuteness, and dwelt upon at greater length, than was 

* Archbishop Whately. 



DEFIPJITION AND PROVINCE OF LOGIC. 3 

required for that purpose alone. More recent writers on logic have 
generally understood the term as it was employed by the able authors 
gf the Port Royal Logic ; viz., as equivalent to the Art of Thinking. 
Nor is this acceptation confined to philosophers, and works of science. 
Even in conversation, the ideas usually connected with the word Logic, 
include at least precision of language, and accuracy of classification : 
and we perhaps oftener hear persons speak of a logical arrangement, 
or expressions logically defined, than of conclusions logically deduced 
from premisses. Moreover, a man is often called a great logician, or a 
man of powerful logic, not for the accuracy of his deductions, but for 
the extent of his command over premisses ; because the general propo- 
sitions required for explaining a difficulty or refuting a sophism, copi- 
ously and promptly occur to him ; as in the case of Chillingworth, or 
Samuel Johnson. Wliether, therefore, we conform to the practice of 
those who have made the subject their particular study, or to that of 
popular writers and common discourse, the province of logic will 
include several operations of the intellect not usually considered to fall 
within the meaning of the terms Reasoning and Argumentation. 

These various operations might be brought within the compass of the 
science, and the additional advantage be obtained of a very simple 
definition, if, by an extension of the term, sanctioned by high authori- 
ties, we were to define logic as the science which treats of the opera- 
tions of the human understanding in the pursuit of truth. For to this 
ultimate end, naming, classification, definition, and all the other opera- 
tions over which logic has ever claimed jurisdiction, are essentially 
subsidiary. They may all be regarded as contrivances for enabling a 
person to know the truths which are needful to him, and to know 
them at the precise moment at which they are needful. Other pur- 
poses, indeed, are also served by these operations; for instance, that 
of imparting our knowledge to others,' But, viewed with regard to 
this purpose, they have never been considered as within the province 
of the logician. The sole object of Logic is the guidance of one's 
own thoughts ; the communication of those thoughts to others falls 
under the consideration of Rhetoric, in the large sense in which that 
art was conceived by the ancients ; or of the still more extensive art 
of Education. Logic takes cognizance of all intellectual operations, 
only as they conduce to our own knowledge, and to our command 
over that knowledge for our own uses. If there were but one rational 
being in the universe, that being might be a perfect logician ; and the 
science and art of logic would be the same for that one person, as for 
the whole human race. > ■ 

§ 4. But, if the definition which we formerly examined included too 
little, that which is now suggested has the opposite fault of including 
too much. 

Truths are known to us in two ways : some are known directly, 
a,nd of themselves ; some through the medium of other truths. The 
former are the subject of Intuition, or Consciousness-; the latter, of 
Inference. The truths known by intuition are the original premisses 
from' which all others are inferred. Our assent to the conclusion 
being grounded upon the truth of the premisses, we never could arrive 
at any knowledge by reasoning, unless something could be known 
antecedently to all reasoning. 



4 ^ . INTRODUCTION. . • 

Examples of truths known to us by immediate consciousness, are 
our own bodily sensations and mental feelings. I know directly, and 
of my own knowledge, that I was vexed yesterday, or that I am hun- 
gry to-day. Examples of truths which we know only by way of 
inference, are occurrences which took place while we were absent, the 
eyents recorded in history, or the theorems of mathematics. The two 
former we infer from the testimony "adduced, or from the traces of 
those past occurrences which still exist ; the latter, from the premisses 
laid down in books of geometry, under the title of definitions and ax- 
ioms. Whatever we are capable of knowing must belong to the one 
class or to the other ; must be in the number of the primitive data, or 
of the conclusions which can be drawn therefrom. 

With the original data, or ultimate premisses of our knowledge; 
with their number or nature, the mode in which they are obtained, or 
the tests by which they may be distinguished; logic, in a direct way 
at least, has, in the sense in which I conceive the science, nothing to 
do. These questions are partly not a subject of science at all, partly 
that of a very different science. 

Whatever is known to us by consciousness, is known beyond possi- 
bility of question. What one sees, or feels, whether bodily or men- 
tally, one cannot but be sure that one sees or feels. No science is 
required for the purpose of establishing such truths ; no rules of art 
can render our knowledge of them more certain than it is in itself 
There is no logic for this portion of our knowledge. 

But we may fancy that we see or feel what we in reality infer. 
Newton saw the truth of many propositions of geometry without read- 
ing the demonstrations, but not, we may be sure, without their flashing 
through his mind. A truth, or supposed truth, which is really the re- 
sult of a very rapid inference, may seem to be apprehended intuitively. , 
It has long been agreed by philosophers of the most opposite schools, 
that this mistake is actually made in so familiar an instance as that of 
the eyesight. There is nothing which we appear to ourselves more 
directly conscious of, than the distance of an object from us. Yet it 
has long been ascertained, that what is perceived by the eye, is at most 
nothing more than a variously colored surface ; that when we fancy 
we see distance, all we really see is certain variations of apparent 
size, and more or less faintness of color ; and that our estimate of the 
object's distance from us is the result of a comparison (made with so 
much rapidity that we are unconscious of making it) between the size 
and color of the object as they appear at the time, and the size and 
color of the same or of similar objects as they appeared when close at 
hand, or when their degi^ee of remoteness was known by other evi- 
dence. The perception of distance by the eye, vv^hich seems so like 
intuition, is thus, in reality, an inference grounded on experience; 
an inference, too, which we learn to make ;. and which we make with 
more and more correctness as our experience increases ; though in 
familiar cases it takes place so rapidly as to appear exactly on a par 
with those perceptions of sight which are really intuitive, our percep- 
tions of color.* 

* This celebrated theory has recently been called in question by a writer of deserved 
reputation, Mr. Samuel Bailey ; but I do not conceive that the grounds on which it has 
been received by philosophers for a century past, have been at all shaken by that gentle- 
man's objections. I have elsewhere said what appeared to me necessary in reply to his 
argument^. — Westminster Review, for October, 1842. 



DEFINITION AND PROVINCE OF LOGIC. 5 

Of the science, therefore, which expounds the operations of the hu- 
nia;i understanding in the pursuit of truth, one essential part is the 
inquiry : What are the truths which are the objects of intuition or 
consciousness, and what are those which we merely infer] But this 
inquiry has never been considered a portion of logic. Its place is in 
another and a perfectly distinct department of Science, which may be 
cal]ed the higher or transcendental metaphysics. For such is the title 
which has been given to that portion of mental philosophy which 
atteijipts to determine what part of the furniture of the mind belongs 
to it originally, and what part is constructed by itself out of materials 
fui-hislied from without. To this science appertain the great and 
much debated questions of the existence of matter ; of the existence 
of spirit, and the distinction between it and matter ; of the reality of 
time and space, as, things without the mind, and distinguishable from 
the objects which are said to exist in them. , For, in the present state 
of the discussion on these topics, it is universally allowed that the 
existence of matter or of spirit, of space or of time, is, in its nature, 
unsusceptible of being proved ; and that whatever is known of them, 
is known by immediate intuition. To the same science belong the 
inquiries into the nature of Conception, Perception, Memory, and 
Belief; all of which are operations of the understanding in the pursuit 
of truth ; but with which, as phenomena of the mind, or with the pos- 
sibility which may or may not exist of analyzing any of them into 
simpler phenomena, the logician as such has no concern. To this 
science must also be referred the following, and all analogous ques- 
tions : To what extent our intellectual faculties and our emotions are 
innate— 'to what extent the result of association. Whether God, and 
duty, are realities, the existence of which is manifest to us a priori by 
the constitution of our rational faculty ; or whether our ideas of them 
are acquired notions, the origin of which we are able to trace and 
explain ; and the reality of the objects themselves a question not of 
.consciousness or intuition, but of evidence and reasoning. 

The province of logic must be restricted to that portion of our knowl- 
edge which consists of inferences from truths previously known; 
whether, those antecedent data be general propositions, or particular 
observations and perceptions. Logic is not the science of Belief, but 
the science of Proof, or Evidence. So far forth as belief professes to 
be founded upon proof, the office of logic is to supply a test for ascer- 
taining whether or not. the belief is well grounded. With the claims 
which any proposition has to belief on its own intrinsic evidence, 
that is, without evidence in the -proper sense' of the Vs^ord, logic has 
nothing to do. 

§ 5. As the far greatest portion of our, knowledge, whether of gen- 
eral truths or Of particular facts, is avowedly matter of inference, 
nearly the whole, not only of science, but of human conduct, is amen- 
able to the authority of logic. , To draw inferences has been said to be 
the great business of life. Every one has daily, hourly, and moment- 
ary need of ascertaining facts which, he has not directly observed ; not 
from any general purpose of adding to his stock of knC>wledge, but 
because the facts themselves are of importance to his interests or to his 
occupations. The business of the magistrate, of the military com- 
mander, of the navigator^ of the physician, of the agricultiuist, is m.erely 



6 INTRODUCTION. 

to judge of evidence, and to act accordingly. They all hav>e to ascer- 
tain certain facts, in order that they may afterwards apply certain rules, 
either devised by themselves, or prescribed for their guidance by" 
others ; and as they do this well or ill, so they discharge well or ill the 
duties of their several callings. It is the only occupation in which the 
mind never ceases to be engaged ; and is the subject, not of logic, but 
of knowledge in general. Our definition of logic, therefore, will be iii 
danger of including the whole field of knowledge, unless we qualify it 
by some further limitation, showing distinctly where the domain of the 
other arts and sciences, and of common prudence ends, and that of 
logic begins. 

The distinction is, that the science or knovdedge of the particular 
subject-matter furnishes the evidence, while logic furnishes the prin- 
ciples and rules of the estimation' of evidence. Logic does not pre- 
tend to teach the surgeon what are the symptoms which indicate a 
violent death. This he must learn from his own experience and obser- 
vation, or from that of others, his predecessors in his peculiar science. 
But logic sits in judgment on the sufficiency of that observation and: 
experience to justify his rules, and on the sufficiency of his rules ta 
justify his conduct. It does not give him proofs, but teaches him what 
makes them proofs, and how he is to judge of them. Logic alone can 
never show that the fact A proves the fact B ; but it can point out to 
what conditions all facts must conform, in order that they may prove 
other facts. To decide whether any given fact fulfils l^hese conditions, 
or whether facts can be found which fulfil them in any given case, 
belongs, exclusively, to the particular art or science, or to our knowl- 
edge of the particular subject. 

It is in this sense that logic is, what Bacon so expressively calls it, 
ars artium ; the science of science itself. All science consists of data 
and conclusions from those data — of proofs, and what they prove :n now, 
logic points out what relations must subsist between data and what- 
ever can be concluded from them- — between proof and everything 
which it can prove. If there be any such indispensable relations, and 
if these can be precisely determined, every particular branch of science> 
as well as every individual in the guidance of his conduct, is bound to 
conform to those ^relations, under the penalty of making false infer- 
ences, of drawing conclusions which are not grounded in the realities 
of things. Whatever has at any time been concluded justly, whatever 
knowledge has been acquired otherwise than by immediate intuition, 
depended upon the observance of the laws which it is the province of 
logic to investigate. If the conclusions are just, and the knov/ledge 
sound, those laws have actually been observed. 

§ 6. "We need not, therefore, seek any further for a solution of the 
question, so often agitated, respecting the utility of logic. If a science 
of logic exists, or is capable of existing, it must be useful. If there be 
rules to which every mind conforms in every instance in which it 
judges rightly, there seem.s little necessity for discussing whether a - 
person is more likely to observe those rules, when he knows the rules, 
than when he is unacquainted with them. 

A science may undoubtedly be brought to a certain, not inconsider- 
able, stage of advancement, without the application of any other logic 
to it than whxit all persons, who are said to have a sound understand- 



DEFINITION AND PROVINCE OF LOGIC. 7 

ing, acquire empirically in the course of tlieir studies. Men judged of 
evidence, and often very correctly, before logic was a science, or tliey 
never could have made it one. And they executed great mechanical 
works before they understood the laws of mechanics. But there are 
limits both to what mechanicians can do without principles of mechan- 
ics, and to what thinkers can do without principles of logic. And the 
limits, in the two cases, are of the same kind. The extent of what 
man can do without understanding the theory of what he is doing, is 
in all cases much the same : he can do whatever is very easy ; ^what 
requires only time, and patient industry. But in the progress of 
science from its easiest to its more difficult problems, every great step 
in advance has had either as its precursor or as its accompaniment and 
necessary condition, a coiTesponding improvement in the notions and 
principles of logic received among the most advanced thinkers. And 
if several of the more difficult sciences are still in so defective a state ; 
if not only so little is proved, but disputation has not terminated even 
about the little which seemed to be so ; the reason, perhaps, is, that 
mien's logical notions have not yet acquired the degree of extension, 
or of accuracy, requisite for the estimation of the evidence proper to 
those particular departments of knowledge. 

§ 7. Logic, then, is the science of the operations of the understand- 
ing which are subservient to the estimation of evidence : both the 
process itself of proceeding from known truths to unknown, and all 
intellectual operations auxiliary to this. It includes, therefore, the 
operation of Naming ; for language is an instrument of thought, as 
well as a means of communicating our thoughts. It includes, also, 
Definition, and Classification. For, the use of these operations (putting 
all other minds than one's own out of consideration) is to serve not 
only for keeping our evidences and the conclusions from them perma- 
nent and readily accessible in the memory, but for so marshaling the 
facts which we may at any time be engaged in investigating, as to 
enable us to perceive more clearly what evidence there is, and to judge 
with fewer chances of error whether it be sufficient. The analysis of 
the instruments we employ in the investigation of truth, is part of the 
analysis of the investigation itself; since no art is complete, unless 
another art, that of constructing the tools and fitting them for the 
purposes of the art, is embodied in it. 

Our object, therefore, mil be to attempt a correct analysis of the 
intellectual process called Reasoning or Inference, and of such other 
mental operations as are intended to facilitate this : as well as, on the 
foundation of this analysis, and j^ciri passu -with it, to bring together or 
frame a set of rules or canons for testing the sufficiency of any given 
evidence to prove any given proposition. 

With respect to the first part of this undertaking, I do not attempt 
to decompose the mental operations in question into their ultimate 
elements. It is enough if the analysis as far as it goes is coiTect, and 
if it goes far enough for the practical pui-poses of logic considered as 
an art. The separation of a contplicated phenomenon into its compo- 
nent parts, is not like a connected and interdependent chain of proof. 
If one link of an argument breaks, the whole drops to the ground ; but 
one step towards an analysi's holds good, and has an independent value, 
though we should never be able to make a second. The results of 



8 INTRODUCTION. 

analytical chemistry are not the less valuable, though it should be dis- 
covered that all which we now call simple substances are really com- 
pounds. All other things are at any rate compounded of those 
elements : whether the elements themselves admit of decomposition, 
is an important inquiry, but does not affect the certainty of the science 
up to that point. 

I shall, accordingly, attempt to analyze the process of inference, 
and the processes subordinate to inference, so far only as may be 
requisite for ascertaining the difference between a correct and an 
incorrect performance of those processes. The reason for thus limit- 
ing our design, is evident. It has been said by objectors to logic, that 
we do not learn to use our muscles by studying their anatomy. The 
fact is not quite fairly stated ; for if the action of any of our muscles 
were vitiated by local weakness, or other physical defect, a knowledge 
of their anatomy might be very necessary for effecting a cure. But 
we should be justly liable to-.the criticism involved in this objection, 
were we, in a treatise on Logic, to carry the analysis of the reasoning 
process beyond the point at which any inaccuracy which may have 
crept into it must become visible. In learning bodily exercises (to 
carry on the same illustration) we do, and must analyze the bodily 
motions, so far as is necessary for distinguishing those which ought to 
be performed from those which ought not. To a similar extent, and 
no further, it is necessary that the logician should analyze the mental 
processes with which Logic is concerned. Any ulterior and minuter 
analysis must be left to transcendental metaphysics ; which in this, as 
in other parts of our mental nature, decides what are ultimate facts, 
and what are resolvable into other facts. And I believe it will be 
found that the conclusions arrived at in this work have no necessary 
connexion with any particular views respecting the ulterior analysis. 
Logic is common ground on which the partisans of Hartley and of 
Reid, of Locke and of Kant, may meet and join hands. Particular 
and detached opinions of all these philosophers will no doubt occasion- 
ally be controverted, since all of them were logicians as well as meta- 
physicians ; but the field on which their great battles have been fought, 
lies beyond the boundaries of our science ; and the views which will 
be here promulgated, may, I believe, be held in conjunction with the 
principal conclusions of any one of their systems of philosophy. 

It cannot, indeed, be pretended that logical principles can be alto- 
gether irrelevant to those more abstruse discussions ; nor is it possible 
but that the view we are led to take of the problem which logic pro- 
poses, must have a tendency favorable to the adoption of some one 
opinion on these controverted subjects rather than another. Logic, 
although differing from the higher metaphysics like the other half of a 
great whole (the one being the science of the appreciation of evidence, 
the other having for its main object to determine what are the propo- 
sitions for the establishment of which evidence is not required), yet 
when viewed under another of its aspects, stands in the same relation 
to this, its sister science, as it does to all the other sciences. For 
metaphysics, in endeavoring to solve its own peculiar problem, must 
employ means, the validity of which falls under the cognizance of logic. 
It proceeds, no doubt, as far as possible, merely by a closer and more 
attentive interrogation of our consciousness, or, more properly speak- 
ing, of our memory ; and so far is not amenable to logic. But where- 



DEFINITION AND PROVINCE OF LOGIC, 9 

ever tliis method is insufficient to attain the end of its inquiries, it must 
proceed, hke other sciences, by means of evidence. Now, the moment 
this science begins to draw inferences from evidence, logic becomes 
the sovereign judge whether its inferences are well-grounded, or what 
other inferences would be so. 

. This influence, however, of logic over the questions which have 
divided philosophers in the higher regions of metaphysics, is indirect 
and remote ; and I can conscientiously affirm, that no one proposition 
laid down in this work has been adopted for the sake of establishing, 
or with any reference to its fitness for being employed in establishing, 
preconceived opinions in any department of knowledge oi* of inquiry 
on which the speculative world is still undecided, 
B 



BOOK I. 

OF NAMES AND PROPOSITIONS. 



^" La scolastique, qui produisit dans la logique, comme dans la morale, et dans une partie 
de la metaphysique, une subtilite, une precision d'idees, dont I'habitude inconnue aux an- 
ciens, a contribue plus qu'on ne. croit au progrfes de la bonne philosophie."— Condor.cet, 
Vie de Turgot. 



CHAPTER I. 

OF THE NECESSITY OF COMMENCING WITH AN ANALYSIS OF LANGUAGE. 

§ 1. It is SO much the estabhshed practice of winters on logic to 
commence their treatises by a few general observations (in most cases, 
it is true, rather meagre) on Terms and their varieties, that it will, per- 
haps, scarcely be required from me, in merely following the common 
usage, to be as particular in assigning my reasons, as it is usually ex- 
pected that those should be who deviate from it. 

^ The practice, indeed, is recommended by considerations far too ob- 
vious to require a formal justification. Logic is a portion of the Art 
of Thinking : Language is evidently, and by the admission of all phi- 
losophers, one of the principal instruments Or helps of thought ; and 
any imperfection in the instrument, or in the mode of employing it, is 
confessedly liable, still more than in almost any other art, to confuse 
and impede the process, and desti^oy all ground of confidence in the 
result. For a mind not previously versed in the meaning and right use 
of the various kinds of words, to attempt the study of methods of phi- 
losophizing, would be as if some one should attempt to make himself 
an astronomical observer, having never learned to adjust the focal dis- 
tance of his optical instruments so as to see distinctly. 

Since Reasoning, or Inference, the principal subject of logic, is an 
operation which usually takes place by means of words, and in all 
complicated cases can take place in no other way, those who have not 
a thorough insight into the signification and purposes of words, will be 
under almost a necessity of reasoning or inferring incorrectly. And 
logicians have generally felt that unless, in the very first stage, they 
removed this fertile source of error ; unless they taught their pupil to 
put away the glasses which distort the object, and to use those which 
are' adapted to his purpose in such a manner as to assist, not perplex, 
his vision ; he would not be in a condition to practise the remaining 
part of their discipline with any prospect of advantage. Therefore it 
is, that an inquiry into language, so far as is needful to guard against 
the errors to which it gives rise, has at all times been deemed a neces= 
eary preliminary to the science of logic. 

But there is another reason, of a still more fundamental natiu'e, why 



12 NAMES AND PROPOSITIONS. 

the import of Words ^liould be the earliest subject of the logician's con- 
sideration : because without it he cannot examine into the import of 
Propositions. Now this is a subject which stauds on the very thresh- 
hold of the science of logic. 

The object of logic, as defined in the Introductory Chapter, is to 
ascertain how we come by that portion of our knowledge (much the 
greatest portion) which is not intuitive ; and by what, criterion we can, 
in matters not self-evident, distinguish between things proved and things 
not proved, between what is worthy and what is unworthy of belief. 
Of the various questions which the universe presents to our inquiring 
faculties, some are soluble by direct consciousness, others only by 
means of evidence. Logic is concerned with these last. The solution, 
by means of evidence, of questions respecting the universe and the 
things contained in it, is the purpose of logic. But before inquiring 
into the mode of resolving questions, it is necessary to inquire, what 
are the questions which present themselves] what questions are con- 
ceivable 1 what inquiries are there, to which men have either obtained,, 
or been able to imagine it possible that they should obtain, an answer ? 
This point is best ascertained by a survey and analysis of Propositions. 

§ 2. The answer to every question wnich it is possible to frame, is 
contained in a Proposition, or Assertion. Whatever can be an object 
of belief, or even of disbelief, must, when put into words, assume the 
form of a proposition. All truth and all error lie in propositions. 
What, by a convenient misapplication of an abstract term, we call a 
Truth, is simply a True Proposition ; and errors are false propositions. 
To know the import of all possible propositions, would be to know all 
questions which can be raised, all matters which are susceptible ofbe- 
ing either believed or disbelieved. How many kinds of inquiries can 
be propounded; how many kinds of judgments can be made; and 
how many kinds of propositions it is possible to frame with a meaning, 
are but different forms of one and the same question. Since, then^ the 
objects of all Belief and of all Inquiry express themselves in propo- 
sitions ; a sufficient scrutiny of Propositions and of their varieties will 
apprise us what questions mankind have actually asked themselves, 
and what, in the nature of answers to those questions, they have actu- 
ally thought they had, grounds to believe. 

Now the first glance at a proposition shows that it is formed by put- 
ting together two names; A proposition, according to the common 
simple definition-, which is sufficient for our purpose, is, discourse, in 
which something is affirmed or denied of so7nething. Thus, in the prop- 
osition, Grbld is yellow, the quality yellow is affirmed of the substance 
gold. In the proposition, Franklin was not born in England, the 
fact expressed by the words horn in England is denied of the man 
Franklin. 

Every proposition consists of three parts: the Subject, the Predi- 
cate, and the Copula. The predic£(.te is the name denoting that which 
is affirmed or denied. The subject is the name denoting the person 
or thing which something is affirmed or denied of The copula is the 
sign denoting that there is an affirmation or denial ; and thereby ena- 
bling the hearer or reader to distinguish a proposition from any other 
kind of discourse. Thus, in the proposition, The earth is round, the 
Predicate is the word round, which denotes the quaUty afiirmed, or 



NECESSITY OF AN ANALYSIS OF NAMES. 13 

(as the phrase is) predicated : tlie earth, words denoting the object 
which that quaUty is affirmed of, compose the Subject; the word is^ 
which serves as the connecting mark between the subject and predi- 
cate, to show that one of them is affirmed of the other, is called the 
Copula. 

Dismissing, for the present, the copula, of which more will be said 
hereafter, every proposition, then, consists of at least two names; 
brings together two names, in a particular manner. This is already a 
first step towards what we are in quest of. It appears from this, that 
for an act of belief, one object is not sufficient; the simplest act of be- 
lief supposes, and has something to do with, two objects : two names, 
to say the least ; and (since the names must be names of something) 
two nameahle things, A large class of thinkers would cut the matter 
short by saying, two ideas. They v/ould say, that the subject and 
predicate are both of them names of ideas; the idea of gold, for in- 
stance, and the idea of yellow ; and that what takes place (or a part 
of what takes place) in the act of belief, consists in bringing (as it is 
often expressed) one of these ideas under the other. But this we are 
not yet in a condition to say : whether such be the coiTect mode of 
describing the phenomenon, is an after consideration. ' The result 
with which for the present we must be contented, is, that in every act 
of belief two objects are in some manner taken cognizance of; that 
there can be no belief claimed, or question propounded, which does 
not embrace two distinct (either material or intellectual) subjects of 
thought : each of them capable or not of being conceived by itself, but 
incapable of being believed by itself. 

I may say, for instance, " the sun." The word has a meaning, and' 
suggests that meaning to the mind of any one who is listening to me. 
But suppose I ask him, Whether it is true : whether he believes it % 
He can give no answer. There is as yet nothing to believe, or to dis- 
believe. Now, however, let me make, of all possible assertions respect- 
ing the sun, the one which involves the least of reference to any object 
besides itself; let me say, " the sun exists." Here, at once, is some- 
thing which a person can say he believes. But here, instead of only 
one, we find two distinct objects of conception : the sun, is one object; 
existence, is another. Let it not be said, that this second conception, 
existence, is involved in the first ; for the sun may be conceived as no 
longer existing. " The sun" does not convey all the meaning that is 
conveyed by "the sun exists:" *' my father" does not include all the 
meaning of " my father exists," for he may be dead ; " a round square" 
does not include the meaning of " a round square exists," for it does 
not, and cannot exist. When I say, ">the sun," **my father," or a 
"round square," I call upon the hearer for no belief or disbelief, nor 
can either the one or th^ other b& afforded me ; but if I say, " the sun 
exists," "my father exists," or "a round square exists," I call for be- 
lief; and should, in the first of tlie three instances meet with it ; in the 
second, with belief or disbelief, as the case might be ; in the third, 
with disbehef. 

§ 3. This first step in the analysis of the object of belief, which, 
though so obvious, will be found to be not unimportant, is the only one 
which we shall find it practicable to make vdthout a preliminary sur- 
vey of language. If we attempt to proceed further in the same path, 



14 NAMES AND PROPOSITIONS. 

that is, to analyze any further the import of Propositions ; we find 
forced upon us, as a subject of previous consideration, the import of 
Names. For every proposition consists of two names ; and every 
proposition affirms or denies one of these names, of the other. Now 
what we do, what passes in our mind, when we affirm or deny two 
names of one another, must depend upon what they are names of; 
since it is with reference to that, and not to the mere names them- 
selves, that we make the affirmation or denial. Here, therefore, we 
find a new reason why the signification of names, and the relation, 
generally, between names and the things signified by them, must oc- 
cupy the preliminary stage of the inquiry we are engaged in. 

It may be objected, that the meaning of names can guide us at most 
only to the opinions, possibly the foolish and groundless opinions, 
which mankind have formed concerning things, and that as the object 
of philosophy is truth, not opinion, the philosopher should dismiss 
words and look into things themselves, to ascertain what questions can 
be asked and answered in regard to them. This advice (which fortu- 
nately no one has it in his power to follow) is in reality an exhortation 
to discard the whole fruits of the labors of his predecessors, and de- 
mean himself as if he were the first person who had ever turned an 
inquiring eye upon nature. What does any one's personal knowledge 
of Things amount to, after subtracting all which he has acquired by 
means of the words of other people 1 Even after he has learnt as 
much as men usually do learn from, others, will the nptions of things 
contained in his individual mind affiDrd as sufficient a basis for a cata- 
logue raisonnee as the notions which are in the minds of all man- 
kind] 

In any enumeration and classification of Things, which does not set 
out from their names, no varieties of things will of course be compre- 
hended but those recognized by the particular inqliirer; and it will 
still remain for him to establish, by a subsequent examination of names, 
that his enumeration has omitted nothing which ought to have been 
included. But if we begin with names, and use them as our clue to 
the things, we bring at once before us all the distinctions which have 
beeii recognized, not by a single inquirer of perhaps limited views, but 
by the collective intelligence of mankind. It doubtless may, and I 
believe it will, be found, that mankind have multiplied the varieties 
unnecessarily, and have imagined distinctions among things where 
there were only distinctions in the manner of naming them. But we 
are not entitled to assume this in the commencement. We must begin 
by recognizing the distinctions made by Ordinary language. If some 
of these appear, on a close examination, not to be fundamental, our 
enumeration of the different kinds of realities may be abridged accord- 
ingly. But to impose upon the facts in the first instance the yoke of 
a theory, while the grounds of the theory are reserved for discussion in 
a subsequent stage, is evidently not a course which a logician can rea- 
sonably adopt. 



NAMES. 15 



CHAPTER 11. 

OP NAMES. 



§ 1. "A NAME, says Hobbes,* " is a word taken at pleasure to serve 
for a mark, which may raise in our mind a thought Hke to some thought 
we had before, and which being pronounced to others, may be to them 
a sign of what thought the speaker hadf before in his mind." This 
simple definition of a name, as a word (or set of words) serving the 
double purpose, of a mark to recall to ourselves the likeness of a 
former thought, and a sign to make it known to others, appears unex- 
,ceptionable. Names, indeed, do much more than this ; but whatever 
else they do, grows out of, and is the result of this : as will appear in 
its proper place. 

Are names more properly said to be the names of things, or of our 
ideas of things 1 The first is the expression in common use ; the last is 
that of some philosophers, who conceived that in adopting it they were 
introducing a highly important distinction. The eminent thinker just 
quoted seems to countenance the latter opinion. "But seeing," he 
continues, " names ordered in speech (as is defined) are signs of our 
conceptions, it is manifest they are not signs of the things them- 
selves; for that the sound of this word stone should be the sign of a 
stone, cannot be understood in any sense but this, that he that hears it 
collects that he that pronounces it thinks of a stone." 

If it be merely meant that the conception alone, and not the thing 
itself, is recalled by the name, or imparted to the hearer, this of course 
cannot be denied. Nevertheless, there seems good reason for adher- 
ing to the common usage, and calling the word sun the name of the 
sun, and not the name of our idea of the sun. For names are not 
intended only to make the hearer conceive what we conceive, but also 
to inform him what we believe. Now, when I use a name for the 
purpose of expressing a belief, it is a belief concerning the thing itself, 
not concerning my idea of it. When I say, "the sun is the cause of 
day," I do not mean that my idea of the sun causes or excites in me 
the idea of day; but that the physical object, the sun itself, is the 
cause from which the outward phenomenon, day, follows as an effect. 
It seems proper to consider a word as the name of that which we 
intend to be understood by it when we use it ; of that which any fact 
that we assert of it is to be understood of; that, in short, concerning 
which, when we employ the word, we intend to give information. 
Names, therefore, shall always be spoken of in this work as the names 
of things themselves, and not merely of our ideas of things. 

But the question now arises, of what things 1 and to answer this it 
is necessary to take into consideration the different kinds of names. 

§ 2. It is usual, before examining the various classes into which 
names are commonly divided, to begin by distinguishing fi'om names 
of every description, those words which are not names, but only parts 

* Cotnputation or Logic, chap. ii. 

t In the original, " had, or had not." These last words, as involvJDg a subtlety foreign to 
our present purpose, I have forborne to quote. 



16 NAMES AND PROPOSITIONS. 

of names. Among such are reckoned particles, as of^ to, truly ^ qfted ; 
the mflected cases of nouns substantive, as me, him, JoTitCs ;^ and even 
adjectives, as large, heavy. These words do not express things ox 
which anything can be affirmed or denied. We cannot say, Heavy 
fell, or A heavy fell ; Truly, or A truly, was asserted ; Of, or An of, 
was in the room. Unless, indeed, we are speaking of the mere words 
themselves, as when we say, Truly is an English word, or, Heavy is 
an adjective. In that case they are complete names, viz. names of 
those particular sounds, or of those particular collections of written 
characters. This employment of a word to denote the mere letters 
and syllables of which it is composed, was termed by the schoolmen 
the suppositio materialis of the word. In any other sense, we cannot 
introduce one of these words into the subject of a proposition, unless 
in combination with other words ; as, A heavy body fell, A truly impor- 
tant fact was asserted, A. member of parliament was in the room. 

An adjective, however, is capable of standing by itself as the predi- 
cate of a proposition ; as when we say. Snow is white ; and occasion- 
ally even as the subject, for we may say. White is an agreeable color. 
The adjective is often said to be so used by a grammatical ellipsis : 
Snow is white, instead of. Snow is a white object; White is an agree- 
able color, instead of, A white color, or. The color of white, is agreeable. 
The Greeks and Romans were permitted, by the rules of their lan- 
guage, to employ this ellipsis universally in the subject as well as in 
the predicate of a proposition. In English, this cannot, generally 
speaking, be done. We may say, The earth is round ; but we cannot 
say. Round is easily moved ; we must say, A round object. This dis- 
tinction, however, is rather grammatical than logical. Since there is 
no difference of meaning between round and a round object, it is only 
custom which prescribes that on any given occasion one shall be used, 
and not the other. We shall therefore, without scruple, speak of 
adjectives as names, whether in their own right, or as representative 
of the more circuitous forms of expression ab.ove exemplified. The 
other classes of subsidiary words have no title whatever to be con- 
sidered as names. An adverb, or an accusative case, cannot under any 
circumstances (except when their mere letters and syllables axe spoken 
of) figure as one of the terms of a proposition. 

Words which are- not capable of being used as names, but only as 
parts of names, were called by some of the schoolmen Syncategore- 
matic terms : fi:om avv, with, and tcarif/opeG), to predicate, because it 
was only with some other word that they could be predicated. A 
word which could be used either as the subject or predicate of a pro- 
position, without being accompanied by any other word, was termed 
by the same authorities a Categorematic term. A combination of one 
or more Categorematic, and one or more Syncategorematic words, as, 
A heavy body, or A court of justice, they sometimes called a mixed 
term ; but this seems a needless multiplication of technical expressions. 
A mix6d term is, in the only useful sense of the word, Categore- 
matic. It belongs to the class of what have been called many-worded 
names. 

* It would, perhaps, be more correct to say that inflected cases are names and something 
more ; and that this addition prevents them from being used as the subjects of propositions. 
But the purposes of our inquiry do not demand that we should enter with scrupulous accu- 
racy into similar minutiae. 



• ' NAMES, 17 

For, as one word is frequently not a name, but only part of a name, 
so a number of words often compose one single name, and no more. 
Thus, in the opening -of the Paradise Lost, these lines — 

the fruit 

Of that forbidden tree, who^e mortal taste 
Brqught death into tlxe world, and all our woe, 
Wit,h loss of Eden, till, one greater Man 
Restore lis, and regain the hUssfui- seat,— 

form in the . estimation of the 'logician.^ only one..riame'; one Categore- 
matic term. A mode.ofdetermming whether any set of words makes 
only one name, or more than one, is by predicating something of it, and 
observing whether, by this predication, we make only one assertion or 
several. Thus, when we say, John Nokes, who was the mayor of the 
town, died yesterday, — by tliis predication we make but one assertion ; 
whence it appears that *' John. Nokes, who was the mayor of the towp,'.'" 
is no more than one name. It is true that in this proposition, besides 
.the assertion that John Nokes died yesterday, there is included another 
assertion, namely, that John Nokes was mayor of the town. But this 
last assertion was already made: we did not make it by adding the 
predicate, " died yesterday." Suppose, however, that the words had 
been, John Nokes, and the mayor of the town, they would have formed 
two names instead of one. For when we say, John Nokes and the 
mayor of the town died yesterday, we make two assertions ; one, tliat 
John ■ Nokes died yesterday ; the other, that the mayor of the town 
died yesterd^ay. • ' 

It being needless to illustrate, ' at :any greater length, the subject of 
liiany-worded names, we proceed to the distinctions which have been 
established among names, not according to the words they are com- 
posed of, but according' to their signification. / . • . 

§ 3. All names are names of something, real or imaginary ,- but all 
things have not names appropriated to them individually. For some 
individual objects we require, and consequently have, separate "distin- 
guishing names ; there is a name for every person, and for every, re- 
markable place. Other objects, oi which we have not occasion to 
speak so frequently, we do not designate by a name of their own ; but 
when the necessity arises for naming them, we do so by putting to- 
gether several words, each oi which, by itself, rnight be and is used for 
an indefinite number of other objects.; as wken I say, this stone: "this" 
and " stone" being, each of them, names that may be used of many 
other objects besides the particular, one meant, although the only ob- 
ject of which they can both be used at tliQ given moment, consistently 
with their signification, may be the one of which I wish to speak. 

Were this the sole purpose for which names that are common to 
more things than one, could be employed ; if they ..only served,, by 
mutually limiting each other, to afibrd a designation for such indi^ddual 
objects, as have no names of their own ; they could only be ranked among 
contrivances for economizing the use of 'language. But it is evident 
^that this is not their sole function. It is by their means that we are 
enabled to assert general propositions ; to affinn or deny any predicate 
of an indefinite number of , things at once. The distinction, therefore, 
between general names, and individibal or singidar names, is. funda- 
mental J and may be considered as the first grand division of names. 
C , 



18 • NAMES AND PROPOSITIONS. 

A general name is familiarly defined, a. name which is capable of 
being truly affirmed, in the same sense, of each of an indefinite number 
of things. An individual or singular name is a name which is only ca- 
pable of being truly affirmed, in the same sense, of one thing. 

Thus, man is capable of being truly affirrned of John, Peter, George, 
and other persons without assignable limits : and it is affirmed of all of 
them in the same sense ; for the word man expresses certain qualities, 
and when we predicate it of those persons,' we assert that they all 
possess those qualities.^ But John is only capable of being truly af- 
firmed of one single person, at least in the same sense. For although 
there are many persons who bear that name, it is not confeiTed upon 
them ,to indicate any qualities, or anything which belongs to them in 
common ; and cannot be said to be^ affirmed of them in any sense at all, 
consequently not in the s^me sense. " The present king of England" 
is also an individual name. For, that there never can be rriore than 
one person at a time of whom it can be tnily affirmed, is implied in 
the meaning" of the words. . . 

It is not unusual, by way of explaining- what is meant by a general 
name, to say that it is the name of a class. But this, though a conve- 
nient mode of expression for some purposes, is objectionable as a defi- 
nition, since it explains the clearer of two things by the more obscure. 
It would be more logical to reverse the proposition, and turn it into a 
definition of the word class : "A class is the indefinite multitude of in- 
dividuals denoted by a general name." 

It is necessary to distinguish general from collective names. A, gen- 
eral name is one which can be predicated of each individual of a mul- 
titude ; a collective name cannot be predicated of each separately, but 
only of all taken together. " The 76th regiment of foot," which is a 
collective name, is not a general but an individual name ; for altliough 
it can be predicated of a multitude of individual soldiers taken jointly, 
it cannot be predicated oi' them sev-erally. We may say, Jones is a 
soldier, and Thompsoli is a soldier, and Srnith is a soldier, but -we can- 
not say; Jones is the 76th regiment, and Thompson is the 76th regi- 
ment, and Smith is the 76th regiment. We Qan pnly say, Jones, 
and Thompson, and' Smith, and Brown, and so, forth, ^(enumerating all 
the soldiers,) are the '76th regiment. . 

*' The 76th regiment" is a collective ^ame, but not a general one : 
" a regiment" is both a collective and -a .general name. General with 
respect to all individual regiments, of eaclrof which separately it can 
OQ affirmed ; collective with respect "to the individual soldiers, of v^hom 
any regiment is composed. 

§ 4. The second general division of names is into Qoncrete and ab- 
stract. A concrete name w, a name which stands for a thing ; an ab- 
stract name is a. name which Stands for an attribute of a thing. Thus, 
John, the sea, this table, are names • of things. White, also, is a name 
of a thing, or rather of things. Whiteness, again, is the name of a 
quality or attribute of those things. Man is a name of many tilings ; 
humanity is a name of an attribute of those things. Old is a name of 
things ; old age is a name of one of their attributes. 

I have used the words concrete and. abstract in the sense annexed to 
them by the schoolmen, who, notwithstanding- the imperfections of their 
philosophy, were unrivalled in the construction of technical language, 



NAMES. * 19 

and whose definitions, in logic at least, tliougli they never went more 
than a'little way into the subject, have seldom, I think, been altered 
but to be' spoiled. A practice, how^ever, has grown up in more modr 
ern times, which, if not introduced by Locke, has gained currency 
chiefly from his example, of applying the expression " abstract name" 
to all names which are the result of abstraction or generalization, and 
consequently to all general names, instead of confining it to the names 
of attributes. The metaphysicians of the Condillac school — whose ad- 
miration of Locke, passing over the profoundest speculations of that 
truly original genius, usually fastens with peculiar eagerness upon his 
weakest points — ^have gone on imitating him in this abuse of language, 
until there is noW some difficulty in restoring the word to its original 
.signification. A more wanton alteration in the meaning of a word is 
rarely to be met with ; for the expression general ^ name, the exact 
equivalent of which exists in all languages I am acquainted with, was 
already available for the purpose to which abstract lidiS, been misap- 
propriated, while the misappropriation leaves that important class of 
words, the naiiles of attributes, without any compact distinctive appel- 
lation. The old acceptation, however, has not gone so completely out 
of use, as to deprive those who still adhere to it of all chance of being 
understood. By ahstract, then, I shall always mean the opposite of 
concrete: by an abstract name, the name of an . attribute ; by a con-^ 
Crete name, the name of an object. 

Do abstract names belong to the class of general, or to that of sin- 
gular names'? Some of them are certainly general. I mean those 
which are names not of one single and definite attribute, but of a class 
of attributes. Such is the word coZor, which is a name common to 
whiteness, redness, &c. Such is even the wqrd whiteness, in respect 
of the different shades of whiteness to which it is applied in common ; 
the word magnitude, in respect of the Various degrees of magnitude 
and the various dimensions of space ; the ^vord weight, in respect of 
the various degrees of weight. Such also is the word attrihute itself, 
.the common name of all particular attributes. But when only one at- 
tribute, neither variable in degree ilor in kiijtl, is designated b^y the 
name ; as visibleness ; tangibleness ; equality ; squareness ; milkwhite- 
ness ; then the name can hardly be considered general ; for though it 
denotes an attribute of many different objects,- the attribute itself is al- 
ways conceived as one, not many. The question is, however, of no 
monient, and perhaps the best way of deciding it would be to consider 
these names as neither general nor individual, but to place them in a 
class apart. ■ 

. It may be objected to our definition of an abstract name, that not 
only the names which we have called abstract, but adjectives,' which 
we have placed in the concrete' class, are names of attiibutes ; that 
w%ite, for example, is as much the name Of the color, as wJiiteness h. 
But ("as before remarked) a word ought to be considered as the nam6 
of that which we intend to be understood by it when we put it to its 
principal use, that is, when we employ ijt in predication. -Wlien we 
say, snow is white, milk is- white, linen is white, we do not mean it to 
be understood that snow, or linen, or milk, is a color. "We mean that 
they are things having the color. The reverse is the case with the 
word whiteness; what we affirm to he whiteness is not snow but the 
color of snow. Whiteness, therefore, is the name of the color exclu- 



20 NAMES AND PROPOSITIONS. 

sively : white is a name of all things whatever having the color ; . a name' 
not of the quality whiteness, but of every white object. It is true, this 
name was given to all those various objects on account of the quality ; and 
we may therefore say, without impropriety, that the quality forms part 
of its signification; but a name can only be said to stand for, or to be a 
name ofj the things of which it can be predicated. We shall presently 
see that all names which can be said to have any signification, all 
names by applying which to an individual we give any information 
respecting that individual, may be said to imply an attribute of some 
sort ; but they are not names of the attribute ; it has its own proper 
abstract name. 

§ 5. This leads us to the consideration of the tjiird great division 
of names, into connotative and non-connotative, the latter sometimes, 
but improperly, called ahsolute. This is one of the most important^ 
distinctions which we shall have occasion to point out, alid one of 
those which go deepest into the nature of language. '' 

A non-connotative term is one which ^signifies a subject only, or an 
attribute only. A connotative term is one which denotes a subject 
and implies an attribute. ^ By a subject is here meant anything which 
possesses attributes. Thus John, or London, or England, are names 
which signify a subject only. Whiteness, length, virtue, signify an 
attribute only. None of these names, therefore, are connotative. But 
white, long, mrtuous, are connotative. The word white, denotes all 
white things, as snow, paper, the foam of the sea, '&c., and implies, or 
as it was termed by thp schoolmen, connotes^ the attribute tvhitenesso 
The word wliite is not predicated of the attribute, but of the subjects, 
snow, &c. ; but when we predicate it of them we imply, or connote, 
that the attribute whiteness belongs to them. The same may be said 
of the other words above cited. Virtuous, for example,- is the name 
of a class, which includes Socrates, Howard, the man of Ross, and an 
undefined number of other individuals, past, present, and to come. 
These individuals, collectively and se^orally, can alone be said with 
propriety to be denoted by the word; of them alone can it properly 
be said to be a name. But it is a name applied to all of them in con- 
sequence of an attribute which they possess in common, the attribute 
which men have agreed to call virtue. It is applied to all beings that 
are considered to possess this attribute ; and to none which are not so 
considered. 

All concrete, general names ate connotative. The word man, for 
example, denotes Peter, Paul, John, and an indefinite number of other 
individuals, of whom, taken as a class, it is the name. But it is 
applied to them,. because th.e'y possess., and to signify that they possess, 
certain attributes. These seem to be, corJDoreity, animal life, ration- 
ality, and a certain external form, which for distinction we call the 
human. Every existing thing, which possessed all these attributes, 
would be called a man ; and anything which possessed none of them, 
or only one, or two, or eyen three of them without the fourth, would, 
not be so called. For example, if in the interior of Africa there were 
to be discovered a race of animals possessing reason equal to that of hu- 
man beings, but with the form of- an elephant, they would not be called 

* Notare, to mark ; co?motare, to mark along with : to msnrk one thiiig with or in addition 
to another. • - • • • 



NAMES. 21 

men. Swift's Houylmhms were, not so called. Or if such newly- 
discovered beings possessed the form of man- without any vestige of 
reason, it is probable that some other name than that of man would be 
found for thent. How it happens that there can be any doubt about 
the matter, will appear hereafter. The word man, therefore, signifies 
air these attributes, and all subjects which possess these attributes. 
But it can be predicated only of the subjects. • What we call rnen, are 
die subjects, the individual Stiles and Nokes ; not the qualities by 
which their humanity is constituted. The name, therefore, is said to 
signify the subjects directly, the attributes indirectly ; it denotes the 
subjects, and implies, or involves, or indicates, or as we shall say 
henceforth, connotes, the attributes. 'It is a connotative name. 

Connotative names have hence been also called denominative^ 
because the subject which they denote is denominated by, or receives 
<a.iiame from, the attribute which they connote. Snow, and other 
objects, receive the^ name white, because they possess the attribute 
which is called whiteness; James and Robert receive the name man, 
because they possess the attributes which are considered to constitute 
humanity. The attribute, or attributes, may therefore -be said to 
denominate those objects, or to give theta a common name. 

It" has been seen that all concrete general names are connotative. 
Even abstract naraes, though tlie names only of attributes, may in 
-so^iie instances be justly considered as connotative ; for attributes 
'theriiselves may have attributes ascribed to them; and a word which 
denotes attributes may connote an attribute of tliQse attribu,tes. It is 
thus, for example, with such a wordi du^ fault ; equivalent to had or 
hurtful quality. This 'word is" a name comrdon to many attributes, 
and. connotes hurtfulness, an atti'ibute of those various attributes. 
When^ for* exam j>le, we say that slowness, in a horse, is a fault, we do 
not mean that the- slow movement, the actual change of place of the 
•slow horse,' has any mischievous effects, but that the property or 
peculiarity of the horse, from which it derives that name, the quality 
of being a slow mover, is an undesirable peculiarity. 

In regard to those concrete names which are .not general but 
individual, a distinction must be made. 

Proper names, are not connotative ; they denote the individuals who 
al-e called by thent ;. but they do not indicate or imply, any attributes 
as belonging to those, individuals;: When we name a. chijd by the 
.name -Mary, or a dog by the name Caesar, these- names are simply 
marks used to enable those individuals to be made subjects of discourse. 
It may be said, indeed, that we m.ust have had some reason for giving 
them those names rather than any others : and this is true ; but the 
flame, once given, becomes independent of the reaso^i. A man rnay 
have been nam.ed John because that was- the name of his father ; a 
town may have been named. Dartmouth, because it is situated at the 
mouth of the Dart. But it is no part of the signification of the word 
John, that the father of the person 'so called bore the same name ; nor. 
^ven of the. word Dartir.outh,' to be situated at the mouth of the Dart. 
If sand should choke up the mouth of the river, or an earthquake 
(Change its course, and remove it to, a distance from the town, there is 
jio reason to think that the name of the town would be changed. That 
•fact, therefore, can form no part of the signification of the Word ; for 
otherwise, when the fact ceased to be tme, the name would cease to 



22 . NAMES AND PROPOSITIONS. 

he applied. » Proper names are attached to fche objects themselves, and 
are not dependent upon the continuance of any attribute of the object, • 
But there is another kind of names, which, although they are 
individual names, that is, predicable only of one object, are really 
connotative. For, although we may give to an individual a name 
utterly unmeaning, which we call a proper name,— a. word which 
answers the purpose of showing what thing it is we are/talking about, 
but not of telling anything about it ; yet a name peculiar to an 
individual is Hot necessarily of this description. It may be significant 
, of some attribute, or some union of attributes, which being possessed by 
no object but one, determines the name exclusively to that individu.ak 
" The sun " is a name of this description ; " Grod," when used by a 
Christian, is another. These, however,, are scarcely examples of what 
.w^ are. now attempting to illustrate, being, in strictness of langua.ge, 
general, and not individual names : for, however they may be i^ Jact 
predicable only of one object, there is nothing in the nieaning of the 
words themselves which implies this : and, accordingly, when we are 
imagining and not affirming, we may speak of many suns ; and the 
majority of mankind have believed, and still believe, that there are 
•many gods. But it is easy to produce words which are real instances 
of connotative individual names. It may be part of the meaning of 
the Connotative name itself, that there exists but one individual possess- 
ing the attribute which it connotes ; as, for instance, " the only, son of 
John Stiles;" ^' the Jirst emperor of Rom,e." Or the attribute con- 
noted may be a connexion with some determinate event, and the 
connexion may be of such a kind as only one individual could have^ 
or may at least be such as only one individual actually had • and thi& 
may be implied in the form of the expression. '^ The father^ of 
Socrates," is an example of the one kind (since Socrates could not 
have had two fatjiers); "the author of the Iliad," "the murderer .of 
Henri Quatre," of the second. For, although it is conceivable that 
more persons than one might have participated in the authorship of the 
Iliad, or in the murder of Henri Quatre, the employment of the article 
tJte implies that, in fact, tliis was not the case.. What is here done .by 
the word tJie, is done in other cases by the context : thus, " Caesar's, 
army " is an individual name, if it appears from the context, that the 
army meant is that which Caesar commanded in a particular battlee. 
The still mor^ general expressions, " the Roman army," or " the 
Christian army," may be individualized in a similar manner. Another 
case of frequent occurrence has already been noticed ; it is the follow- 
ing. The name, being a m,any-woi*ded one, may consist, in. the first 
place, of a general name, capable therefore in itself of being affirmed 
of more things than one, but which is, in the second place, so limited 
by other words joined with it^ that the entire expression can only be 
predicated of one object, consistently with the meaning of the general 
term. . This is exemplified in such an instance a» the following : " the 
present prime minister of England." -Prime Minister of England is a 
general name ; the attributes which it connotes may be possessed by 
an indefinite number of persons : in succession however, not simulta- 
neously ; since the meaning of the word itself imports" (among other 
things) that there can be only one such person at a time. This being 
the case, and the application of the name being afterwards limited by 
the word present, to such individuals as possess the attributes at ob& 



NAMES. " - ■ 23 

indivisible point of time, it becomes applicable only to ,orie individual. 
And as this appears from the meaning of the name, withaut any 
extriiisic proof, it is strictly an individual name. 

From the preceding observations it will easily be collected, that 
whenever the names given to objects. convey any information, that is, 
whenever they have properly any meaning, the m€>aning' resides not 
in what they denote, hut in what the j connote. The only names of 
objects which connote nothing are proper names; and. these have, 
strictly speaking, n-o signification. 

If, like the robber in the Arabian Nights, we tnake a mark with 
chalk upon a house to enable us to know it again,' the mark has a 
purpose, but it has not properly any meaning. The chalk does not 
jdeclare anything about the .house; it does not mean. This is such a 
person's house, or This is a house which contains booty. The. object 
of making the mark is merely distinction. I say to myself, All these 
houses are so nearly alike, that if I lose sight of them I shall not again 
be able to distinguish that which I am now looking at from any of 
the others ; I must therefore contrive to make the appearance of this 
one house unlike that of the others, that I may hereafter know, when 
I see the mark — not indeed any attribute of the house — but simply 
that it is the same house which I am now looking at. Morgiana 
chalked all the other houses in a similar manner, and defeated the 
scheme : how % simply by obliterating the difference of appearance 
between that house and the others. The chalk was still there, but it 
no longer served the purpose of a distinctive mark. 

When we impose a proper name, we perform an operation in some 
degree analogous to what the robber intended in chalking the house. 
We put a mark, not indeed upon the object itself, but,' if I may so 
speak, upon the idea of the object. A proper name is but an unmean- 
ing mark which w^e connect in our minds with the idea of the object, 
in order that whenever the mark meets our eyes or occurs to our 
thoughts, we may think of that individual object. Not being attached 
to the thing itself, it does not enable us, as the chalk did, to distin- 
guish the object when we see it; but it enables us to distinguish it 
when it is spoken of, either in the records of our own experience, or 
in the discourse of others ; to know that what we find asserted in any 
proposition of which it is the subject, is asserted of the individual thing 
with which we were previously acquainted. 

When vve predicate of anything its proper name ; when we say, 
pointing to a man, this is Brown or Smith, or pointing to a city, that 
it is York, we do not, merely by so doing, convey to the hearer any 
information about them, except that those are their, names; By 
enabling him to identify the individuals, we may connect them with 
information previously possessed by him;' by saying. This is York, 
we may tell hini that it contains the Minster. But this' is in virtue of 
what he has previously heard concerning York ; not by anything 
implied in the name. It is otherwise when objects are spoken of by. 
connotative names. When we say, The town is built of marble, we 
give the hearer what may be entirely riev/ information, and this merely 
by the significati-on of the many-worded connotative name, " built of 
marble." Such names are not- signs of the mere objects, invented 
because we have occasion to think and. speak of those objects individ- 
ually ; but signs which accompany an attribute : a kind of livery iij 



24 • NAMES AND PROPOSITIONS. • _ 

-vyliidb the attribute clothes all objects which are recognized as .possess- 
ing it. They are not raere marks', but more, that is to say, significant 
marks; and the connotation is what constitutes their significance. 
; As a proper name is said to be the. name of the one individual 
which it is predicated of, so (as well from the importance of adhering 
to analogy, as for the other reasons formerly assigned) a connotativ.e 
name ought to be considered a name of all the various individuals 
which it is predical)le of, or in other vy^ords denotes, and not of what it 
connotes. But by learning what things it is a name of, we do not 
learn the meaning of the name : for to. the same thing we may, with 
equal propriety, apply many names, not equivalent in meaning.. Thus, 
I call a certain man by the name Sophroniscus : I call him by another 
name. The father of Socrates. Both these are names of the game 
individual, but their meaning is altogether different ; • they are applied 
to that individual for two different purposes; the one, • merely to 
distinguish him from other persons who are, spoken of; .the other^ to 
indicate a fact relating to him, the fact that Socrates was his son. I 
■further apply to him these other expressions : a man, a Greek, an 
Athenian, a sculptor, an old man, an honest man, a brave' man.. All 
these are names of Sophroniscus, not indeed of him alone, but of him. 
and each of an indefinite number of other hum-ari beings; Each of 
these names is applied to .Sophroniscus for a different reason, and by 
each whoever understands its meaning is apprised of a distinct fact or 
number of facts concerning him; but those who knew nothing about 
the names except that they were applicable to Sophroniscus, Would 
be altogether ignorant of their meaning.. It is even conceivable that ■ 
I might know, every single individual. of whom a given name could be 
with truth affirmed, and yet could not be said, to know- the meaning of 
the name. A child knows who are its brothers and sisters j long .before 
if has any definite cpnception' of the nature of the facts which are 
involved in the signification of those words. 

In some cases it is not.easy to decide precisely how much, a particular' 
word does or does not connote;,, th^ is, we do not exactly know (the 
case not having arisen) what degi^ee of difference in the object 'would 
Occasion a difference in the name. Thus, it is cleat that the word- 
man, besides animal life and rationality, connotes also a certain ex- 
ternal form ;. but it would be impossible to say precisely what form *. 
that is, to -decide how great a deviation from the form ordinarily found 
in the beings whom we are accustomed to call men, would suffice in a 
newly-discover'ed race to mako us, refuse them the nanie- of man. 
nationality, alsO, being a quality which admits of degrees, it has never 
been settled what is "the lowest degree of that quality which would 
entitle any creature to be_ considered a human being. In all "such 
cases, the meaning of the general name is so far unsettled, and vague j 
mankind have not come to. any positive agreement about the matter. 
Whon we come to treat .of classification, we shall have occasion to 
show under what conditions -this vagueness may exist without, practical . 
inconvenienqe ; arid cases will appear, in which the ends of- language 
are better promoted by it> than by complete precision ; in order that,- 
in natural history, for instance, individuals or. species' of. no very 
marked character may^be raiaged with those more strongly character-' 
ized individuals- or species to which, in all their properties takeU' 
togethei', .they ^ear tlie nearest resemblance,. ' , * 



. .. • NAMES. 25 

But this partial uncertainty in the connotation of names can only be 
free from mischief when, guarded by strict, precautions. One of the 
chief sources, indeed, of lax habits of thought, is the custom of using 
connotative terms without a distinctly ascertained connotationy and. with 
1^0 more precise notion of their meaning than can be loosely collected 
fi'om observing what objects they are used to denote.. It is in this 
manner" that we all acquire, and inevitably so, our first knovv^ledge- of 
•our. vernacular language. A child learns the meaning of the words 
man, or white, by hearing them applied to a variety of individual objects,' 
and- 'finding out, by a. process^ of generalization and analysis of which 
he is but impei'fe!ctly conscious, what those diflferent objects have in 
cdrriraon. In the case of these two words the process is so easy as to 
require no assistance from culture; the objects" called human beings, 
^nd the objects called white, differing from all others by qualities of 
.a peculiarly definite and obvious character. But in many Other cases, 
objects bear a general resemblance to one another, v/hichleadsto their- ' 
being faniiliajfly, classed together under a common name, while, without 
more analytic habits than the generality of mankind possess, it is not 
immediately apparent what are. the particular attributes, upon the pos- 
session of which in common by thorn all, their general resemblance 
dppehds. When this is the case, men use the name without any re- 
cognized connotation, that is, without any precise meaning; they talk, 
and consequently think, vaguely, and remain contented to attach only 
the same deorree of sio^nificance to their own words, which a child three 
years old -attaches to the words brother and sister. The child at least 
is seldom puzzled by the starting up of new individuals, on whom he 
is ignorant whether ol* not to confer the title ; because there is usually 
an 9,uthority close at hand competent to solve all. doubts. But a similar 
resource does not exist .in the generality of cases; and new objects are ■ 
continually presenting themselves to men, vi^omen, and 'childi,'en, which 
they are called upon to class proprio • moUi. They, accordingly, do 
tiiis On no other principle than that of superficial similarity, giving to 
each new object the name of that familiar. object, the idea of which it 
most readily recalls; or which, on a cursory inspection, it seems to. 
them most to resemble : as an unknown substance found irithe groun'(i 
will be called; according to its texture, earth, sand, or a stone." In this 
manner, names, creep on from subject to subject, until' all traces of a 
common nieaning sometimes disappear, and the word comes to denote 
a -number of things not only independently of any common attribute, 
but which have actually no attribute in common; or. none but what is 
shared, by other things to, which the name is Capriciously refuseik* 
Even philosophers have aided in this perversion of general language 
from its purpose ; sometirii.es because, like the vulgar, they knew no 
better; and sometimes in deference to that-^ aversion' :to ad.mit new 

■ * It would be well if this natural degeneracy of language took place only in Vae hands of 
fRe ignorant vulgar ; but some of the mo^t remarkable instances are to be found in terms 
of art, and among techiiically educated persons, such as EngUsh lawyer^. Felony, for€x^ 
ample, is a law term, with the sound of which all ears are familiar ; but there is no lawyer' 
who would undertake to tell what a felony is, otherwise than by enumerating the various 
kinds of offences which are s"o called. Originally the word felony had a ineaning ; it deno- 
ted all offences, the penalty of which included forfeiture of goods; but subsequent acts' of 
Parliament have declared various offences to be felonies without enjoining that penalty, 
and have taken away the penalty from others which continue nevertheless to be called felo- 
nies, insomuch, that the acts so called have now no property whatevey jn commonj save tha* 
of being unlawful and punish'able. - '- " ' ■ ■ 

D • ' 



26 NAMES AND PROPOSITIONS. 

%vords., which induces mankind, on all subjects not considered technical, " 
to attempt to make the original small stock of names serve with lout 
little augmentation to express a constantly increasing number of objects 
and distinctions, and, consequently, to express them in a manner pro- 
gressively more and more imperfect. 

To what degree this loose mode of classing and denominating objects 
has rendered the vocabulary of mental and moral philosophy unfit for 
the purposes of accurate thinking, is best known to whoever has most 
reflected on the present condition of those branches of knowledge. 
Since, however, the introduction of a new technical language as >the 
vehicle of speculations on moral subjects, would not, in this country at 
least, be tolerated, arid if tolerated, would deprive those subjects of 
the benefit of the habitual feelings, which have gi'own round the estab- 
lished phrases and the recognized groups, and vehich would not for a 
long, time take an equally strong hold of new ones ; the problem for 
the philosopher, and one of the most difficult which he has to resolve, 
is, in retaining the existing phraseology, how best to alleviate its im- 
perfections. This can only be accomplished by giving to every general 
concrete name which he has frequent occasion to predicate, a definite 
and fixed connotation ; in order that it may be known what attributes, 
when we call an object by that name, we really mean to predicate of 
the object. And the question of most nicety is, how to give this fixed 
connotation to a name, with the least possible change in the objects 
which the name is habitually employed to denote ; with the least pos- 
sible disarrangement, either by adding or subtraction, of the group of 
objects which it serves, in however imperfect a manner, to circumscribe 
and hold together ; and with the least vitiation of the truth of any 
propositions which are commonly received as true. 

This desirable purpose, of giving a fixed connotation where it is 
wanting, is the end aimed at whenever any one attempts to give a defi-- 
nition of a general name already in use ; every definition of a conno- - 
tative name being an attempt either merely to declare, or to declare - 
and analyze, the. connotation of the name. And the fact, that no ques- 
tions which have arisen in the moral sciences have been subjects of 
keener controversy than the definitions of almost all the leading expres- 
sionis, is a proof how great an extent the evil to which we have 
adverted has attained! 

Names with indeterminate connotation are riot to be confounded 
with names which have more than one connotation, that is to say, with 
ambiguous words. A word may have several meanings, but . all of 
them fixed and recognized ones ; as the word post, for example, or the 
work box, the various senses of which it would be endless to enumer- 
ate. And the paucity of existing names, in comparison with the 
demand for them, may often render it advisable and even necessary to 
retain a name in this multiplicity of acceptatioris,. distinguishing these 
60 clearly as to prevent their being confounded with One another. 
Suplr a word may be considered as two or more 'names, accidentally 
writteij and spoken alike.* •' . . / 

* Before quitting the subject 'of connotative names, it 'is proper to observe, that the only 
recent writer Who, to my knowledge, has adopted from the schoolmen the word io connote, 
Mr. Mill, in his Analysis of the Phenomena of the Human Mind, employs it in a signification 
<liflfercnt from that in which it is. here used. . He uses the word in a sense coextensive with 
i^s etymology, -applying it to every case in which a name, while pointing directly to one 
thmg, (which is, consequently, termied its-sig'nification), includes also a tacit reference to 



NAMES. » 27 

§6. The fourth principal division of names, is into positive s^ndnegative. 
Positive, as man, tree, good; negative, as not-man, not-tree, not-good. 
To every positive concrete name, a corresponding negative one might 
be framed. After giving a name to any one thing, or to any plurahty 
of things, we might create a second name which should be a name of 
all things whatever except that particular thing or things. These neg- 
ative names are employed whenever we have occasion to speak collec-' 
tively of all things other than some thing or class of things. When 
the positive name is coniiotative, the corresponding negative name is 
connotative likewise ; but in a peculiar way, connoting not the pres- 
ence but the absence of an attribute. Thus, not-ioliite denotes all 
thino-s whatever except white things ; and connotes the attribute of not 
possessing whiteness. For the non-possession of any given attribute 
is also an attribute, and may receive a name as such; and thus nega- 
tive concrete names may obtain negative abstract names to correspond. 
to them. 

Names which are positive in form are often negative in reality, and 
others are really positive though their form is negative. The word 
inconvenient, for example, does not express the mere absence of con- 
venience ; it expresses a positive attribute, that of being the cause of 
discomfort or annoyance. So the word unpleasant, notwithstanding its 
negative form, does not connote the mere absence of pleasantness, but 
a less degree of what is signified by the word painful, v/hich, it is 
hardly necessary to say, is positive. Idle, on the other hand, is a word 
which, though positive in form, expresses nothing but what would bd 
signified either by the phrase not working, or by the phrase not dis-^ 
posed to work ; and soher, either by not drunk or by not drunken. 

There is a class of names called privative. A privative name is 

some other thing. In the case considered in the text, that of concrete general names,, his. 
language and mine are the converse of one another. Considering (very justly) the signifi- 
cation of the name to lie in the attribute, he speaks of the word as noting the attribute, and 
connoting the things- possessing the attribute. And he describes abstract names .as being 
properly concrete names with their connotation dropped : whereas, in my view, it is the 
denotation which would be said to be dropped, what was previously connoted becoming the 
whole signification. ' ' ■ . 

In adopting a phraseology at variance with that which so high an authority, and one 
which I am less likely than any other person to undervalue, has deliberately sanctioned, I 
have been influenced by the urgent necessity -for a term exclusively appropriated to express 
the manner in which a concrete general name serves to mark the attributes which are in- 

.volved in its signification. This necessity can scarcely be. felt in its full force by any one 
who has not found by experience, how vain is the attempt to communicate clear ideas on 
the philosophy of language without such a word. It is hardly an exaggeration to say, that 
some' of the most prevalent of the errors with which logic has been infected, and a large 
part of the cloudiness and confusion of ideas which have enveloped it, would, in all proba- 
bility, have been avoided, if a term had been in common use tb express exactly what I have 
signified by the term to connote. And the schoolmen, to whom we are indebted for the 
greater part of our logical language, gave us this also, and in this very sense. For, although 
some of their general expressions countenance the use of the word in the more extensive 
and vague acceptation in which it is taken by Mr. Mill, yet when they had to define it spe- 
cifically as a technical term, and to fix its meaning as such, with that admirable precision 

, which always characterized th-eir definitions, they clearly explained that nothing was said 
to be connoted except /orTns, which word may generally, in their writings,- be understood as 
synonymous with attributes. 

Now, if the word to connote, so well suited to the purpose to which they applied it, "be di. 
verted from that purpose by being taken to fulfil another, for which it does not seem to me to 
be at all required ; I am unable to find any expression to replace it, but such as are commonly 
employed in a sense so much more general, that it would be useless attempting to associate 
them peculiarly with this precise idea. Such are the words, to involve, to imply, &c. By 
employing these, I should fail of attaining the object for which alone the name is needed, 
namely, to distinguish this particular kind of involving and implying from all other kinds, 
and to assure to it the degree of habitual attention which its importance demands. 



28 ' ■ PfAMES AND PROPOSITIONS. 

equivalent in its signification to a positive and a negative name taken 
together ; being the name of something which has once had a partic- 
ular attribute, or for soriie other reason might have been expected to 
have it, but which has it not. Such • is the word hlmd, which is not 
equivalent to not seeing, or to not capable of seeing, for it would not,., 
except by a poetical or rhetorical- figure, be applied to .stocks and 
stones. A thing is not usually said to be blind, unless the class to 
which it is most familiarly referred, or to which it is referred on the , 
particular pccasioh, be dhiefly composed of things which can see, as 
in the case of a blind man, or a blind horse ; or unless it is. supposed 
for any reason that it ought to see; as in saying of a:man, that he 
rushed blindly into an abyss, or of philosophers or the clergy that" the 
greater part of them are blind guides. The names called privative, 
therefore, connote two things : the absence of certaiii attributes, and 
the presence of others, fi'om which the presence also of the former 
might naturally have been expected. 



§ 7. The fifth leading division of names, is into relative and ^^^^^u^.^^ 
or let us rather say, relative and non-relative ; for the word absolute 
is put upon much too hard duty in metaphysics, not to be v^Uingly 
spared whOn its services can be dispensed, with. It resembles the 
word civil in the language of jurisprudence, which stands for the 
opposite of criminal, the opposite of ecclesiastical, the opposite of mil- 
itary, the opposite of political, in short, the opposite of any positive 
word which wants a negative; ' 

Relative names aze such as father, son ; ruler, subject ; like ; equal ; ■ 
wnlike ; unequal; longer, shorter ; cause, effect, ' Their characteristic 
property is, that they are always given in pairs." Every relative name 
which is predicated of an object, supposes another object (or objects), 
of which we may- predicate either that sarrie name or another relative 
name which is said to be' the correlative oi the former. Thus, vv^heri 
we call any person a son,^we suppose other persons who must be called 
parents. Wlien we call any event a cause, we suppose another event 
which' is an effect. ■ .When we say of any distance that it is longer, we 
suppose another distance- which is shorter. Wlien we say of any object 
that it is like, we mean that it is like sOmc' other object, which is also 
said to be like the 'first. In this case, both objects receive the same 
name; the relative' term is its own correlative. 

It is evident that these words, when concrete, are, dike other con-- 
Crete general ijaraes, eonnotative .: they denote a subject, and connote 
an attribute :' and each of them has or might have a corresponding 
abstract narne to denote the attribute connoted by the concrete. Thus 
the concrete ZiZ;<3 has its abstract likeness; the concretes, father and 
son, have the abstracts, paternity and filiation. The concrete name 
connotes an attribute, and the abstract name which answers to it 
denotes that attribute. But of what nature is the attribute % '' Wherein 
consists the peculiaiity in the connotation of a relative name ? 

The attribute signified by a relative name, say some, is a relation ; " 
and this they give, if not as a sufficient explanation, at least' as the only 
one. attainable. If they are asked, What then is a relation 1 , they do 
not profess to be able to tell. It is .generally regarded as something 
peculiarly jrecondite and mysterious. I cannot, however, perceive in 
what respect it is more so than any other attribute ; indeed, it appears 



NAMES. 29 

to me to be so in a somewhat less degree. I conceive, rather, that it 
is by examining into the signification of relative names, or. in other 
Tvords, into the nature of the attribute which they conilote, that a clear 
insight may best be obtained into the nature of all attributes ; of all 
that is meant by an attribute. 

- It is xDbvious, in fact, that if we take any two correlative names, y^- 
tlier and son, for instance^ altliough the objects cZenoted by the names are 
different, they both, in a certain sense, connote the same thing. They 
cannot, indeed, be said to connote the same attribute ; to be a father 
is not the same thing as to be a son. But when we call oile man a 
father', another his son, what we mean to affirm is a set of facts, which 
are exactly the same in both cases. To predicate of A that he is the 
■father of Bj and of B that he is the son of A, is to assert one and the 
same fact in different words. The two propositions are exactly equiv- 
alent : neither of them asserts more or asserts less than the other. The 
paternity of A and tile filiation of B are not two facts, but two modes 
of expressing the same fact. That fact, when analyzed, consists of a 
•series of physical events or phenomeng,, in which both A and B are 
parties concerned, and fi'om which they both derive names. Wliat 
those names really connote is this series of events ; that is the meaning 
and the whole meaning, which either of them is intended to convey. 
The series of events maybe said to constitute the relation; the school- 
men called it the foundation of the XQldXion, fundamentum relationis. 

In this manner any fact, or series of facts, in which two different 
objects are implicated, and which is therefore predicable of both of 
them, may be either considered as constituting ^n attribute of the one, 
or an attribute of the other. According as we consider it in the for- 
mer or in the latter aspect, it is connoted by the one or the other of the 
two correlative names. Father connotes the fact, resj'arded as consti- 
tuting an attribute of A : son connotes the same fact, as constituting an 
attribute of B. It may evidently be regarded with equal propriety in 
either light. And all that appears necessary to account for the exist- 
ence of relative names, ig, that whenever there is a fact, in which two 
individuals are alike concerned, an attribute grounded on that fact 'may 
be ascribed to either of these individuals. 

A name, therefore, is said to be relative, when, over and above the 
object which it denotes, it implies in its signification the existence of 
another object, also deriving a denomination from the same fact which 
is the ground of the first name. Or (to express the same meaning m, 
other words) a name is relative, when, being the name of one thing, 
its signification cannot be explained but by mentioning another. Or 
we may state, it thus: — -when the -"name cannot be employed in dis- 
course, so as t9 have a meaning, unless the name of some other thing 
than what it is itself the name of, be either expressed or understood. 
We may take our choice among these definitions. ,They, are all, at 
bottom, equivalent, being modes of variously expressing this one dis- 
tinctive circumstance— that every other attribute of an- object might, 
without any contradiction^ be conceived still to exist if all objects be- 
sides that one were annihilated ;* but those of its attributes which are 
expressed by relative names would on that supposition be s-wept away. 

* Or rather all objects, except itself and the percipient mind ; for, as we shall see here- 
after, to ascribe any attribute to an object necessarily implies a mind to perceive it. 



30 NAMES AND PROPOSITIONS. 

§ 8. Names have been further distinguished into univocal and {Equiv- 
ocal: these, however, are. not two kinds of names, but two different 
modes of employing names. A name is univocal, or applied univo- 
cally, with respect to all things of which it can be precicated in the 
same sense; but it is sequivocal, 6r applied sequivocally, as respects 
those things of which it is predicated in different senses. It is scarcely 
necessary to give instances of a fact so familiar as the double meaning 
of a word. In realityj as has been already observed, an eequivocal or 
ambiguous word is not one name, but two names, accidentally coinci- 
ding- in sound. File standing for an iron instrument, and^^e standing 
for a line of soldiers, have no more title to be considered one word, 
because v^ritten alike, than grease and Greece have, because they are 
pronounced alike! They are one sound, appropriated to form two dif- 
ferent words. 

An intermediate case is that of a name m^q^ analogically on :mel^- 
phoricajly ; that is; a name which is predicated of two things, not 
univocally, or exactly in ,the same signification, but in significations 
somewhat similar, and which being derived one ft^om the other, one Of 
them may be considered the primary, and the other a secondary sig- 
nification. As . when we speak of a brilliant light, and a brilliant 
achievement. The word is not applied in the same sense to the light 
and to the achievement ; but having been applied to the light in its 
original sense, that of brightness to the eye, k is transferred to the 
achievement in a derivative signification, supposed to be somewhat 
like the primitive onel The word, however, is just as properly two 
hames instead of one, in this case, as in that of the most perfect am^^ 
biguity. And one of the commonest forms of fallacious reasoning 
arising from ambiguity, is that of arguing from a metaphorical expres-. 
sion as if it were literal; that is, as if a^vv^ord, when applied metaphor- 
ically, were the same name as when takei> in its original Sense : which 
will be seen more particularly in its plac,e,. . -' . . 



OF THE THINGS DENOTED BY NAMES. 



§ 1. Looking back now to the commencement of our inquiry, let us 
attempt to measure how far it has advanced. Logic, we found, is the 
Theory of Proof. But proof supposes something provable, which must 
be' a Proposition or Assertion ; since .nothing but a Proposition can be 
an object of belief, or therefore of proof. A Proposition is, discourse 
whipll afKpns or denies something of some other thing. This is one 
step : there must, it geems, be two things concerned in every act of 
ibelj-ef. • But what -are tkese Things 1. They can be no other than thoee 
signified by the two n^mes, which being joined together by a co]3ula 
constitute the PropositiQn. If, therefore, we knew what all Names 
signify, we should know .ovety thing which is", capable either of being 
made a object of afhrmation or denial, or of being itself affirmed or 
denied of -a subject. We have accordingly, in the preceding chapter, 
reviewed the various kinds of Names, in order to ascertain what is sig- 



T^HINGS DENOTED BY NAMES. 31 

nified by eacli of them. And we have now came.d this survey far 
enough to be able to take an account of its results, and to exhibit an 
enumeration of all the kinds of Things which are capable of being 
made predicates, or of having anything predicated of them : after 
which to determine the unport of Predication, that is, of Propositions, 
can be no arduous task. 

• The necessity of an enumeration of Existences, as the basis of Logic, 
did not escape the attention of the schoolmen, and of their master, 
Aristotle, the most comprehensive, if not the most sagacious, of the 
ancient philosophers. The Categories, or Predicaments — the former 
a Crreek word, the latter its literal translation in the Latin language — • 
yere intended by him and his followers as an enumeration of all things 
capable of being named ; an enumeration by the smnma genera\ i. e. 
the most extensive classes into which things could be disti,-ibuted ; 
which, therefore, were so many* highest Predicates, one or other of 
which was supposed capable of being affirmed with truth of every 
nameable thing whatsoever. The following are the classes into which, 
according to this school of philosophy, Things in general might be re- 
duced : — • . ' , • - / 



■ ^Ovaca, 


Substantia. 


Jioaov, 


Quantitas, 


liolov, 


Qualitas. 


Ilpog re, 


E-elatio.. 


UoLslv, 


Actio,- 


Haaxetv, 


Passio, 


'TLov^ 


Ubi. 


Hots, 


Quando, 


Kelodai, 


■. Situs, 


. E;\;ay, 


Habitus, 



The imperfectioiis of this classification are too obvious to require^ 
and its merits are not sufficient to reward, a minute examination. It 
is' a mere catalogue of the distinctions rudely -marked out by the lan- 
guage of familiar life, with little or no attempt ;to penetrate, by philo- 
sophic analysis, to xhe ratio7iale qygiil of those common distinctions. 
Such an analysis, however superficially conducted, would have shown 
the enumeration to be both redundant and defective. Some objects 
are omitted, and others repeated several times under different heads. 
It is like a division of animals into inen, quadrupeds, horses, asses-, and 
ponies. That, for instance, could not be a very comprehfsnsive view 
of the nature of Relation whicli could exclude action^ passivity^ and lo- 
cal situation from tliat category. The same observation applies to the' 
categories Quando (or position in tinie) and L^bi (or position in space) ; 
while tli6 distinction between tlie latter and Situs, is merely verbal. 
The incongruity of erecting into a sumrrtUm genus the class which fqnns 
the tenth category is manifest.. On the other hand, the enumeration 
takes no notice of anything besides substances and attributes. • In what 
category are we to place sensations, or any other feelings, and states 
of mind; as hope, joy, fear ; "^ sound, smell, taste ; pain, pleasure; 
thought, judgment, conception, and the hke %'. Probably aE these 
would have been placed by the Aristotelian school in the categories of 
actio ^w^L fassio ; and the relation of such of them as are active, to 
their objects, and of such of them as are passive, to their causes, woiild 
rightly be so placed ; but the things themselves, the feelings or States 



^2 r * NAMES AND PROPOSITIONS. 

of mind wi'ongly. Feelings, or states of consciousness, are assuredly 
to be counted among realities, but they cannot be reckoned either 
among substances or attributes. - , 

§ 2. Before recommencing, under better auspices, the attempt made 
witb such imperfect success by the great founder of the science of logic, 
we must take notice of an unfortunate ambiguity in all the concrete 
names which correspond to the most general of all abstract terms, the 
word Existence. When we have occasion for a name which shall be 
capable of denoting whatever exists, as contradistinguished from non- 
entity or Nothing, there is hardly a Word applicable to the purpose 
which is not also, and even more familiarly, taken in a sense in which 
it denotes only substances. But substances are not, all that exist; 
attributes, if such things are to be spoken of, must bo said to exist; 
feelings also exist. Yet when we^ speak of an object, or of a thing, we 
are almost always supposed to mean a substance. There seems a kind 
of contradiction in using- such an expression as that one tiling is merely 
an attribute of another thing. And the announcement of a Classifica-. 
tion of Things would, I believe, prepare most readers for an enumqj"- 
ation like those in natural history, beginning with the great divisions 
of animal, vegetable, and mineral, and subdividing them into classes 
and orders. If, rejecting the word Thing, we endeavor to find another 
of a more general import, or at least more exclusively confined to that 
general import, a w^ord denoting all that exists, and connoting only simple 
existence ; no word might be presumed fitter for such a purpose than 
heing : originally the present participle of a verb which in one of its 
meanings is exactly equivalent to the verb exist; and therefore suitable, 
even by its grammatical formation, to be the concrete of the abstract ex- 
istence. But this word, strange as the fact may appear, is still more com- 
pletely spoiled for the purpose which it seemed expressly made for, 
than the word Thing. Being is, by custom, exactly synonymous vdth 
substance ; except that it is free from a -slight taint of a second ambigu- 
ity ; being applied impartially to matter and to mind, while substance, 
though originally and in strictness applicable to both, is apt to suggest 
in preference the idea of matter. Attidbutes are never called Beings ; 
nor are Feelings. ' A Being is that which excites feelings, and which 
possesses attiibutes. The soul is called a Being; God and angels are 
called Beings ; but if we were to say, extension, color, wisdom, virtue 
are beings, we should perhaps be suspected of thinking with some of 
the ancients, that the cardinal virtues are animals ; or, at the least, of 
holding with the, Platonic school the doctrine of self-existent Ideas, or 
with the followers of Epicurus that of Sensible Forms, which detach 
themselves in every direction from bodies, and by coming in contact 
with ,our organs, .cause our perceptions. We should be supposed, in 
short, to believe that Attributes are Stibstances. 

In consequence of this perversion, of the word Being, philosophers 
looking about for something to supply its place,, laid their hands upon 
the word Entity, a piece of barbarous Latin,, invented by the schoolmen 
to be used as an abstract na^me, in which class its grammatical form 
would seem to place 4t ; but being seized by logicians in distress to 
stop a leak in their terminology, it has. ever since been used as a con- 
crete name. The kindred word essence, born at the same time, and of 
the same pareiits, scarcely underwent a moi:e complete ti'ansformation 



THINGS DENOTED BY NAMES. 33 

when, from being the abstract of the verb to he, it came to denote some- 
thing sufficiently concrete to be inclosed in a glass bottle. The word 
Entity, since it settled down into a concrete name, has retained its 
universality of signification somewhat less unimpaired than any of the 
names before mentioned. Yet the same gi'adual decay to which, after 
a certain age, all the language of psychology seems liable, has been at 
work even here. If you call virtue wi entity, you are indeed somewhat 
less strongly suspected of believing it to be a substance than if you 
called it-, a being; but you are by no means free from the suspicion. 
Every word which was originally intended to connote mere existence, 
seems, after a time, to enlarge its connotation to sejjarate existence, or 
existence freed from the condition of belonging to a substance ; which 
condition being precisely what constitutes an attribute, attributes are 
gradually shut out, and along with them feelings, which, in ninety-nine 
cases out of a hundred, have no other name than that of the attribute 
which is grounded upon them. Strange that when the greatest em- 
barrassment felt by all who have any considerable number of thoughts 
to express, is to find a sufficient variety of words fitted to express them, 
there should be no practice to which even philosophers are more ad- 
dicted than that of taking valuable words to express ideas which are 
sufficiently expressed by other words already appropriated to them. 

When it is impossible to obtain good tools, the next best thing is to 
understand thoroughly the defects of those we have. I have therefore 
warned the reader of the ambiguity of the very names which, for want 
of better, I am necessitated to employ. It must now be the writer's 
endeavor so to employ them as in no case to leave his meaning doubtful 
or obscure. No one of the above terms being altogether ambiguous, I 
shall not confine myself to any onie, but shall employ on each occasion 
the word which seems least likely in the particular case to lead to a 
misunderstanding of my meaning ; nqr do I pretend to use either these 
or any other words with a rigorous adherence to one single sense. 
To do so would often leave us without a word to express what is sig- 
nified by a known word in some one or other of its senses; unless 
authors had an unlimited license to coin new wotds, together with 
(what it would be more difficult to assume) unlimited power of making 
their readers adopt them. Nor would it be wise in a writer, on a 
subject involving so much of abstraction, to deny himself the advantage 
derived from even an improper use of a term, when, by means of it 
some familiar association is called up which brings the meaning home 
to the mind, as it were by a flash. 

The difficulty, both to the writer and reader, of the attempt which 
must be made to use vague words so as to convey a precise meaning, 
is not wholly a matter of regret. It is not unfitting that logical treatises 
should afford an example of that, to facilitate which is among the most 
important uses of logic. Philosophical language will for a long time, 
and popular language perhaps always, retain so miuch of vagueness,' 
and ambiguity, that logic would be of little value if it did not, among 
its other advantages, exercise the understanding in doing its work 
neatly and correctly with these imperfect tools, , 

After this preamble it is time to proceed to our enumeration. We 
shall commence with Feelings, the simplest class of naiheable things ; 
the term Feeling being of course understood in its most enlarged 
sense. . - ■ • 

E '. 



34 NAMES AND PROPOSITIONS. , 

I. Feelings, or States op Consciousness. 

§ 3. A Feeling and a State of Consciousness are, in^ the language of 
philosophy, equivalent expressions : everything is a Feeling, of vi^hich 
the mind is conscious : everything w^hich it feels, or, in other words, 
which forms a part of its own sentient existence. In popular language 
Feeling is not always synonymous with State of Consciousness ; being 
often taken more peculiarly for those states which are conceived as 
belonging to the sensitive, or to the emotional, phasis of our nature, 
and sometimes, with a still narrower restriction, to the emotional 
alone : as distinguished from what are conceived as belonging to^ the 
percipient, or intellectual phasis. But this is an admitted departure 
from correctness of language ; just as, by a popular perversion the 
exact converse of this, the word Mind is withdrawn from its rightful 
generality of signification, and restricted to the intellect. The still 
greater perversion by which Feeling is sometimes confined not only 
to bodily sensations, but to the sensations of a single sense, that of 
touch, needs not be more particularly adverted to. 

Feeling, in the proper sense of the term, is a genus, of which 
Sensation, Emotion, and Thought, are subordinate species. Under the 
word Thought is here to be included whatever we are internally con- 
scious of when v/e are said to think ; from the consciousness we have 
when we think of a red color without having it before our eyes, to the 
most recondite thoughts of a philosopher or poet. Be it remembered, 
however, that by a thought is to be understood what passes in the mind 
itself, and not any object external to the mind, v/hich the person is 
commonly said to be thinking of. He may be thinking of the sun, or 
, of God, but the sun and God are, not thoughts; his mental image, 
however, of the sun, and his idea of God, are thoughts ; states of his . 
mind, not of the objects themselves: and so also is his belief of the 
existence of the sun, or of God; or his disbelief, if the case be so. 
Even imaginary objects, (which are said to exist only in our ideas,) 
are to be distinguished from our ideas of them. I may think of a 
hobgoblin, as I may think of the loaf which was eaten yesterday, or 
of the flower which will bloom to-morrow. But the hobgoblin which 
never existed is not the same thing with my idea of a hobgoblin,. any 
more than the loaf which once existed is the same thing with my idea 
of a loaf, or the flower which does not yet exist, but which will exist, 
is The same with my idea of a flower. They afe all, not tlioughts, 
but objects of thought; though at the present time all the objects are 
alike non-existent. 

\vi like manner, a Sensation is to be carefully distinguished from 
the object which causes the sensation ; our sensation of white from, a 
white object ; nor is it less to be distinguished from the atU'ibute 
whiteness, which we Ascribe to the object in consequence of its exci- 
ting the sensation. Unfortunately for clearness and due discrimination 
in considering these subjects, our sensations seldom receive separate 
naTnes. We have a name for the objects which produce in us a 
certain sensation ; the word ivhite. We have a, name for the quality 
in those objects, to which we ascribe the sensation; the name white- 
ncs.s. But when we speak of the sensation itself, (as we have not 
occasion to do this often except in our philosophical speculations,) 
language, which adapts itself for the most part only to the common 



THINGS DENOTED BY NAMES. 35 

iises of -life, lias provided us with no single-worded or immediate desig- 
nation ; we must employ a circumlocution, and say. The sensation of 
white, or The sensation of whiteness ; we must denominate the sensation 
either from the object, or from the attribute, by which it is excited. 
Yet the sensation, though it never does, might very well be conceived to 
exist, without anything whatever to excite it. We can conceive it as 
arising spontaneously in the mind. But if it so arose, we should have 
no name to denote it which would not be a misnomer. In the case of 
our sensations of hearing we are better provided ; we' have the word 
Sound, and a whole vocabulary of words to denote the various kinds 
p£ sounds. For as we are often conscious of these sensations in the 
absence of any^^e;*6'e/?^i^Ze object, we can more easily conceive having 
them in the absence of any object whatever. We need only shut our 
eyes and listen to -- music, to have a conception of a universe with 
nothing in it except sounds, and ourselves hearing them ; and what is 
easily conceived separately, easily obtains a separate name. But in 
general our names of sensations. denote indiscriminately the sensation 
and the attribute. Thus, color stands for the sensations of white, red, 
&c., but also for the quality in the colored object. VVe talk of the 
colors of things as among their lyropcrties. 

.§ 4. In the case of sensations, another distinction has also to be kept 
in view, which is .often confounded, and never without mischievous 
consequences. This is, the distinction between the sensation itself, 
and the state of the bodily organs which precedes the sensation, and 
which constitutes the physical agency by which it is produced. One 
of -the sources of confusion on this subject is the division commonly 
made, of feelings into Bodily and Mental. Philosophically speaking, 
.there is no foundation at all- for this distinction :' even sensations are 
states of the sentient mind, not states of the body, as distinguished 
fi-om it. , What I am conscious of when I see the color blue, is a feel- 
ing of blue color, which is one tiling ; the picture on my retina, or. the 
phenon^ieiion of hitherto mysterious nature which takes place in my 
optic nerve or in, my brain, is another thing, of which I am not at all 
conscious,, and- which scientific ipivestigation alone could have apprised 
me of These are states of my body; but the sensation of blue, which 
is the consequence of these states of body, is not a state of body; that 
which perceives and is conscious is called Mind. When sensations 
are called bodily feelings, it is only as being the class of feelings which, 
are immediately occasioned by bodily states ; whereas the other kinds 
of feelings, thoughts, for instance, or emotions, are immediately excited 
not by anything acting upon the bodily organs, but by sensations, or 
by previous thoughts. This, however, is a distinction not in our feel- 
ings, but in the agency which produces our feelings ; all of them when 
actually produced are states of mind. 

Besides the affection of our bodily "organs from without, and the 
sensation thereby produced in our minds,- many \vi'iters admit a third 
link in the chain of phenomena, which they term a Perception, and 
which consists in tlie recognition of an -external object as the exciting 
cause of the sensation. This perception, they say, is an act of the 
mind, proceeding from its own spontaneous activity, while in sensation 
the mind is passive, being merely acted upon by the outward object. 
And according to some philosophers it is by an act of the mind, similar 



36 ' NAMES AND PROPOSITIONS. 

to perception, except in not being preceded by any sensation, that we 
recognize the existence of God, of tbe soul, and other hyperphysicai 
reahties. 

These acts of perception, whatever be the conclusion ultimately 
come to respecting their nature, must, I conceive, take their place 
among the varieties of feelings or states of mind. In so classing them, 
I have not the smallest intention of declaring or insinuating any theory 
as to the law of mind in which these mentaLprocesses may be supposed 
to originate, or the conditions under which they may be legitimate or 
the reverse. Far less do I mean (as Mr. Whewell seems to suppose 
must be meant in an analogous case*) to indicate that as they are 
" 7nerely states of mind," it is superfluous to inquire into their distin- 
guishing peculiarities. I abstain from the inquiry as irrelevant to the 
science of logic. In these so-called perceptions, or direct recognitionst 
by the mind of objects, whether physical or spiritual, which are ex- 
ternal to itself, I can see only cases of belief; but of belief which 
claims to be intuitive, or independent of external evidence. When a 
stone lies before me, I am conscious of certain sensations which I 
receive from it ; but when I say that these sensations come to me frorii 
an external object which I perceive, the meaning of these words is, that 
receiving the sensations, I intuitively believe that an external cause of. 
those sensations exists. The laws of intuitive belief, and the conditions 
under which it is legitimate, are a subject which, as we have already 
so often remarked, belongs not to logic, but to the higher or transcen- 
dental branch of metaphysics. 

To the same region of speculation belongs all that can be said re- 
specting the distinction which the German metaphysicians and their 
French and English followers, (among whom Mr, Whewell is one "of 
the most distinguished,) so elaborately draw between xYiq acts of the 
mind and its merely passive states ; between what it receives from, 
and what it gives to, the crude materials of its experience, I am aware 
that with reference to the view which those writers take of the primary 
elements of thought and knowledge, this distinction is fundamental. 
But for our purpose, which is to examine not the original groundwork 
of our knowledge, but how we come by that portion of it which is not 
original; the difference between active and passive states of mind is of 
secondary importance. For us, they all are states of mind, they all 
are feelings; by which, let it be said once more, I mean to imply 
nothing of passivity, but simply that they are psychological facts, facts 
which take place in the mind, and to be carefully distinguished from 
the external or physical facts with which they may be connected, either- 
as effects or as causes. 

§ 5. Among active states of mind, there is, however, one species 
which merits particular attention, because it forms a principal part of 
the connotation of some important classes of names. ~^ I mean volitions, 
or acts of the will. When we speak of sentient beings by relative 
names, a large portion of the connotation of the name usually consists 
of the actions of those beings ; actions past, present, and possible or pro- 
bable future. Talie, for instance, the words Sovereign and Subject. 
What meaning do these words convey, but that of innumerable actions, 

* Philosophy of the Inductive Sciences, Yoli.^.^O. 



THINGS DENOTED BY NAMES. 37 

done or to be done by tlie sovereign and the subjects, to or in regard 
to one another reciprocally ] So with the words physician and patient, 
leader and follower, master and servant. In many cases the words 
also connote actions which would be done under certain contingencies 
by persons other than those denoted : as the words mortgagor and 
mortgagee, obligor and obligee, and many other words expressive of 
legal relation, which connote what a court of justice would do to 
enforce the legal obligation if not fulfilled. There are also words 
which connote actions previously done by persons other than those 
denoted either by the name itself or by its correlative ; as the word 
brother. From these instances, it may be seen how large a portion of 
the connotation of names consists of actions. Now, what is an action ? 
Not one thing, but a series of two things : the state of mind called a 
volition, followed by an effect. The volition, or intention to produce 
the effect, is one thing; the effect produced in consequence of the 
intention is another thing; the two together constitute the action. I- 
form the purpose of instantly moving my arm ; that is a state of my 
mind ; my arm (not being tied nor paralytic) moves in obedience to my 
purpose ; that is a physical fact, consequent upon a state of mind. 
The intention, when followed by the fact, or, (if we prefer the expres- 
sion,) the fact when preceded and caused by the intention, is called the 
action of moving my arm. 

: § 6. Of the first leading division of nameable things, viz.. Feelings 
or States of Consciousness, we began by recognizing three sub-divi- 
sions : Sensations, Thoughts, and Emotions. The first two of these 
we have illustrated at considerable -length; the third. Emotions, not 
being perplexed by similar ambiguities, does, not require similar exem- 
plification. And, finally, we have found it necessary to add to these 
three a fourth species, commonly known by the name Volitions. With- 
out seeking to prejudge the metaphysical question whether any mental 
state or phenomenon can be found which is not included in one or 
other of these four species, it appears to me that the amount of illus- 
tration bestowed upon these may, so far as we are concerned, suffice 
for the whole genus. "We shall, therefore, proceed to the two remain- 
ing classes of nameable things ; all things which are external to the 
mind being considered as belonging either to the class of Substances 
or to thax of Attributes. 

II. Substances. 

Logicians have endeavored to define Substance and Attribute ; 
but their definitions are not so much attempts to draw a distinction 
between the things themselves, as instructions what difference it is 
customary to make in the grammatical structure of the sentence, 
according as you are speaking of substances or of attributes. Such 
definitions are rather lessons of English, or of Greek, Latin, or Ger- 
man, than of mental philosophy. An attribute, say the school logi- 
cians, must be the attribute o/* something : color, for example, must be 
the color of something ; goodness must be the goodness of something : 
and if this something should cease to exist, or should cease to be _con- 
nected with the attribute, the existence of the attribute would be at 
■Ml end. A substance, on the contrary, is self- existent ; in speaking 



.38 NAMES AND PROPOSITIONS. 

about it, we need not put of after its name, A stone is not tlie stone 
o/'any thing ; the moon is not the moon (^/^ anything, but simply the moon. 
Unless, indeed, the name which we choose to give to the substance 
be a relative name ; if so, it must be followed either by of, or by some 
other particle, implying, as that preposition does, a reference to some- 
thing else : but then the other characteristic peculiarity of an attribute 
would fail ; the something might be destroyed, and the substance might 
still subsist. Thus, a father must be the father of something, and so 
far resembles an attribute, in being referred to something besides him- 
self: if there were no child, there would be no father : but this, when 
We look into the matter, only means that we should not call him father. 
The man called father might still exist, though the child were annihi- _ 
lated ; and there would be no contradiction in supposing him to exist,, 
although the whole universe , except himself were destroyed. But 
destroy all white substances, and where would be the attribute white- 
ness ] Whiteness, without any white thing, is a contradiction in terms. 

This is the nearest approach to a solution of the difficulty, that will 
be found in the common treatises on logic. It will scarcely be thought 
to be a satisfactory one. If an attribute is distinguished from a sub- 
stance by being the attribute of something, it seems highly necessary 
to understand what is meant by of: a particle which needs explanation 
too much itself to be placed in front of the explanation of anything 
else. And as for the self-existence of substances, it is very true that a 
substance may be conceived to exist without any other substance, but 
so also may an attribute without any other attribute : and we can no 
rnore imagine a substance without attributes than we can imagine 
attributes without a substance. 

Metaphysicians, however, have probed the question deeper, and given 
an account of Substance considerably more satisfactory than this. Sub- 
stances are usually distinguished as Bodies or Minds. Of each of these, 
philosophers have at length provided us with a definition .which seems 
unexceptionable. . , ^ ^ ' • ■ ' - 

§ 7. A Body, according to the received doctrine of modern nletaphy-' 
sicians, may be defined, the external cause to which we ascribe our 
sensations. When I see and touch a piece of gold, I am conscious of 
a sensation of yellow color, and sensations of hardness and weight; 
and by varying the mode of handling, I may add to these sensations 
many others completely distinct from them. Tfie sensations are all of 
which I am directly conscious ; but I consider them as jDroduced by 
something not only existing independently of my will, but external to 
my bodily organs and to my mind. This external something I call a 
Body. 

It may be asked, how come we to ascribe our sensations to any 
external cause % and is there sufficient ground for so ascribing them ? 
It is known, that there are metaphysicians who have raised a contro- 
versy on the point; maintaining the paradox, that we are not warranted 
in referring our sensations to a cause, such as we understand by the 
word Bodyj or to any cause whatever, unless, indeed, the First Cause. 
Though we have no concern here with this controversy, nor with the 
metaphysical niceties on which it turns, one of the best ways of showing 
-what is meant by Substance is, to consider what position it is necessary 
to take up,'' in order to maintain i^s existence against opponents. 



THINGS DENOTED BY NAMES. 39 

It" is certain, then, that a part of our notion of a body consists of the 
notion of a number of sensations of our own, or of other sentient beings, 
habitually occurring simultaneously. My conception of the table at 
which I am writing is compounded of its visible form and size, which 
are complex sensations of sight ; its tangible form and size, which are 
complex sensations of our organ of touch and of our muscles ; its 
weight, which is also a sensation of touch and of the muscles ; its color, 
which is a sensation of sight ; its hardness, which is a sensation of the 
muscles ; its composition, which is another word for all the varieties of 
sensation Vv'^hich we receive under various circumstances from the wood 
of which it is made ; and so forth. All or most of these various sensa- 
tions frequently are, and, as we learn by experience, always might be, 
experienced simultaneously, or in many different orders of succession, 
at our own choice : and hence, the thought of any one of them makes 
us think of the others, and the whole become mentally amalgamated into 
one mixed state of consciousness, which, in the language of the school 
of Locke and Hartley, is termed' a Complex Idea. 
^ Now tliere are philosophers who have argued as follows : — if we 
' take ah orange, and conceive it to be divested of its natural color 
without acquiring any new one ; to lose its softness without becoming 
hard, its roundness without becoming square or pentagonal, or of any 
other regular or irregular figure whatever ; to be deprived of size, of 
weight, of taste, of smell ; to lose all its mechanical and all its chemical 
properties, arid acquire no new ones ; to become, in short, invisible, 
intangible, and imperceptible not only by all our senses, but by the 
senses of all other sentient beings,' real or possible; nothing, say these 
philosophers, would remain. For of what nature, they ask, could be 
. the residuum 1 and by what token could it manifest its presence 1 To 
the unreflecting its existence seems to rest on the evidence of the 
senses. But to the senses nothing is apparent except the sensations. 
We know, indeed, that these sensations are bound together by some 
law; they do not come together at random, but according to a systematic 
.order, which is part of the order established in the universe. When 
we experience one of these sensations; we usually experience the others 
also, or know that we have it iix our power to experience them. But 
a fixed law of connexion, making the sensations, occur together, does 
hot, say these philosophers, necessarily require what is called a sub- 
stratum to support them. The conception of a substratum is but one 
of many possible forms in which that connexion presents itself to our 
imagination ; a mode of, as it vv^ere, realizing the idea. If there be 
such a substratum, suppose it this instant annihilated by the fiat of 
Omnipotence, and let the sensations continue to occur in the same 
order, and how would the substratum be missed 1 By what signs 
should we be able to discover that its existence had terminated ] should 
we not have as much reason to believe that it still existed, as we now 
have 1 and if we should not then be waiTanted in believing it, how 
can we be so nowl A body, therefore, according to these meta- 
physicians, is not anything intrinsically different from the sensations . 
which the body is said to produce in us ; it is, in short, a set of sensa- 
tions joined together according to a fixed law. 

These ingenious speculations have at no time in the history of phi- 
losophy made many proselytes ; but the controversies to which they 
imve given rise, and the doctrines which have been developed in the 



40 NAMES AND PROPOSITIONS. 

attempt to find a conclusive answer to them, liave been fruitful of im- 
portant consequences to the Science of Mind. The sensations (it was 
answered) which we are conscious of, and which we receive not at 
random, but joined together in a certain uniform manner, imply not 
only a law or laws of connexion, but a cause external to our mind, 
which cause, by its own laws, determines the laws according to which 
the sensations are connected and experienced. The schoolmen used 
to call this external cause by the name we have already employed, a 
suhstratum ; and its attributes (as they expressed themselves) inhered,, 
literally stuch, in it. To this substratum the name Matter is usually 
given in philosophical discussions. It was soon, however, acknowl- 
edged by all who reflected on the subject, that the existence of matter 
could not be proved by extrinsic evidence. The answer, therefore, 
now usually made to Berkeley and his followers is^ that the belief is 
intuitive; that mankind, in all ages, have felt themselves compelled, by 
a necessity of their nature, to refer their sensations to an external 
cause : that even those who deny it in theory, yield to the necessity in 
practice, and both in speech, thought, and feeling, do, equally with the^ 
vulgar, acknowledge their sensations to be the effects of something ex- 
ternal to them : this knowledge, therefore, is as evidently intuitive as 
our knowledge of our sensations themselves is intuitive. And here 
the question merges in the fundamental problem of transcendental 
metaphysics; to which science we leave it. 

. But although the extreme doctrine of the Idealist metaphysicians, 
that objects are nothing but our sensations and the laws which connect 
them, has appeared to few subsequent thinkers to be worthy of assent; 
the only point of much real importance is one upon which those meta- 
physicians are now very generally considered to have made out their 
case : viz., that all we know of objects is the sensations which they give 
us, and the order of the occurrence of those sensations. Kant himself, 
on this point, is as explicit as Berkeley or Locke. However firmly 
convinced that there exists an universe of " Things in themselves," 
totally distinct from the universe of phenomena, or of things as they 
appear to our senses; a,nd even when bringirig into use the technical 
expression [Noumenon^ to denote what the thing is in itself, as con- 
trasted with tlie representation of it in our minds ; he allows that this 
representation (the matter of which, he says, consists of our sensations, 
though the form is given by the laws of the mind itself) is all we knov7 
of the object, and that the real nature of the Thing is, and by the con- 
stitution of our faculties ever must remain, at least in this sublunary 
existence, an impenetrable mystery to us.* There is not the slightest 

* 1 have much pleasure in quoting a passage in which this doctrine is laid down in the 
dearest and strongest terms by M! Cousm, the most distinguished living teacher of German 
philosophy out of Germany, whose authority on this side of the question is the more valu- 
able, as his philosophical views are generally those of the post-Kantian movement, repre- 
sented by Schelling and Hegel, whose tendencies are much more objective and ontological 
than those of their master, Kant. 

" Nous Savons qu'il existe quelque chose hors de nous, parceque nous ne pouvons expli- 
quer nos perceptions sans les rattacher a des causes distinctes de nous-m^mes ; nous savons 
de plus que ces causes, dont nous ne connaissons pas d'ailleurs I'essence, produisent les 
effets les plus variables, les plus divers, et m6me les plus contraires, selon qu'elles rencon- 
trent telle nature ou telle disposition du sujet. Mais savons-nous quelque chose de plus? 
et meme, vu le caract^re indetermine des causes que nous concevons dans les corps, y a-t-il 
quelque chose do plus a savoir ? Y a-t-il lieu do nous enquerir si nous percevons les choses 
telles qu'elles sent ? Non evidemment. . . . . Je ne dis pas que le probleme esf. insoluble, ^76 
dis qu'il est absurde et enferme une contradiction. Nous ne savons pas ce que ccs causes sont en. 
elles-memes, et la raison nous defend de chercher a le connaitre : mais il est bien evident ^ 



THINGS DENOTED BY NAMES. 41 

reason for believing that what we call the sensible qualities of the ob- 
ject are a type of anything inherent. in itself, or bear any affinity to its 
own nature. A cause does not, as such, resemble its effects ; an east 
wind is not like the feeling of cold, nor is heat like the steam of boiling 
water : why then should matter resemble oirr sensations ] Why should 
the inmost nature of fire or water resemble the impressions made by 
these objects upon our senses 1* And if not on the principle of resem- 
blance, on what other principle can the manner in which objects affect 
us through pur senses afford us any insight into the inherent nature of 
those objects'? It may therefore safely be laid down as a truth both 
obvious in itself, and admitted by all whom it is at present necessary 
to take into consideration, that, of the outward world, we know and 
can know absolutely nothing, except the sensations which we ex- 
perience from it. Those, however, who still look upon Ontology as 
a possible science, and think, not only that bodies have an essen- 
tial constitution of their own, lying deeper than our perceptions, but 
that this essence or nature is not altogether inaccessible to human in- 
vestigation, cannot expect to find their refutation here. The question 
depends upon the nature and laws of Int^iitive Knowledge, and is not 
within the province of logic. 

§ 8. Body having now been defined the external cause, and (accord- 
ing to the more reasonable opinion) the hidden external cause, to which 
we refer, our sensations ; it remains to frame a definition of Mind, 
Nor, after the preceding observations, will this be difficult. For, as 
our conception of a body is that of an unknown exciting cause of 
sensations, so our conception of a mind is that of an unknown recipient, 
or percipient, of them; and not of them alone, but of all our other 
feelings. As body is the mysterious something which excites the 
mindN to feel, so mind is the inyterious something which feels, and 

priori, qu'eZZes ne sont pas en elles-memes ce qxCclles sont par rapport a nous, puisque la presence 
du sujet mo^ifie necessairement leur action. . Supprimez tout sujet sentant, il est certain 
que ces causes agiraient encore puisqu'elles continueraient d'exister ; mais elles agiraient 
autrement ; elles seraient encore des qualites et des proprietes, mais qui ne resembleraient 
a rien de ce que nous connaissons. Le feu ne manifesterait plus aucune des proprietes que 
nous lui connaisons :. que serait-il ' C'est ce que nous ne saurolis jamais. Cest d'ailleurs 
peut-etre un probleme qui ne repugne pas seulement a la nature de noire esprit, mais a Vessence- 
m^me des choses. Quand m6me en effet-on supprimerait par la pensee tous les suje^ sentants,- 
il faudrait encore admettre qi^e nul corps ne manifesterait ses proprietes autrement qu'en 
relation avec un sujet quelconque, et dans ce cas ses proprietes ne seraient encore que relatives : 
en sorte qu'il me parait fort raisonnable d'admettre que les proprietes determinees des corps 
n'existent pas independamment d'un sujet quelconque, et que quand on demande si les pro- 
prietes de la matiere sont telles que nous les percevons, il faudrait voir auparavant si elles 
sont en tant que determinees, et dans quel sens il est vrai de dire qu'elles sont." — Cours 
d''Histoire de la PTiilosophie Morale au I8?ne siecle, 8me lec^on. _ - 

* An attempt, indeed, has been made by Reid and others, to establish that, although some 
of the properties we ascribe to objects exist only in our sensations, others exist in the things 
themselves, being such as cannot possibly be copies of any impression upon the senses ; and 
they ask, from what sensation our notions of extension and figure have been derived ? The 
gauntlet thrown down by Reid was taken up by Brown, who, applying greater powers of 
analysis than had previously been applied to the notions of extension and figure, showed 
clearly vvhat are the sensations fromwhich those notions are derived, viz., sensations of 
touch, combined with sensations of a class previously too little adverted to by metaphysi- 
cians, those which have their seat in our muscular frame. Whoever wishes to be more 
particularly acquainted with this admirable specimen of metaphysical analysis may consult 
the first volume of Brown's Lectures, or Mill's Analysis of the Mind. 

On this subject also, the authority of M. Cousin may be quoted in favor of conclusions re- 
jected by some of the most eminent thinkers of the school to which he belongs. M. Cousin 
recognizes, in opposition to Reid, the essential subjectivity of our conceptions of the primary 
qualities of matter, as extension, solidity, &c., equally with those of color, heat, and the 
remainder of what are called secondary qualities.-^Cowrs, ut supray 9me le9on. 

.F , 



42 NAMES AND PROPOSITIONS. 

thinks. It is unnecessary to give in tlie case of mind, as we gave in 
the case of matter, a particular statement of the skeptical system by 
which its existence as a Thing in itself, distinct from the series of what 
are denominated its states, is called in question. But it is necessary 
to remark, that on the inmost nature of the thinking principle, as well 
as on the inmost nature of matter, we are, and with our human facul- 
ties, must alvv^ays remain, entirely in the dark. All which we ai'e 
aware of, even in our own minds, is (in the words. of Mr. Mill) a cer- 
tain "thread of consciousness;" a series of feelings, that is, of sensa- 
tions, thoughts, emotions, and volitions, more Or less numerous and 
complicated. There is a something I call Myself, or, by another form 
of expression, my mind, which I consider as distinct from these sensa- 
tions, thoughts, &c. ; a something which I conceive to be not the 
thoughts, but the being that has the thoughts, and which I can conceive 
as existing for ever in a state of quiesence, without any thoughts at all. 
But what this being is, although it is myself, I have no knowledge, 
further than the series of its states of consciousness. As bodies mani- 
fest themselves to me only through the sensations of which I regard 
them as the causes, so the thinking principle, or mind, in my own 
nature, makes itself known to me only by tho feelings of which it is con- 
scious. I know nothing about myself, save my capacities of feeling or 
being conscious (including, of course, thinking and willing) : and were 
I to learn anything new concerning myself, I cannot with my present 
faculties conceive this new information to be anything else, than that I 
.have soipe additional capacities, before unknown to me, of feeling, 
thinking, or willing. ' 

Thus, then, as body is the unsentient cause to which we are nat- 
tirally prompted to refer a certain portion of our feelings, so mind may 
%e described as the sentient subject (in the German sense of the term) 
of all feelings ; that which has or feels them. But of the nature of 
either body or mind, further than the feelings which the former excites, 
and which the latter experiences, we do not, according to the best 
existing doctrine, know anything ; and if anything, logic has nothing 
to do with it, or with the rhanner in which the knowledge is acquired. 
With this result we may conclude this portion of our subject, and pass 
to the third and only remaining class or division of Nameable Things. 

III. Attributes: and, first. Qualities. 

§ 9. From what has already been said of Substance, what is to be 
said of Attribute is easily deducible. For if we know not, and cannot 
know,, any thing of bodies but the sensations which they excite in us or 
others, those sensations must be all that we can, at bottom, mean by their 
attributes ; and the distinction which we verbally make between the 
properties of things and the sensations we receive from them, must 
originate in the convenience of discourse rather than in the nature of 
what is denoted by the terms. 

Attributes are usually distributed under the three heads of Quality, 
Quantity, and Relation. We shall come to the two latter presently: 
in the first place we shall confine ourselves to the former. 

Let us take, then, as our example, one of what are termed the sen- 
sible qualities of ol)jects, and let that example be whiteness. AVTien 
we ascribe whiteness to any substance, as,, for instance, snow ; when 



THINGS DENOTED BY NAMES. 43 

we say that snow has the quahty whiteness, what do We really assert ! 
Simply, that when snow is present to our organs, we have a particular 
sensation, which we are accustomed to call the sensation of white. But 
how do I know that snow is present ? Obviously by the sensations 
wliich I derive from it, and not otherwise. I infer that the object is 
present, because it gives me a certain assemblage or series of sensa- 
tions. And when I ascribe to it the attribute whiteness, my meaning 
is only, that, of the sensations composing this group or series, that 
which I call the sensation of white color is one. 

This is one view which may be taken of the subject. But there is 
also another, and a different view. It may be said, that it is true we 
hnow nothing of sensible objects, except the sensations they excite in: 
us; that the fact of our receiving from snow the particular sensatioji 
which is called the sensation of white, is the ground on which we as- 
cribe to that substance the quality whiteness ; the sole proof of its pos- 
sessing that quality. But because one thing may be the sole evidence 
of the existence of another thing, it does not follow that the two are 
one and the same. The attribute whiteness (it may be said) is not 
the fact of our receiving the sensation, but something in the object it- 
self; a j96»^^7er inherent in it; somethings virtue of which the object 
produces the sensation. And when we affirm that snow possesses the 
attribute whiteness, we do not merely assert that the presence of snow 
produces in us. that sensation, but that it does so through, and by rea~ 
son of, that power or quality. 

For the purposes of logic it is not of material importance which of 
these views we adopt. The full discussion of the subject belongs to 
the department of inquiry so often alluded to under the name of the 
higher metaphysics ; but it may be said here, that for the doctrine of 
the existence of a peculiar species of entities called qualities, I can see 
no foundation except in a tendency of the human mind which is the 
cause of many delusions. .1 mean, the disposition, wherever we meet 
with two names which are not precisely synonymous, to suppose that 
they must be the names of two different things ; whereas in reality 
they may be names of the same thing viewed in two different lights, 
which is as much as to say under different suppositions as to surround- 
ing circumstances. Because quality mid. sensation cannot be put in- 
discriminately one for the Other, it is supposed that they cannot both 
signify the same thing, namely, the impression or feeling with which 
we are affected through our senses by the presence of an object: al- 
though there is at least no absurdity in supposing that this identical 
impression or feeling may be called a- sensation when considered 
merely in itself, and a quality when regarded as emanating from any 
one of the numerous objects, the presence of which to our organs ex- 
cites in our minds that among various other sensations or feelings. 
And if this be admissible as a supposition, it rests with 'those who con- 
tend for an entity ^er se called a quality, to show that their opinion is 
preferable, or is anything in fact but a lingering remnant of the scho- 
lastic doctrine of occult causes ; the very absurdity which Moliere so 
happily ridiculed when he made one of his pedantic physicians account 
for the fact that " I'opium endormit," by the maxim " parcequ'il a une 
vertu soporifique." 

It is evident that when the physician stated that opium had "une 
vertu soporifique," he did not account for, but merely asserted over 



44 NAMES AND PROPOSITIONS. 

again, tlie fact that it endormit. In like manner, when we say that 
snow is white because it has the quality of whiteness, we are only re- 
asserting in more technical language the fact that it excites in us the 
sensation of white. If it be said that the sensation must have some 
cause, I answer, its cause is the presence of the object. When we 
have asserted that as often as the object is present, and our organs in 
their normal state, the sensation takes place, we have stated all that 
we know about the matter. There is no need, after assigning a cer- 
tain and intelligible cause, to suppose an occult cause besides, for the 
purpose of enabling the real cause to ■pj?(5duce its effect. If I am 
asked, why does the presence of the object cause this sensation in me, 
I cannot tell : I can only say that such is my nature, and the nature 
of the object: the constitution of things, the scheme of the universe, 
will have it so. And to this we must at last come, even after interpo- 
lating the imaginary entity. Wliatever number of link^ the chain of 
causes and effects may consist of, how any one link produces the one 
which is next to it remains equally inexplicable to us. It is as easy 
to comprehend that the object should produce the sensation directly 
and at once, as that it should produce the same sensation by the aid 
of something else called the power of producing it. 

But as the difficulties which may be felt in adopting this view of 
the subject cannot be removed without discussions transcending th^ 
bounds of our science, I content myself with a passing indication, and 
shall, for the purposes of logic, adopt a language compatible with either 
view of the nature of qualities. I shall say, — what at least admits of 
no dispute,-— that the quality of whiteness ascribed to the object snow, 
is grounded upon its exciting in us the sensation of white ; and, adopt- 
ing the language already used by the school logicians in the case of 
the kind of attributes called Relations, I shall term the sensation of 
white the foundation of the quality whiteness. For logical purposes 
the sensation is the only essential part of what is meant by the word ; 
the only part which we ever can be concerned in proving. When ' 
that is proved the quality is proved; if an object excites a sensation, 
it has, of course, the power of exciting it. 

IV. Relations. 

§ 10. The qualities of a body, we have said, are the attributes 
grounded upon the sensations which the presence of that particular 
body to our organs excites in our minds. But when we ascribe to any 
object the kind of attribute called a Relation, the foundation of the 
attribute must be something in which other objects are concerned 
besides itself and the percipient. 

As there may with propriety be said to be a relation between any 
two things to which two correlative names are or may be given ; we 
may expect to discover what constitutes a relation in general, if we 
enumerate the principal cases in which mankind have imposed correl- 
ative names, and observe what all these cases have in common. 

What, then, is the character which is possessed in common by states 
of circumstances so heterogeneous and discordant as these : one thing 
like another ; one thing unlike another ; one thing near another ; one 
thing far from another; one thing before, after, along with another; 
one thing greatpr, eqiial, less^ than another; one thing the cause of an- 



THINGS DENOTED BY NAMES. 45 

Other, the effect of another; one person the master, servant, child, 
parent, husband, wife, sovereign, subject, attorney, client, of another, and 
so on ? 

Omitthig, for the present, the case of Resemblance (a relation which 
requires to be considered separately), there seems to be one thing 
common to all these cases, and only one ; that in each of them there 
exists or occurs, or has existed or occurred, some Jact or phenomenon, 
into which the two things which are said to be related to each other, 
both enter as parties concerned. Tliis fact, or phenomenon, is what 
the Aristotelian logicians called the fundamentum rclationis. Thus in 
the relation of greater and less between two magnitudes, the funda- 
mentum, reloMonis is the fact that whenone of the two magnitudes is 
applied to the other, it more than covers it ; and cannot, by any new 
arrangement of parts, be entirely brought within the boundaries of the 
other object. In the relation of master and servant, tYie fundamentum 
relationis is the fact that the one has undertaken, or is compelled, to 
perform certain services for the benefit, and at the bidding, of the other. 
In that of husband and wife, \\\e fundamentum relationis consists of the 
facts that the parties are a man and a woman, that they have promised 
certain things with certain formalities, and are in consequence invested 
by the law with certain rights, and subjected to certain duties. Exam- 
ples might be indefinitely multij^lied, but it is already obvious that 
whenever two things are said to be related, there is some fact, or series 
of facts, into which they both enter ; and that whenever any two things 
are involved in some one fact, or series of facts, we may ascribe to those 
two things a mutual relation grounded on the fact. Even if they have 
nothing in common but what is common to all things, that they are 
members of the universe, we call that a relation, and denominate them 
fellow-creatures, fellow-beings, or fellow-denizens of the universe. But 
in proportion as the fact into which the two objects enter as parts is 
of a rnore special and peculiar, or of a more complicated nature, so 
also is the relation grounded upon it. And there are as many con- 
ceivable relations as there are conceivable kinds of f&.ct in which two 
things can be jointly concerned. 

In the same manner, therefore, as a quality is an attribute grounded 
upon the fact that a certain sensation or sensations are produced in us 
by the object, so an attribute grounded upon some fact into which the 
object enters jointly with another object, is a relation between it and 
that other object. But the fact' in the latter case consists of the very 
same kind of elements as the fact in the former : namely, states of 
consciousness. In the case last cited, for example, the relation of 
husband and wife ; the fundamentum relationis consists , entirely of 
thoughts, emotions, sensations, and vt^litions (actual or contingent), 
either of the parties themselves or of other parties concerned in the 
same series of transactions, as, for instance, the intentions which would 
DO formed by a judge in case a complaint were made tO his tribunal 
of the infringementof any of the legal obligations imposed by marriage; 
and the acts which the judge would perform in consequence; acts 
being (as we have already seen) another word for intentions followed 
by an effect, and that effect (agaiij) being but another word fOr sensa- 
tions, or some other feelings, occasioned either to oneself or to some-, 
body' else. There is no part whatever of what the names expressive 
of the relation imply, that is not resolvable into states of consciousness ; 



46 ' NAMES AND PROPOSITION'S. 

outward objects being, no daubt, supposed tlirougliout sts the causes 
by wbicb'Some of those states of consciousness ure excited, and miiids 
as the subjects by which all of them are experienced, but neither the 
external objects nor the minds making their existence known other- 
wise than by the gtates of consciousness. 

Cases of relation are not always so complicated as that to which we 
last. alluded. The simplest of all cases of relation are those expressed 
by the words antecedent and consequent, and by the word simultane" 
ous. If we say, for instance, that dawn preceded sunrise, the fact in 
which the two things, dawn and sunrise, were jointly concerned, con- 
sisted only of the two things themselves : no third thing entered into 
the fact or phenomenon at all ; unless, indeed, we choose to call the 
succession of the two objects a third thing; but their succession is not 
something added to the things themselves ; it is something involved in 
them. Dawn and sunrise announce themselves to our consciousness 
by two successive sensations: our consciousnegs of the succession of 
these sensations is not a third sensation or feeling added to them; we 
Ii,ave not first the two feelings, and then a feeling of their succession. 
To have two feelings at all, implies having them either successively, or 
else simultaneously. Sensations, or other feelings, being given, suc- 
cession and simultarieousness are the two conditions, to the alternative' 
of which they are subjected by the nature of our faculties ; and no one 
has been able, or needs expect, to analyze the matter any further. 

§ 11. In a somewhat similar position are two other sorts of relation, 
Likeness and Unlikeness. I have two sensations; we will suppose 
them to be simple ones; two sensations of white, or one sensation of 
white and another of black. I call the first two sensations like ; the last 
two unlike. What is the fact or phenomenon constituting the funda- 
mentum of this relation 1 The two sensations first, and then what- we 
call a feeling of resemblance, or a feeling of want of resemblance. Let 
us confine ourselves ,to the former case. Resemblance is evidently a feelr 
ing ; a state of the consciousness of the observer. Whether the feeling 
of the resemblance of the two colors, be a third state of consciousness, 
which I have aftei' having the two sensations of dolor, or whether (like 
the feeling of their succession) it is involved-, in the sensations them- 
selves,, jnay be a matter of discussion. But i=n either case, these feel- 
ings of resemblance, and of its opposite, dissimilarity, are parts of our 
nature ; and parts so far from being, cap able of analysis, that they are 
pre-supposed in every attempt to analyze any of our other feelings. 
Likeness and unlikeness, therefore, as well as antecedence, sequence, 
and simultaneousness, must stand apart among relations,, as xhmg^^sui 
generis. They are attributes grounded on facts, that is, on states, of 
consciousness,, but on states which are peculiar, unresolvable, and 
inexplicable. , - 

But, although likeness or unlikeness cannot be resolved into any- 
thing else, complex cases of likeness or unlikeness can be resolved into 
simpler ones. When we.say of two things which consist of j^arts, that 
they are like one another, the likeness of the whole does admit of analy- 
sis ; it is compounded of likenesses between the Variotis parts respec- 
tively. Of how vast a variety of resemblances of parts must that re- 
semblance be composed, which induces us to say that a portrait, or a 
landscape, is like its original. If one person rninjics another with :any 



THINGS DENOTED BY NAMES. 47 

success, of how many simple likenesses must the general or complex 
likeness be compounded : likeness in a succession of bodily postures; 
lU^eness in voice, or in the accents and intonations . of the voice; like- 
ness in the choice of words, and in the thoughts or sentiments express- 
ed, whether by word, countenance, or gesture. 

All likeness and unlikeness of which we have any cognizance, re- 
solve themselves into likeness and unlikeness between states of our 
own, or some other mind. Wlien we say that one body is like another, 
(since "v^e know nothing of bodies, but the sensations which they ex- 
cite,) we mean really that there is a resemblance between the sensa- 
tion^ excited by the two bodies, or between some portion at least of 
these sensations. If we say that two attributes are like one another, 
(since we know nothing of attributes e:xcept the sensations or states of 
feeling on which they are grounded,) we mean really that those sensa^ 
tions, or states of feeling, resemble each other. We may also say that 
two relations are alike. The fact of resemblance betjveen relations is 
sometimes called analogy, forming one of the numerous meanings of 
that word. The relation in which Priam stood to Hector, namely, that 
of father and son, resembles the relation in which Philip stood to Alex- 
ander ;. resembles it so closely that they are called the same relation. 
The relation in which Cromwell stood to England resembles the rela- 
tion in which Napoleon stood to France, though not so closely as to be 
called the same relation. The meaning in both these instances must 
be, that a resemblance existed between the facts which constituted the 
fundamentum relationis. 

. This resemblance may exist in all conceivable gradations, from 
perfect undistinguishableness to something very slight indeed. When 
we say, that a thought suggested to the mind of a person of genius is 
like a seed cast into the ground, because the former produces a multi- 
tude of other thoughts, and the latter a multitude of other seeds, this is 
saying that between the relation of an inventive mind to a thought 
contained in it,'^.and the relation of a fertile soil to a seed contained in 
it, there exists a resemblance : the real resemblance being in the two 
fundamenta relationis, in each of wliich there occurs a germ, producing 
by its development a multitude of other tilings similar to itself. And 
as, whenever two objects are jointly concerned in a phenomenon, this 
constitutes a relation between those objects ; so, if we suppose a second 
pair of objects concerned in a second phenomenon, the slightest resem- 
blance between the two phenomena is sufficient to admit of its being- 
said that the two relations resemble ; provided, of course, the points 
of resemblance are found in those portions of thp two phenomena 
respectively which are connoted by the relative names. 

While speaking of resemblance, it is necessary to take notice of an 
ambiguity of language, against which scarcely any one is sufficiently 
on his guard. Resemblance, when it exists in the highest degToe of 
all, amounting to undistinguishableness, is often called identity, and 
the two similar things are said to, be the same. I say often, not always ; 
for we do not say that two visible objects, two persons for instance, 
are the same, because they are. so much alike that one might be mis- 
taken for the other : but w^ constantly use thi$ mode of expression 
when speaking of feelings ; as when I "say that the sight of .any object 
gives me the ^^TTze sensation, or emotion to-day that it did yesterday, or 
the same which it gives to some other |)erson. This is -evidently an 



48 NAMES AND PROPOSITIONS. 

incorrect application of the word same ; for tlie feeling which I had 
yesterday is gone, never to return ; what I have to-day is another feel- 
ing, exactly like the former perhaps, but distinct from it; and it is 
evident that two different persons . cannot be experiencing the same 
feeling, in the sense in which we say that they are both sitting at the 
same table. By a similar ambiguity we say, that two persons are ill 
of the same, disease ; that two people hold the same office ; not in the 
sense in which we say that they are engaged in the same adventure, 
or sailing in the same ship, but in the sense that they fill offices exactly 
similar, though, perhaps, in distant places. Great confusion of ideas 
is often produced, and many fallacies engendered, in otherwise enlight- 
ened understandings, by not being sufficiently alive to the fact '^.in 
itself not always to be avoided), that they use the same name to -express 
ideas so different as those of identity and undistinguishable resemblance. 
Among modern writers. Archbishop Whately Stands almost alone in 
having drawn attention to this distinction, and to the ambiguity con- 
nected with it.* 

Several relations, generally called by other names, are teally cases 
of resemblance. As for example, equality; which is but another word 
for the exact resemblance commonly called identity, considered .as 
subsisting between things in respect of their quantity. And this ex- 
ample forms a suitable transition to the third and last of the three heads, 
under which, as already remarked, Attributes are commonly arranged. 

. ' V. Quantity. 

§ 12.,, Let us imagine two things, between which there is no differ- 
-ence (that is, no dissimilarity), except in quantity alone : for instance, 
a gallon of water, and more than a gallon of water. A gallon of water, 
like any other external object,, makes its presence known to us by g. 
set of sensations which it excites. Ten gallons of water are also an» 
external object, making its presence known to. us in a similar manner; 
dnd as we do not mistake ten gallons of water for a gallon of water, 

* " Same (as well as < One,' * Identical,' and other words derived from them) Is used fre- 
quently in a sense very different from its primary one, as applicable to a single object, being- 
employed to denote great similarity. When several objects are undistinguishably alike, one 
single description will apply equally, to any of them ; and thence they are said to be all of one 
and the same nature, appearance, &c., as, e.g., when we say ' this house is built of the same 
stone with such another,' we only mean that the stones are undistinguishable in their qual- 
ities ; not that the one buildrag was pulled down, and the other constructed with the ma-' 
terials. Whereas sameness, in the primary sense, does not even necessarily imply similar- 
ity'; for if we say of any man, that he is greatly altered since such a time, we understand, 
and, indeed, imply by the very expression, that he is one person, though different in several 
qualities. It is worth observing, also, that Same, in the secondary sense, admits, accord- 
ing to popular usage, of degrees. We speak of two things being nearly the same, but 
not entirely ; personal identity does not admit of degrees. Nothing, perhaps, has contribu- 
ted more to the error of Realism Ihan inattention to this ambiguity. When several persons 
are said to have One and the Sa7ne opinion, thought, or idea, men, overlooking the true simple 
statement of the case, which is, that they are all thinking, alike, look for something more 
abstruse and mystical, and imagine there must be some One Thing, in the primary sen§e, 
though not an individual, which is present at once -in the mind of each of these persons ; 
and thence readily sprung Plato's Theory of Ideas, each of which was, according to him, 
one real,. eternal object, existing entire and complete in each of the individual objects that 
are known by one name. . . . The Hindoos of the present day, from observing the similar 
symptoms which are known by the name of small-pox, and the communication of the like 
from one patient to another, do not merely call it (as we do) one disease, but believe (if we 
may credit the accounts given) that the small-pox is a goddess, who becomes incarnate in 
each infected patient." — Logic ; Appendix on Ambiguous Terms, p. 298. My references to 
this work are always to the first edition. 



THINGS DENOTED BY NAMES. 49 

it is plain that tlie set of sensations is more or less different in the two 
cases. In like manner, a gallon of water, and a gallon of Madeira, 
are two external objects, making their presence known by two sets of 
sensations, which sensations are different from each other. In the first 
case, however, we say that the difference is in quantity ; in the last 
there is a difference in quality, while the quantity of the water and of 
the Madeira is the same. What is the real distinction between the 
two cases ? It is not the province of Logic to analyze it ; nor to decide 
whether it is susceptible of analysis or not. For us the following con- 
siderations are sufficient. It is evident that- the sensations I receive 
from the gallon of water, and those I receive from the gallon of 
Madeira, are not the same, that is, not precisely alike ; neither are 
they altogether unlike: they are partly similar, partly dissimilar; and 
that in which they resemble is precisely that in which alone the gallon 
of water and the ten gallons do not resemble. That in which the 
gallon of w^ater and the gallon of wine are like each other, and in 
which the gallon and the ten gallons of water are unlike each other, is 
called their quantity. This likeness and unlikeness I do not pretend 
to explain, no more than any other kind of likeness or unlikeness. 
But my object is to show, that when we say of two things that they 
differ in quantity, just as when we say that they differ in quality, the 
Eissertion is always grounded upon a difference in the sensations which 
they excite. Nobody, I presume, will say, that to see, or to lift, or to 
drink, ten gallons of water, does not include in itself a different set of 
sensations from those of seeing, lifting, or drinking one gallon ; or that 
to see or handle a foot-rule, and to see or handle a yard-measure made 
exactly like it, are the same sensations. I do not undertake to say 
what the difference in the sensations is. Everybody knows, and 
nobody can tell ; no more than any one could tell what white is, to a 
person who had never had the sensation. But the difference, so far as 
cognizable by our faculties, lies in the sensations. Whatever difference 
we say there is in the things themselves, is, in this as in all other cases, 
grounded, and grounded exclusively, on a difference in the sensations 
excited by them. . 

VI. Attributes Concluded. 

§ 13. Thus, then, all the attributes of bodies which are classed under 
Quality or J^uantity, are grounded upon the sensations which we 
receive from those bodies, and may be defined, the powers which the 
bodies have of exciting those sensations. And the same general 
explanation has been found to apply to most of the attributes usually 
classed under the head of Relation. They, too, are gTounded upon 
some fact or phenomenon into which the related objects enter as parts ; 
that fact or phenomenon having no meaning and no existence to us, 
except the series of sensations or other states of consciousness by 
which it makes itself known : and the relation being simply the power 
or capacity which the object possesses, of taking part along with the 
coiTelated object in the production of that series of sensations or states 
of consciousness. We have been obliged, indeed, to recognize a 
somewhat different character in certain peculiar relations, those of 
succession and simultaneity, of likeness and unlikeness. These, not 
being grounded on any fact or phenomenon distinct fi'om the related 



50 NAMES AND PROPOSITIONS. 

objects themselves, do not admit of the same kind of analysis. But 
these relations, though not, like other relations, grounded upon states 
of consciousness, are themselves states of consciousness : resemblance 
is nothing but our feeling of resemblance ; succession is nothing but 
our feeling of succession. Or, if this be disputed, (and we cannot^ 
without transgi-essing the bounds of our science, discuss it here,) at 
least our knowledge of these relations, and even our possibility of 
knowledge, is confined to those which subsist between sensations or 
other states of consciousness : for, though we ascribe resemblance, or 
succession, or simultaneity, to objects and to attributes, it is always in 
virtue of resemblance or succession or simultaneity in the sensations 
or states of consciousness which those objects excite, and on which 
those attributes are grounded. 

§ 14. In the preceding investigation we have, for the sake of sim- 
plicity, considered bodies only, and omitted minds. But what we 
have said is applicable, mutatis mutandis^ to the latter. The attributes 
of minds, as well as those of bodies, are grounded upon states of feel- 
ing or consciousness. But in the case of a mind, we have to consider 
its own states, as well as those which it produces in other minds. 
Every attribute of a mind consists either in being itself affected in a 
certain way, or affecting other minds in a certain way. Considered 
in itself, we can predicate nothing of it, but the series of its own feel- 
ings. When we say of any mind, that it is devout, or superstitious, or 
meditative, or cheerful, we mean that the ideas, emotions, or volitions 
implied in those words, form a frequently recurring part of the series 
of feelings, or states of consciousness, which fill up the sentient exist- 
ence of that mind. 

In addition, however, to those 'attributes of a mind, which are 
grounded upon its own states of feeling, attributes may also be ascribed 
to it, in the same manner as to a body, grounded on the feelings which 
it excites in other minds. A mind does not, indeed, like a body, excite 
sensations, but it may excite thoughts or emotions. The most important 
example of attributes ascribed on this ground is, the employment of 
terms expressive of approbation or blame. When, for example, we 
say of any character, or (iii other words) of any mind, that it is 
admirable, we mean that the contemplation of it excites the sentiment 
of admiration ; and indeed somewhat more, for the word implies that 
we not only feel admiration, but approve that sentiment m ourselves. 
In some cases, under the semblance of a single attribute, two are 
really predicated : one of them, a state of the mind itself; the other, 
a state with which other minds are affected by thinking of it : as when 
we say of any one that he is generous. The word generosity ex- 
presses a "certain state of mind,, but being a term of praise, it also 
expresses that this state of mind excites in us another mental state, 
called approbation: The assertion made, therefore,- is two-fold, and 
of the following purport : Certain feelings form habitually a part of 
this person's sentient existence ; and, moreover, the idea of those feel- 
ings of his excites the sentiment of approbation in ourselves or others. 

As we thus ascribe attributes to minds on the ground of ideas and 
emotions, so may we to bodies on similar grounds, and not solely on 
the ground of sensations : as in speaking of the beauty of a statue ; 
since this attribute is gi'ounded upon the peculiar feeling of pleasure 



THINGS DENOTED BY NAMES. 51 

which the statue produces in our minds, and which is not a sensation, 
but an emotion. 

VII. General Result. 

§ 15. Our survey of the varieties of Things which have been, or 
which are capable of being, named — which have been, or are capable 
of being, either predicated of other Things, or made themselves the 
subject of predications — is now complete. 

Our enumeration commenced with Feelings. These we scrupulously 
distinguished from the objects which excite them, and from the organs 
by which they are, or may be supposed to be, conveyed. Feelings are 
of four sorts : Sensations, Thoughts, Emotions, and Volitions. What 
are called perceptions are merely a particular case of Belief, and be- 
lief is a kind of thought. Actions are merely volitions followed by an 
effect. If there be any other kind of mental state not included under 
these subdivisions, we did not think it necessary or proper in this place 
to discuss its existence, or the rank which ought to be assigned to it. 

After Feelings we proceeded to Substances. These are either 
■Bodies or Minds, Without entering into the gi'ounds of the meta- 
physical doubts which have been raised concerning the existence of 
Matter and Mind as objective realities, we stated as sufficient for us 
the conclusion in which the best thinkers are now very generally 
agreed, that all we can know of Matter is the sensations which it gives 
us, and the order of occurrence of those sensations ; and that while the 
substance Body is the unknown cause of our sensations, the substance 
Mind is the unknown percipient. 

The only remaining class of Nameable Things is Attributes ; and 
these are of three kinds. Quality, Relation, and Quantity, Qualities, 
like substances, are known to us no otherwise than by the sensations 
or other states of consciousness which they excite ; and while, in 
compliance with common usage, we have continued to speak of them 
as a distinct class of Things, we showed that in predicating them no 
one means to predicate anything but those sensations or states of 
consciousness, on which they may be said to be gi'ounded, and by 
which alone they can be defined. Relations, except the simple cases 
of likeness and unlikeness, succession and simultaneity, are similarly 
gTOunded upon some fact, or phenomenon, that is, upon some series of 
sensations or states of consciousness, more or less complicated. The 
third species of attribute. Quantity, is also manifestly grounded upon 
something in our sensations or states of feeling, since there is an indu- 
bitable difference in the sensations excited by a larger and a smaller 
bulk, or by a gi'eater or a less degi'ee of intensity, in any object of 
sense or of consciousness. All attributes, therefore, are to us nothing 
but either our sensations and other states of feeling, or something inex- 
tricably involved therein ; and to this even the peculiar and simple 
relations just adverted to are not exceptions. Those peculiar rela- 
tions, however, are so important, and, even if they might in strictness 
be classed among our states of consciousness, are so fundamentally 
distinct from any other of those states, that it would be a vain subtlety 
to confound them under that common head, and it is necessary that 
they should be classed apart. 

As the result, therefore, of our analysis, we obtain the following as 
an enumeration and classification of all Nameable Things : — 



52 NAMES AND PROPOSITIONS. 

1st. Feelings, or States of Consciousness. • . 

2nd. The Minds which experience those feehngs. 

3rd. The Bodies, or external objects, which excite certain of those 
feelings, together with the powers or properties whereby they excite 
them; these last being included rather in compliance with common 
opinion, and because their existence is taken -for gi-anted in the com- 
mon language from which I cannot prudently deviate, than because the 
recognition of such powers or properties as real existences appears to 
me warranted by a sound philosophy. 

4th, and last. The Successions and Co-existences, the Likenesses 
and Unlikenesses, between feelings or states of consciousness. Those 
relations, when considered as subsisting between other things, exist in 
reality only between the states of consciousness which those things, if 
bodies, excite, if minds, either excite or experience. 

This, until a better can be suggested, must serve us as a substitute 
for the abortive Classification of Existences, termed the Categories of 
Aristotle. The practical application of it will appear when we com- 
mence the inquiry into the Import of Propositions ; in other words, 
when we inquire what it is which the mind actually believes, when it 
gives what is called its assent to a proposition. 

These four classes comprising, if the classification be ccirrect, all 
Nameable Things, these or some of them must of course compos.e the 
signification of all names ; and of these or some of them is made up 
whatever we call a fact. 

For distinction's sake, every fact which is solely composed of feel- 
ings or states of consciousness considered as such, is often called a 
Psychological or Subjective fact ; while every fact which is composed, 
either wholly or in part, of something different from these, that is, of 
substances and attributes, is called an Objective fact. We may say, 
then, that every objective fact is grounded on a corresponding subjec- 
tive one; and has no meaning to us (apart from the subjective fact 
which corresponds to it)^ except as a name for the unknown and in- 
scrutable process by which that subjective or psychological fact is 
brought to pass. . - 



CHAPTER IV, ^ 

OF PROPOSITIONS. 

§ 1. In treating of Propositions, as already in treating of Names, 
some considerations of a comparatively elementary nature respecting 
their form and varieties must be premised, before entering upon that 
analysis of the import conveyed by them, which is the real subject and 
purpose of this preliminary book. 

A proposition, we have before said, is a portion of discourse in which 
a predicate is affirmed or denied of a subject. A predicate and a sub- 
ject are all that is necessarily required to make up a proposition : but 
as we cannot conclude from merely seeing two names put together, 
that they are a predicate and a subject, that is, that one of them is in- 
tended to be affirmed or denied of the other, it is necessary that there 



PROPOSITIONS. 53 

should be some mode or form of indicating that such is the intention ; 
some sign to distinguish a predication from any other kind of discourse. 
This is sometimes done by a shght alteration of one of the words, called 
an inflection; as when we say, Fire burns; the change of the second 
word from burn to burns showing that we mean to affirm the predicate 
burn of the subject fire. But this function is more commonly fulfilled 
by the word is, when an affiiTnation is intended; is not, when a nega- 
tion; or by some other part of the verb to be. The word which thus 
serves the pui*pose of a sign of predication is called, as we formerly 
observed, the copula. It is of the utmost importance that there should 
be no indistinctness in our conception of the nature and office of the 
copula; for confused notions respecting it are among the causes which 
have spread mysticism over the' field of logic, and perverted its specu- 
lations into logomachies. 

It is apt to be supposed that the copula is much more than a mere 
sign of predication ; that it also signifies existence. In the proposition, 
Socrates is just, it may seem to be implied not only that the quality 
just can be affirmed of Socrates, but moreover that Socrates is, that is 
to say, exists. This, however, only shows that there is an ambiguity in 
the word is; a word which not only performs the function of the copula 
in affirmations, but has also a meaning of its own, in virtue of which it 
may itself be made the predicate of a proposition. That the employ- 
ment of it as a copula does not necessarily include the affirmation of 
existence, appears from such a proposition as this, A centaur is a fiction 
of the poets ; where it cannot possibly be implied that a centaur exists, 
since the proposition itself expressly asserts that the thing has no real 
existence. 

Many volumes might be filled with the frivolous speculations con- 
ceming the nature of Being (to bv, ovola, Ens, Entitas, Essentia, and 
the like), which have arisen fi'om overlooking this double meaning of 
the words to be; from supposing that when it signifies to exist, and 
when it signifies to be some specified thing, as to be a man, to be Soc- 
rates, to be seen or spoken of, to be a phantom, even to be a nonentity, 
it must still, at bottom, answer to the same idea; and that a meaning 
must be found for it whichj^hall suit all these cases. The fog which 
rose fi'om this narrow spot diffused itself at an early period over the 
whole surface of metaphysics. Yet it becomes lis not to triumph over 
the gigantic intellects of Plato and Aristotle because we are now able 
to preserve ourselves from many errors into which they, perhaps inev- 
itably, fell. The fire-teaz-er of a modern steam-engine produces by his 
exertions far greater effects than Milo of Crotono could, but he is not 
therefore a stronger man. The Greeks seldom knew any langTiage 
but their own. This rendered it far more difficult for them than it is 
for us, to acquire a readiness in detecting ambiguities. One of the 
advantages of having systematically studied a plurality of languages, 
especially of those languages which philosophers have used as the 
vehicle of their thoughts, is -the practical lesson we learn respecting 
. the ambiguities of words, by finding that the same word in one language 
corresponds, on different occasions, to different words in another. 
Ik^Tien not thus exercised, even the strongest understandings find it 
difficult to believe that things which have a common name, have not in 
some respect or other a common nature; and often expend much labor 
not only unprofitably but mischievously (as was frequently done by 



54 NAMES AND PROPOSITIONS. 

the two philosophers just mentioned), on vain attempts to discover in 
what this common nature consists. But, the habit once formed, intel- 
lects much inferior are capable of detecting even ambiguities which 
are common to many languages : and it is surprising that the one now 
jmder consideration, though it exists in the modern languages as well 
as in the ancient, should have been overlooked by almost all authors. 
The quantity of futile speculation which had been caused by a mis- 
apprehension of the nature of the copula, was hinted at by Hobbes ; 
but Mr. Mill* was, I believe, the first who distinctly characterized the 
ambiguity, and pointed out how many errors in the received systems of 
philosophy it has had to answer for. It has indeed misled the modems 
scarcely less than the ancients, though their mistakes, because our un- 
derstandings are not yet so completely emancipated from their influ- 
ence, do not appear equally ridiculous. 

We shall now briefly review the principal distinctions which exist 
among propositions, and the technical terms most commonly in use to 
express those distinctions ' • 

§ 2. A proposition being a portion of discourse in which soniething 
is affirmed or denied of something, the first division of propositions is 
into affirmative and negative. An affirmative proposition is that in 
which the predicate is affirmed, of the subject ; as Caesar is dead. A 
negative proposition is that in which the predicate is denied of the 
subject; as, Caesar is not dead. The copula in this last species of 
proposition, consists of the words is not, which are the sign of negation ; 
is being the sign of affirmation. 

Some logicians, among whom may be mentioned Hobbes, state this 
distinction differently ; they recognize only one form of copula, is, and 
attach the negative sign to the predicate. " Caesar is dead," and 
" Caesar is not dead," according to these writers, are propositions 
agreeing not in the subject and predicate, but in the subject only. 
They do not consider " dead," but " not dead," to be the predicate of 
the second proposition, and they accordingly define a negative proposi- 
tion to be one in which the predicate is a negative name. The point, 
though not of much practical moment, desprves notice as an example 
(not unfrequent in logic) where by means of an apparent simplification, 
but which is merely verbal, matters are made more complex than before. 
The idea of these writers was, that they could get rid of the distinction 
between affirming and denying, by treating every case of denying as 
the affirming of a negative name. But what is meant by a negative 
name ? A name expressive of the absence of an attribute. So that 
when we affirm a negative name, what we are really predicating is 
absence and not presence : we are asserting not that anything is, but 
that something is not ; to express which operation no word seems so 
proper as the word denying. The fundamental distinction is between 
a fact and the non-existence of that fact ; between seeing something and 
not seeing it, between Caesar's being dead and his not being dead ; 
and if this were a merely verbal distinction, the generalization which 
brings both within the same form of assertion would be a real simpli- 
fication: the distinction, however, being real, and in the facts, it is 
the generalization confounding the distinction that is merely verbal; 

^Analysis of the Phenomena of the Human Mind, i 126 et seqq. 



PROPOSITIONS. 55 

and tends to obscure the subject, by treating the difference between 
two kinds of truths as if it were only a difference between two kinds of 
words. To put things together, and to put them or keep them asunder, 
will remain different operations, whatever tricks we may play with 
language. 

A remark of a similar nature may be applied to most of those dis- 
tinctions among propositions which are said to have reference to their 
modality : as, difference of tense or time ; the sun did rise, the sun is 
rising, the sun will rise. All these differences, like that between affirm- 
ation and negation, might be glossed over by considering the incident 
of time as a mere modification of the predicate : thus, The sun is an 
ohject having risen, The sun is an object now rising, The sun is an ohject 
to rise hereafter. But the simplification would be merely verbal. Past, 
present, or future, do not constitute so many different kinds of rising ; 
they are designations belonging to the event asserted, to the sun's rising 
to-day. They affect, not the predicate, but the applicability of the 
predicate to the particular subject. That which we affirm to be past, 
present, or future, is not what the subject signifies, nor what the pre- 
dicate signifies, but specifically and expressly what the predication 
signifies.; what "is expressed only by the proposition, as such, and not 
by either or both of the terms. Therefore the circumstance of time is ' 
properly considered as attaching to the copula, which is the sign of 
predication, and riot to the predicate. If the same cannot be said of 
such modifications as these, Caesar may be dead ; Caesar is perhaps 
dead ; It is possible that Caesai' is dead ; it is only because these fall 
altogether under another head, being properly assertions not of any- 
thing relating to the fact itself, but of the state of our owti mind in 
regard, to it; namely, our absence of disbelief of it. Thus, ''Caesar 
may be dead " means " I am not sure that Caesar is alive." 

§ 3. The next division of propositions is into Simple and Complex. 
A simple proposition is that in which one predicate is affirmed or 
denied of one subject. A complex proposition is that in which there 
is more than one predicate, or more than one subject, or both. 

At first sight this decision has the air of an absurdity ; a solemn dis- 
tinction of things into one and more than one ; as if we were to divide 
horses into single horses and teams of horses. And it is true that what 
is called a complex proposition is often not a proposition at all, but 
several propositions, held together by a conjunction. Such, for exam- 
ple, is this, Caesar is dead, and Brutus is alive : or even this,- Caesar is 
dead, but Brutus is alive. There are here two distinct assertions ; and 
we might as well call a street a complex house, as these two propo- 
sitions a complex proposition. It is true that the syncategorematic 
words and and but have a meaning, but that meaning is so far from 
making the two propositions one, that it adds a third proposition to 
them. All particles are abbreviations, and generally abbreviations of 
propositions ; a kind of short-hand, whereby that which, to be expressed 
fully, would have required a proposition or a series of propositions, is 
suggested to the mind at once. Thus the words, Caesar is dead and 
Brutus is alive, are equivalent to these : Caesar is dead ; Brutus is 
alive; it is my wish that the two preceding propositions should be 
thought of together. If the words were, Caesar is dead but Brutus is 
alive, the sense would be equivalent to the same three propositions 



56 N^MES AND PROPOSITIONS. 

together with a fourth; ''between the two preceding propositions 
there exists a contrast :" viz., either between the two facts themselves, 
or between the feehngs with which it is my wish that they should be 
regarded. 

In the instances cited, the two propositions are kept visibly distinct, 
each subject having its separate predicate, and each predicate its sepa- 
rate subject. For brevity, however, and to avoid repetition, the pro- 
positions are often blended together : as in this, *' Peter and James 
preached at Jerusalem and in Galilee," which contains four propo- 
sitions : Peter preached at Jerusalem, Peter preached in- Galilee, 
James preached at Jerusalem, James preached in Galilee. 

We have seen that when the two or more propositions comprising 
what is called a complex proposition, are stated absolutely, and not 
under any condition or proviso, it is not a proposition at all, but a plu- 
rality of propositions ; since what it expresses is not a single assertion, 
but several assertions, which, if true when joined, are true also when 
separated. But there is a kind of proposition which, although it con- 
tains a plurality of subjects and of predicates, and may be said in one 
sense of the word to consist of several propositions, contains but one 
assertion ; and its truth does not at all imply that of the simple propo- 
sitions which compose it. An example of this is, when the simple 
propositions are connected by the particle or ; as, either A is B or C 
is D ; or by the particle ^/'; as A is ^ if C is D. In the former case, 
the proposition is called disjunctive, in the latter conditional: the name 
Jiypothetical was originally common to both. As has been well 
remarked by Archbishop Whately and others,- the disjunctive form is 
resolvable into the conditional; every disjunctive proposition being 
equivalent to two or more conditional ones. " Either A is B or C is 
D," means, *' if A is not B, C is D ; and if C is not D, A is B." All 
hypothetical propositions, therefore, though disjunctive in form, are 
conditional in meaning; and the words hypothetical and conditional 
may be, as indeed they generally are, used synonymously. Propo- 
sitions in which the assertion is not dependent upon a condition, are 
said, in the language of logicians, to be categorical. 

An hypothetical proposition is not, like the pretended complex pro- 
positions which we previously considered, a mere aggregation of 
simple propositions. The simple propositions which form part of the 
words in which it is couched, form no part of the assertion which it 
conveys. When we say. If the Koran come& fi'om God, Mahomet is 
the prophet of God, We do not intend to affirm either that the Koran 
does come from God, or that Mahomet is really his prophet. Neither 
of these simple propositions may be true, and yet the truth of the 
hypothetical proposition may be indisputable. What is asserted is 
not the truth of either of the propositions, but the inferribility of the 
one from the other. What, then, is the subject, and what the predi- 
cate of the hypothetical proposition ] " The Koran " is not the subject 
of it, nor is " Mahomet :" for nothing is affirmed or denied either of 
the Koran or of Mahomet. The real subject of the predication is the 
entire proposition, " Mahomet is the prophet of God;" and the affirai- 
ation is, that this is a legitimate inference from the proposition, '' The 
Koran comes from God." The subject and predicate, therefore, of an 
hypothetical proposition are names of propositions. The subject is 
some one proposition. The predicate is a general relative name 



PROPOsiTioNa. 57 

applicable to propositions ; of this form — " an inference from so and 
so.". A fresh instance is here afforded of the remark, that all particles 
are abbreviations ; since "i/* A is B, C is D," is found to be an abbre- 
viation of the follovv^ing : " The proposition C is D, is a legitimate 
inference from the proposition A is B." 

The distinction, therefore, between hypothetical and categorical 
propositions is not so great as it at first appears. In the conditional, 
as w^ell as in the categorical form, one predicate is affirmed of one sub- 
ject, and no more : but a conditional proposition is a proposition con- 
cerning a proposition ; the subject of the assertion is itself an assertion. 
Nor is this a property peculiar to hypothetical propositions. There 
are other classes of assertions concerning propositions. Like other 
things, a proposition has attributes which may be predicated of it. 
The attribute predicated of it in an hypothetical proposition, is that 
of being an inference from a certain other proposition. But this is 
only one of many attributes that might be predicated. We may say. 
That the whole is greater than its part, is an axiom in mathematics : 
That the Holy Ghost proceeds from the Father alone, is a tenet of 
the Grreek Church : The doctrine of the divine right of kings was re- 
nounced by Parliament at the Revolution : The infallibility of the Pope 
has no countenance from Scripture. In all these cases the subject of 
the predication is an entire proposition. That which these different 
predicates are affirmed of, is the proposition, " the whole is greater 
than its part;" the proposition, ^^ the Holy Ghost proceeds from the 
Father alone:" the proposition, '' kings have a divine light;" the prop- 
osition, "the Pope is infallible." 

Seeing, then, that there is much less difference between hypotheti- 
cal propositions and any others, than one might be led to imagine 
from their form, we should be at a loss to account for the conspicuous 
position which they have been selected to fill in treatises on Logic, if 
we did not remember that what they predicate of a proposition, namely, 
its being an inference from something else, is precisely tlmt one of its 
attributes with which most of all a logician is concerned. 

§ 4. The next of the common divisions of Propositions is into Uni- 
versal, Particular, Indefinite, and Singular : a distinction founded 
upon the degi'ee of generality in which the name, which is the subject 
of Xhe proposition, is to be understood. The following are examples: 

Ml men are mortal — Universal. 

Some men are mortal— - Particular. 

Man is mortal — • ' Indefinite. 

Julius CcBsar is mortal — Singular. 

The proposition is Singular, when the subject is an individual name. 
The individual name needs not be a proper name. *' The Founder of 
Christianity was crucified," is as much a singular proposition as 
" Christ was crucified." 

When the name, which is the subject of the proposition, is a general 
name, we may intend to affirm or deny the predicate, either of all the 
things that the subject denotes, or only of some. When the predicate 
is affirmed or denied of all and each of the things denoted by the sub- 
ject, the proposition is universal ; when of some non-assignable portion 
of them only, it is particular. Thus, All men are mortal ; Every man 
is mortal ; are universal propositions. No man is immortal, is also an 
H 



58 NAMES AND PROPOSITIONS. 

universal proposition, since the predicate, immortal, is denied of each 
and every individual denoted by the term man ; the negative propo- 
sition being exactly equivalent to the following, Every man is not-im- 
mortal. But "some men are wise," ''some men are not wise," are 
particular propositions ; the predicate wise being in the one ease 
affirmed and in the other denied not of each and every individual de- 
noted by the term man, but only of each and every one of some por- 
tion of those individuals, without specifying what portion ; for if this 
were specified, the proposition would be changed either into a singu- 
lar proposition, or into an universal proposition with a different subject; 
as, for instance, " all instructed men are wise." There are other forms 
of particular propositions: as, '' Most tdlQh are incapable of self-govern- 
ment :" it being immaterial how large a portion of the subject the 
predicate is asserted of, as long as it is left uncertain how that portion 
is to be distinguished from the rest. 

When the form of the expression does not clearly show whether the 
general name which is the subject of the proposition is meant to stand 
for all the individuals denoted by it, or only for some of them, the 
proposition is commonly called Indefinite ; but this, as Archbishop 
Whately observes, is a solecism, of the same nature as that committed 
by some grammarians when in their list of genders they enumerate the 
doubtful gender. The speaker must mean to assert the proposition 
either as an universal or as a particular proposition, though he has 
failed to declare which : and it often happens that though the words 
do not show which of the two he intends, the context, or the custom 
of speech, supplies the deficiency. Thus, when it is affirmed that 
" Man is mortal," nobody doubts that the assertion is intended of all 
human beings, and the word indicative of universality is commonly 
omitted only because the meaning is evident without it. 

When a general name stands for each and every individual which it 
is a name of, or in other words, which it denotes, it is said by logicians 
to be distributed, or taken distributively. Thus, in the proposition, 
All men are mortal, the subject, Man, is distributed, because mortality 
is affirmed of each and every man. The predicate Mortal, is not dis- 
tributed, because the only mortals who are spoken of in the proposition 
are those who happen to be men ; while the word may, for aught that 
appears (and in fact does), comprehend under it an indefinite number 
of objects besides men. In the proposition, Some men are mortal, 
both the predicate and the subject are undistributed. In the following, 
No men are perfect, both the predicate and subject are distributed. 
Not only is the attribute perfection denied of the entire class Man, 
but that class is severed and cast out from the whole of the class Per- 
fect, and not merely from some part of that class. 

This phraseology, which is of great service in stating and demon- 
strating the rules of the syllogism, enables us to express very con- 
cisely the definitions of an universal and a particular proposition. An 
universal proposition is that of which the subject is distributed ; a par- 
ticular proposition is that of which the subject is undistributed. 

There are many more distinctions among propositions than those we 
have here stated, some of them of considerable importance. But, for 
explaining and illustrating these, more suitablaopportunities vnll occur 
in the sequel. 



IMPORT OF PROPOSITIONS. 59 

CHAPTER V. 

OF THE IMPORT OF PROPOSITIONS. 

§ 1, An inquiry into the nature of Propositions must have one of 
two objects : to analyze the state of mind called Belief, or to analyze 
what is believed. All language recognizes a difference between a doc- 
trine or opinion, and the act of entertaining the opinion ; between as- 
sent, and what is assented to. 

Logic, according to the conception here formed of it, has no con- 
cern with the nature of the act of judging or believing; the considera- 
tion of that act, as a phenomenon of the mind, belongs to another 
science. Philosophers, however, from Descartes downwards, and es- 
pecially from the era of Leibnitz and Locke, have by no means ob- 
served this distinction ; and would have treated with great disrespect 
any attempt to analyze the import of Propositions, unless founded 
upon an analysis of the act of Judgment. A Proposition, they would 
have said, is but the expression in words of a Judgment, The thing 
expressed, not the mere verbal expression, is the important matter. 
When the mind assents to a proposition, it judges. Let us find out 
what the mind does when it judges, and we shall know what proposi- 
tions mean, and not otherwise. 

Conformably to these \4ews, almost all the writers on Logic in the 
last two centuries, whether English, German, or French, have made 
their theory of Propositions, from one end to the other, a theory of 
Judgments. They considered a Proposition, or a Judgment, for they 
used the two words indiscriminately, to consist in affirming or denying 
one idea of another. To judge, was to put two ideas together, or to 
bring one idea under another, or to compare two ideas, or to perceive 
the agreement or disagreement between two ideas : and the whole 
doctrine of Propositions, together with the theory of Reasoning (always 
necessarily founded upon the theory of Propositions), was stated as if 
Ideas, or Conceptions, or whatever other term the writer preferred as 
a name for mental representations generally," constituted essentially the 
subject matter and substance of those operations. 

It is, of course, true, that in any case of judgment, as for instance 
when we judge that gold is yellow, a process takes place in our minds 
of which some one or other of these theories is a partially correct ac- 
count. We must have the idea of gold and the idea of yellow, and 
these two ideas must be brought together in ■ our mind. But in the 
first place, it is evident that this is only a part of what takes place ; for 
we may put two ideas together without any act of belief ; as when we 
merely imagine something, such as a golden mountain ; or when we 
actually disbelieve : for in order even to disbelieve that Mahomet was 
an apostle of God, we must put the idea of Mahomet and that of an 
apostle of God together. To determine what it is that happens in the 
case of assent or dissent besides putting two ideas together, is one of 
the most intricate of metaphysical problems. Bat whatever the solu- 
tion may be, we may venture to assert that it can have nothing what 
ever to do ^vith the import of propositions ; for this reason, that propo- 
sitions (except where the mind itself is the subject treated of) are not 
assertions respecting our ideas of things, but assertions respecting the 



60 NAMES AND PROPOSITIONS. 

things tliemselves. In order to believe tlmt gold is yellow, I must, 
indeed, have the idea of gold and the idea of yellow, and something 
having reference to those ideas must take place in my mind ; but my 
belief has not reference to the ideas, it has reference to the things. 
What I believe is a fact relating to the outward thing, gold, and to the 
impression made by that outward thing upon the human organs ; not 
a fact relating to my conception of gold, which would be a fact in my 
mental history, not a fact of external nature. It is true, that in order to 
believe this fact in external nature, another fact must take place in my 
mind, a process must be performed upon my ideas ; but so it must in 
everything else that I do. I cannot dig the ground unless I have the 
idea of the ground, and of a spade, and of all the other things I am 
operating upon, and unless I put those ideas together. But it would 
be a very ridiculous description of digging the ground to say that it is 
putting one idea into another. Digging is an operation which is per- 
formed upon the things themselves, although it cannot be performed 
unless I have in my mind the ideas of them. And so in like manner, 
believing is an act which has for its subject the facts themselves, 
although a previous mental conception of the facts is an indispensable 
condition. • When I say that fire causes heat, do I mean that my idea 
of fire causes my idea of heat] No: I mean that the natural pheno- 
menon, fire, causes the natural phenomenon, heat. When I mean to 
assert anything respecting the ideas, I give them their proper name, I 
call them ideas : as when I say, that a child's idea of a battle is unlike 
the reality, or that the ideas entertained of the Deity have a great 
effect on the characters of mankind. 

The notion that what is of primary importance to the logician in a 
proposition, is the relation between the two ideas corresponding to 
the subject and predicate (instead of the relation between the two 
'phenomena which they respectively express), seems to me one of the 
most fatal errors ever introduced into the philosophy of L ogic ; and 
the principal cause why the theory of the science has made such incon- 
siderable progress during the last two centuries. The treatises on 
Logic, and on the branches of Mental Philosophy connected with 
Logic, which have been produced since the intrusion of this cardinal 
eiTor, though sometimes written by men of extraordinary abilities and 
attainments, almost always tacitly imply a theory that the investigation 
of truth consists in contemplating and handling our ideas, or concep- 
tions of things, instead of the things themselves : a process by which, 
I will venture to affirm, not a single truth ever was arrived at, except 
truths of psychology, a science of which Ideas or Conceptions are 
avowedly (along with other mental phenomena) the subject-matter. 
Meanwhile, inquiries into every kind of natural jDhenomena were 
incessantly establishing great and fruitful truths on the most important 
subjects, by processes upon which these views of the nature of Judg- 
ment and Reasoning threw no light, and in which they afforded no 
assistance whatever. No wonder that those who knew by practical 
experience how truths are come at, should deem a science futile, which 
consisted chiefly of such speculations. What has been done for the 
advancement of Logic since these doctrines came into vogue, has been 
done not- by professed logicians, but by discoverers in the other sci- 
ences ; in whose methods of investigation many great principles of 
logic, not previously thought of, have successively come forth into light, 



IMPORT OF PROPOSITIONS. 61 

but 'Who have generally committed the error of supposing that nothing 
whatever was known of the art of philosophizing by the old logicians, 
because their modern interpreters have written to so little purpose 
respecting it. 

We have to inquire, then, on the present occasion, not into Judg- 
ment, but judgments ; not into the act of believing, but into the thing 
believed. What is the immediate object of belief in a Proposition 1 
What is the matter of fact signified by it 1 Wliat is it to wHch, when 
I assert the proposition, I give my assent, and call upon others to give 
theirs 1 What is that which is expressed by the form of discourse 
Called a Proposition, and the conformity of which to fact constitutes 
the truth of the proposition 1 ^ 

§ 2. One of the clearest and most consecutive thinkers whom this 
country or the world has produced, I mean Hobbes, has given the fol- 
lowing answer to this question. In every proposition (says he), what 
is signified is, the beUef of the speaker that the predicate is a name of 
the same thing of which the subject is a name ; and if it really is so, 
the proposition is true. Thus the proposition, All men are living be- 
ings (he would say), is true, because living being is a name of every- 
thing of which 7na?i is a name., All men are six feet high is not true, 
because six feet high is not a name of everything (though it is of some 
things) of which W(2?^ is a name. 

What is stated by Hobbes as the definition of a true proposition, 
must be allowed to be a property which all true propositions possess. 
The subject and predicate being both of them names of things, if they 
were names of quite different things the one name could not, consist- 
ently with its signification, be predicated of the other. If it be true 
that some men are copper-colored, it must be true- — and the proposi- 
tion does really assert — that among the individuals denoted by the 
name man, there are some who are also among those denoted by the 
name copper-colored. If it be true that all oxen ruminate, it must 
be true that all the individuals denoted by the name ox are also among 
those denoted by the name ruminating ; and whoever asserts that all 
oxen ruminate, undoubtedly does assert that this relation subsists be- 
tween the two names. 

The assertion, therefore, which, according to Hobbes, is the only 
one made in any proposition, really is made in every proposition : and 
his analysis has consequently one of the requisites for being the true 
one.. We may go a step further ; it is the only analysis that is rigor- 
ously true of all propositions without exception. What he gives as 
the meaning of propositions, is part of the meaning of all propositions, 
and the whole meaning of some. This, however, only shows what an 
extremely minute fragment of meaning it is quite possible to include 
within the logical fonnula of a proposition. It does not show that no 
proposition means more. To warrant us in putting together two words 
with a copula between them, it is really enough that the thing or things 
denoted by one of the names should be capable, without violation of 
usage, of being called by the other name also. If then this be all the 
meaning necessarily implied in the form of discourse called a Proposi- 
tion, why do I object to it as the scientific definition of what a propo- 
sition means % Because, though the mere collocation which makes the 
proposition a proposition, conveys no more meaning than Hobbes con- 



62 NAMES AND PROPOSITIONS. 

tends for, that same collocation combined with other circumstances, 
thsljbrm combined with other matter, does convey more, and much 
more. 

The only propositions of which Hobbes' principle is a sufficient ac- 
count, are that limited and unimportant class in which both the predi- 
cate and the subject are proper names. For, as has already been 
remarked, proper names have strictly no meaning; they are mere 
niarks for individual objects: and when a proper name is predi- 
cated of another proper name, all the signification conveyed is, that 
both the names are marks for the same object. But this is precisely 
what Hobbes produces as a theory of predication in general. His 
doctrine is a full explanation of such predications as these : Hyde was 
Clarendon, or, Tully is Cicero. It exhausts the meaning of those 
propositions. But it is a sadly inadequate theory of any others. That 
it should ever have been thought of as such, can be accounted for only 
by the fact, that Hobbes, in common with the other Nominalists, be- 
stowed little or no attention upon the connotation of words ; and sought 
for their meaning exclusively in what they denote : as if all names had 
been (what none but proper names really are) marks put upon indi- 
viduals ; and as if there were no difference between a proper and a 
general name, except that the first denotes only one individual, and the 
last a greater number. 

It has been seen, however, that the meaning of all names, except 
proper names and that portion of the class of abstract names which are 
not connotative, resides in the connotation. When, therefore, we are 
analyzing the meaning of any proposition in which the predicate and 
the subject, or either of them, are connotative names, it is to the con- 
notation of those terms that v^e muSw exclusively look^ and not to what 
they denote, or in the language of Hobbes (language so far correct) are 
names of 

In asserting that the truth of a proposition depends upon the con- 
' formity of import between its terms, as, for instance, that the proposi- 
tion, Socrates is wise, is a true proposition, because Socrates and wise 
are names applicable to, or, as he expresses it, names of the same per- 
son ; it is very remarkable that so powerful a thinker should not have 
asked himself the question. But how came they to be names of the same 
person? Surely not because such was the intention of those who in- 
vented the words. When mankind fixed the meaning of the word 
wise, they were not thinking of Socrates, nor when his parents gave 
him the name Socrates, were they thinking of wisdom. The names 
happen to fit the same person because of a certain y<zc^^, which fact was 
not known, nor in being, when the names were invented. If we want 
to know what the fact is, we shall find the clue to it in the connotation 
of the names. 

A bird, or a stone, a man, or a wise man, means simply, an object 
having such and such attributes. The real meaning of the word man, 
is those attributes, and not John, Peter, Thomas, &c. The word 
mortal, in like manner connotes a certain attribute or attributes ; and 
when we say, All men are mortal, the meaning of the proposition is, 
that all beings which possess the one set of attributes, possess also the 
other. If, in our experience, the attributes connoted by man are 
always accompanied by the attribute connoted by mortal, it will follow 
as a consequence, that the class man will be wholly included in the 



IMPORT OF PROPOSITIONS. 63 

class mortal, and that mortal will be a name of all things of which man 
is a name ; but why 1 Those objects are brought under the name, by 
possessing the attributes connoted by it : but their possession of the 
attributes is the real condition on which the truth of the proposition 
depends ; not their being called by the name. Connotative names do 
not precede, but follow, the attributes which they connote. If one 
attribute happens to be always found in conjunction with another 
attribute, the concrete names which answer to those attributes will of 
course be predicable of the same subjects, and may be said, in Hobbes' 
language (in the propriety of which on this occasion I fully concur), to 
be two names for the same things. But the possibility of a concurrent 
application of the two names, is a mere consequence of the conjunction 
between the two attributes, and was, in most cases, never thought of 
when the names were invented and their signification fixed. That the 
diamond is combustible, was a proposition certainly not dreamed of 
when the words Diamond and Combustible received their present 
meaning ; and could not have been discovered by the most ingenious 
and refined analysis of the signification of those words. It was found 
out by a very different process, namely, by exerting the five senses, 
and learning from them, that the attribute of combustibility existed in 
all those diamonds upon which the experiment w^as tried ; these being 
so numerous, and the circumstances of the experiments such, that what 
was true of those individuals might be concluded to be true of all sub- 
stances " coming within the name," that is, of all substances possessing 
the attributes which the name connotes. The assertion, therefore, 
when analyzed, is, that wherever we find certain attributes, there will 
be found a certain other attribute : which is not a question of the sig- 
nification of names, but of the laws of nature ; the order existing among 
phenomena. 

§ 3. Although Hobbes' theory of Predication has not, in the terms 
in which he stated it, met with a very favorable reception from philos- 
ophers, a theory virtually identical wdth it, and not by any means so 
perspicuously expressed, may almost be said to have taken the rank of 
an established opinion. The most generally received notion of Predi- 
cation decidedly is, that it consists in referring something to a class, i. e., 
either placing an individual under a class, or placing one class under 
another class. Thus, the proposition, Man is mortal, asserts, according 
to this view of it, that the class man is included in the class mortal. 
" Plato is a philosopher," asserts that the individual Plato is one of 
those who compose the class philosopher. If the proposition is nega- , 
tive, then instead of placing something in a class, it is said to exclude 
something from a class. Thus, if the following be the proposition, 
The elephant is not carnivorous ; what is asserted (according to this 
theory) is, that the elephant is excluded from the class carnivorous, or 
is not numbered among the things comprising that class. There is no 
real difference except in language, between this theory of Predication 
and the theory of Hobbes. For a class is absolutely nothing but an 
indefinite number of individuals denoted by a general name. The 
name given to them in common, is w^hat makes them a class. To refer 
anything to a class, therefore, is to look upon it as one of the things 
which are to be called by that common name. To exclude it from a 
class, is to say that the common name is not applicable to it. 



64 NAMES AND PROPOSITIONS. 

How widely these views of predication have prevailed, is evident 
from this, that they are the basis of the celebrated Dictum de omni et 
nullo. When the syllogism is resolved, by all who treat of it, into an 
inference that w;hat is true of a class is true of all things whatever that 
belong to the class ; and when this is laid down by almost all professed 
logicians as the ultimate principle to which all reasoning owes its 
validity; it is clear that in the general estimation of logicians, the 
propositions of which reasonings are composed can be the expression 
of nothing but the process of dividing things into classes, and referring 
everything to its proper class. 

This theory appears to me a signal example of a logical error very 
often committed in logic, that of vorepov nporepov, or explaining a 
thing by something which presupposes it. When I say that snow is 
white, I may and ought to be thinking of snow as a class, because I 
am asserting a proposition as true of all snow : but I am certainly not 
thinking of white objects as a class ; I am thinking of no white object 
whatever except snow, but only of that, and of the sensation of white 
which it gives me. When, indeed, I have judged, or assented to the 
propositions, that snow is white, and that several other things also are 
white, I gradually begin to think of white objects as a class, including 
snow and those other things. But this is a conception which followed, 
not preceded, those judgments, and therefore cannot be given as an 
explanation of them. Instead of explaining the effect by the cause, 
this doctrine explains the cause by the effect, and is, I conceive, founded 
upon a latent misconception of the nature of classification. 

There is a sort of language very generally prevalent in these dis- 
cussions, which seems to suppose that classification is an arrangement 
and grouping of definite and known individuals : that when names 
were imposed, mankind took into consideration all the individual ob- 
jects in the universe, made them up into parcels or lists, and gave to 
the objects of each list a common name, repeating this operation toiies 
quoties until they had invented all the general names of which language 
consists ; which having been once done, if a question subsequently 
arises whether a certain general name can be truly predicated of a 
certain particular object, we have only (as it were) to read the roll of 
the objects upon which that name was conferred, and see whether the 
object about which the question arises, is to be found among them. 
The framers of language (it would seem to be supposed) have prede- 
termined all the objects that are to compose each class, and we have 
only to refer to the record of an antecedent decision. 
, So absurd a doctrine will be owned by nobody when thus nakedly 
stated ; but if the commonly received explanations of classification and 
naming do not imply this theory, it requires to be shown how they ad- 
mit of being reconciled with any other. 

General names are not marks put upon definite objects ; classes are 
not made by drawing a line round a given number of assignable indi- 
viduals. The objects which compose any given class are perpetually 
fluctuating. We may frame a class without knowing the individuals, 
or even any of the individuals, of which it will be composed : we may 
do so while believing that no such individuals exist. If by the meaning 
of a general name are to be understood the things which it is the name 
of, no general name, except by accident, has a fixed meaning at all, or 
ever long retains the same meaning. The only mode in which any 



IMPORT OF PROPOSITIONS. 65 

general name lias a definite meaning, is by being a name of an indefi- 
nite variety of things, namely, of all things, known or unknown, past, 
present, or future, which possess certain definite attributes. When, 
by studying not the meaning of words, but the phenomena of nature, 
we discover that these attributes are possessed by some object not pre- 
viously known to possess them, (as when chemists found that the dia- 
mond was combustible), we include this new object in the class ; but 
it did not already belong to the class. We place the individual in the 
class because the proposition is true ; the proposition is not true be- 
cause the object is placed in the class. 

It will appear hereafter in treating of reasoning, how much the 
theory of that intellectual process has been vitiated by the influence 
of these erroneous views, and by the habit which they exemplify of 
assimilating all the operations of the human understanding which have 
truth for their object, to processes of mere classification and naming. 
Unfortunately, the minds which have been entangled in this net are 
precisely those which have escaped the other cardinal error commented 
upon in the beginning of the present chapter. Since the revolution 
which dislodged Aristotle from the schools, logicians may almost be 
divided into those who have looked upon reasoning as essentially an 
affair of Ideas, and those who have looked upon it as essentially an 
affair of Names. 

One thing it is but just to remark. Although Hobbes' theory of 
Predication, according to the well known remark of Leibnitz, and the 
avowal of Hobbes himself,* renders truth and falsity completely arbi- 
trary, with no standard but the will of men, it must not be concluded 
that either Hobbes, or any of the other philosophers who have in the 
main agreed with him, did, in fact, consider the distinction between 
truth and eri'or as less real, or attached one jot less of importance to it, 
than other people. To suppose that they did so would argue total 
unacquaintance with their other speculations. But this shows how- 
little hold their doctrine possessed over their own minds. No person 
at bottom ever imagined that there was nothing more in truth than 
propriety of expression ; than using language in conformity to a pre- 
vious convention. With whatever illusions even profound thinkers 
may have satisfied themselves when engaged in finding a general solu- 
tion for a metaphysical problem ; when they came to the practical ap- 
plication of their doctrines, they were always prepared with some 
means of explaining the solution away. When the inquiry was 
brought down from generals to a particular case, it has always been 
acknowledged that there is a distinction between verbal and real ques- 
tions ; that some false propositions are uttered from ignorance of the 
meaning of words, but that in others the source of the eiTor is a mis- 
apprehension of things ; that a person who has not the use of language 
at all may form propositions mentally, and that they may be untrue, 
that is, he may believe as matters of fact what are not really so. This 
last admission cannot be made in stronger terms than it is by Hobbes 
himself ;t though he will not allow such erroneous belief to be called 

* " From hence also this may be deduced, that the first truths were arbitrarily made by 
those that first of all imposed names upon things, or received them from the imposition of 
others. For it is true (for example) that mmi is a living creature, but it is for this reason, 
that it pleased men to impose both these names on the same thing." — Computation or Logic, 
ch. iii., sect. 8. 

t " Men are subject to err not only in affirming and denying, but also in perception, and. 



66 NAMES AND PROPOSITIONS. 

falsity, but only error. And, moreover, he has himself laid dov/n, in 
other places, doctrines in which the true theory of predication is by 
implication contained. He distinctly says that general names are given 
to things on account of their attributes, and that abstract names are the 
names of those attributes. " Abstract is that which in any subject de- 
notes the cause of the concrete name And these causes of names 

are the same with the causes of our conceptions, namely, some power 
of action, or affection, of the thing conceived, which some call the man- 
ner by which anything works upon our senses, but by most men they 
are called accidents.^'* It is strange that having gone so far, he should 
not have gone one step farther, and seen that what he calls the cause 
of the concrete name, is in reality the meaning of it ; and that when we 
predicate of any subject a name which is given because of an attribute 
(or, as ho calls it, an accident), our object is not to affirm the name, but^ 
by means of the name, to affirm the attribute. 

§ 4. Let the predicate be, as we have said, a connotative term; and 
to take the simplest case first, let the subject be a proper name: ''The 
summit of Chimborazo is white." The word white connotes an attri- 
bute which is possessed by the individual object designated by the 
words, " summit of Chimborazo," which attribute consists in the phys- 
ical fact of its exciting in human beings the sensation which we call a 
sensation of white. It will be admitted that, by asserting the propo- 
sition, we wish to communicate information of that physical fact, and 
are not thinking of the names, except as the necessary means of ma- 
king that communication. The meaning of the proposition, therefore, 
is, that the individual thing denoted by the subject, has the attributes 
connoted by the predicate. 

If we now suppose the subject also to be a connotative name, the 
meaning expressed by the proposition has advanced a step further in 
complication. Let us first suppose the proposition to be universal, as 
well as affirmative : " All men are mortal." In this case, as in the 
last, what the proposition asserts (or expresses a belief in), is, ot 
course, that tlie objects denoted by the subject (man) possess the 
attributes connoted by the predicate (mortal). But the characteristic 
of this case is, that the objects are no longer individually designated. 
They are pointed out only by some of their attributes : they are the 
objects called men, that is, the beings possessing the attributes con- 
noted by the name man ; and the only thing known of them may be 
those attributes : indeed, as the proposition is general, and the objects 
denoted by the subject are therefore indefinite in number, most of them 
are not known individually at all. The assertion, therefore, is not, as 
before, that the attributes which the predicate connotes are possessed 
^y ^^y given individual, or by any number of individuals previously 
known as John, Thomas, Richard, &c., but that those attributes are 
possessed by each and every individual possessing certain other attri- 

in silent cogitation Tacit errors, or the errors of sense and cogitation, are made by 

passing from one imagination to the imagination of another different thing; or by feigning 
that to be past, or future, which never was, nor ever shall be; as when, by seeing the ijn- 
age of the sun in water, we imagine the sun itself to be there ; or by seeing swords, that 
there has been, or shall be, fighting, because it uses to be so for the most part; or 
when from promises we feign the rnind of the promisor to be such and such ; or, lastly, 
when from any sign we vainly imagine something to be signified vvhich is not. And errors 
of this sort are common to all .things that have sense." — Computation or Logic, ch. v., sect. 1. 
* lb., ch. iii., sect. 3. 



IMPORT OF PROPOSITIONS. 67 

butes ; that whatever has the attributes connoted by the suDJect, has 
also those connoted by the predicate ; that the latter set of attributes 
constantly accompany the former set. Wliatever has the attributes of 
man has the attribute of mortality ; mortality constantly accompanies 
the attributes of man. 

If it be remembered that every attribute is grounded upon some fact 
or phenomenon, either of outw^ai-d sense or of inward consciousness, 
and that to possess an atti'lbute is another phrase for being the cause 
of, or forming part of, the fact or phenomenon upon which the attribute 
is grounded ; we may add one more step to complete the analysis. 
The proposition which asserts that one attribute always accompanies 
another attribute, does really assert thereby no other thing than this, 
that one phenomenon always accompanies another phenomenon ; inso- 
much that where we find the one, we have assurance of the existence 
of the other. Thus, in the proposition, All men are mortal, the word 
man connotes the attributes which we ascribe to a certain kind of living 
creatures, on the ground of certain phenomena which they exhibit, 
and which are partly physical phenomena, namely the impressions 
made on our senses by their bodily form and structure, and partly 
mental phenomena, namely the sentient and intellectual life which they 
have of their own. All this is understood when we utter the word 
man, by any one to whom the meaning of the word is kno\vn. Now, 
when we say, Man is mortal, we mean that wherever these various 
physical and mental phenomena are all found, there we have assurance 
that the other physical and mental phenomenon, called death, will not fail 
to take place. The proposition does not affirm toJien ; for the connota- 
tion of the word mortal goes no further than to the occurrence of the phe- 
nomenon at some time or other, leaving the precise time undecided. 

§ 5. We have already proceeded far enough not only to demonstrate 
the eiTor of Hobbes, but to ascertain the real import of by far the 
most numerous class of propositions. The object of belief in a propo- 
sition, when it asserts anything more than the meaning of words, is 
generally, as in the cases which we have examined, either the coexist- 
ence or the sequence of two phenomena. At the very commencement 
of our inquiry, we found that every act oi belief implied two Things ; 
we have now ascertained what, in the most frequent case, these two 
things are, namely two Phenomena, in other words, two states of 
consciousness ; and what it is whicii tlie proposition affirms (or denies) 
to subsist between them, namely either succession, or coexistence. 
And this case includes innumerable instances which no one, previous 
to reflection, would think of referring to it. Take the following 
example : A generous person is worthy of honor. Wlio would expect 
to recognize here a case of coexistence between phenomena % But so 
it is. The attribute which causes a person to be termed generous, is 
ascribed to him on the gi'ound of states of his mind, and particulars of 
his conduct: both are phenomena; the former are facts of internal 
consciousness, the latter, so far as distinct from the former, are physical 
facts, or perceptions of the senses. Worthy of honor, admits of a 
similar analysis. Honor, as here used, means a state of approving 
and admiring emotion, followed upon occasion by corresponding out- 
ward acts. " Worthy of honor" connotes all this, together with our 
approval of the act of showing honor. All these are phenomena j 



68 NAMES AND PROPOSITIONS. 

States of internal consciousness, accompanied or followed by physical 
facts. AVlien we say, A generous person is worthy of honor, we affirm 
coexistence between the two complicated phenomena connoted by the 
two terms respectively. We affirm, that wherever and whenever the 
inward feelings and outward facts implied in the word generosity, 
have place, then and there the existence and manifestation of an inward 
feelino-, honor, would be followed in our minds by another inward 
feeling, approval. 

After the analysis in a former chapter of the import of names, many 
examples are not needed to illustrate the import of propositions. 
When there is any obscurity or difficulty, it does not lie in the mean- 
ing of the proposition, but in the meaning of the names which compose 
it ; in the complicated nature of the connotation of many words ; the 
immense multitude and prolonged series of facts which often constitute 
the phenomenon connoted by a name. But where it is seen what the 
phenomenon is, there is seldom any difficulty in seeing that the asser- 
tion conveyed by the proposition is, the coexistence of one such 
jDhenomenon with another ; or the succession of one such phenomenon 
to another : their covjunction, in short, so that where the one is found, 
we may calculate on finding both. 

This, however, though the most common, is not the only meaning 
which propositions are ever intended to convey. In the first place, 
sequences and coexistences are not only asserted respecting Phe- 
nomena ; we make propositions also respecting those hidden causes of 
phenomena which ai'e named substances and attributes. A substance, 
however, being to us nothing but either that which causes, or that 
which is conscious of, phenomena ; and the same being true, mutatis 
viutandis, of attributes ; no assertion can be made, at least with a 
meaning, concerning these unknown and unknowable entities, (beyond 
their mere existence), except in virtue of the Phenomena by which 
alone they manifest themselves to our faculties. When we say, Socrates 
was contemporary with the Peloponnesian war, the foundation of this 
assertion, as of all assertions concerning substances, is an assertion 
concerning the phenomena which they exhibit, — namely, that the series 
of facts by which Socrates manifested himself to mankind, and the 
series of mental states which constituted his earthly existence, went 
on simultaneously with the series of facts known by the name of the 
Peloponnesian war. ^ Still, the proposition does not assert that alone ; 
it asserts that the Thing in itself, the noumenon Socrates, was existing, 
and doing or experiencing those various facts, during the same time. 
Coexistence and sequence, therefore, may be affirmed or denied not 
only between phenomena, but between noumena, or between a noume- 
non and phenomena. And there is one kind of assertion which may 
be made respecting noumena, independently of the phenomena which 
are their sensible manifestation ; the assertion of their simple exist- 
ence. But what is a noumenon 1 an unknown cause. In affiiTning, 
therefore, the existence of a noumenon, we affirm causation. Here, 
therefore, arc two additional kinds of fact, capable of being asserted 
in a proposition. Besides the propositions which assert Sequence or 
Coexistence, there are some which assert simple Existence ; and 
otliers assert Causation, which, subject to the explanations which will 
follow in the Third l^ook, must be considered provisionally as a distinct 
and pocuhar kind of assertion. 



IMPORT OF PROPOSITIONS. 69 

§ 6. To these four kinds of matter-of-fact or assertion, must be 
added a fifth, Resemblance. This was a species of attribute which 
we found it impossible to analyze ; for which no ftindamcntum^ distinct 
from the objects themselves, could be assigned. In addition to prop- 
ositions which assert a sequence or coexistence between two phenom- 
ena, there are therefore, also, propositions which assert resemblance 
between them : as. This color is like that color ; — The heat of to-day is 
equal to the heat of yesterday. It is true that such an assertion might 
with some plausibility be brought within the description of an affirma- 
tion of sequence, by considering it as an assertion that the simulta- 
neous contemplation of the two colors \^ followed by a specific feeling 
termed the feeling of resemblance. But there would be nothing 
gained by encumbering ourselves, especially in this place, with a 
generalization which may be looked upon as strained. Logic does 
not undertake to analyze things into their ultimate elements. Resem- 
blance between two phenomena is more intelligible in itself than any 
explanation could make it, and under any classification must remain 
specifically distinct from the ordinary cases of sequence and coexistence. 

It is sometimes said that all propositions whatever, of which the 
predicate is a general name, do, in point of fact, affirm or deny resem- 
blance. All such propositions affirm that a thing belongs to a class ; 
but things being classed together according to their resemblance, 
everything is of course classed with the things which it resembles 
most ; and thence, it may be said, when we affirm that gold is a 
metal, or that Socrates is a man, the affirmation intended is, that gold 
resembles other metals, and Socrates other men, more nearly than 
they resemble the objects contained in any other of the classes co- 
ordinate with these. 

There is some slight degree of foundation for this remark, but no 
more than a slight degree. The arrangement of things into classes, 
such as the class metal, or the class man, is grounded indeed upon a 
resemblance among the things which are placed in the same class, but 
not upon a mere general resemblance : the resemblance it is grounded 
upon consists in the possession by all those things, of certain common 
peculiarities ; and those peculiarities it is which the terms connote, 
and which the propositions consequently assert ; not the resemblance : 
for though when I say, Gold is a metal, I say by implication that if 
there be any other metals it must resemble them, yet if there were no 
other metals I might still assert the proposition %vith the same mean- 
ing as at present, namely, that gold has the various properties implied 
in the word metal ; just as it might be said, Christians are men, even 
if there were no men who were not Christians ; or as the expression, 
Jehovah is God, might be used by the firmest believer in the unity of 
the godhead. Propositions, therefore, in which objects are referred to 
a class because they possess the attributes constituting the class, are 
so far from asserting nothing but resemblance, that they do not, prop- 
erly speaking, assert resemblance at all. 

But we remarked some time ago (and the reasons of the remark 
will be more fully entered into in a subsequent Book), that there is some- 
times a convenience in extending the boundaries of a class so as to 
include things which possess in a very inferior degi'ee, if in any, the 
characteristic properties of the class, — provided they resemble that 
class more than any other, insomuch that the general propositions 



70 NAMES AND PROPOSITIONS. 

wliich are tnie of the class will be nearer to being true of those things 
than any other equally general propositions. As, for instance, there 
are substances called metals which have very few of the properties by 
which metals are commonly recognized ; and almost every great family 
of plants or animals has a few anomalous genera or species on its 
borders, which are admitted into it by a sort of courtesy, and concern- 
ino- which it has been matter of discussion to what family they properly 
belonged. Now when the class-name is predicated of any object of 
this description, we do, by so predicating it, affirm resemblance and 
nothing more. And in order to be scrupulously con-ect, it ought to 
be said, that in eveiy case in which we predicate a general name, we 
affirm, not absolutely that the object possesses the properties designa- 
ted by the name, but that it either possesses those properties, or if it 
does not, at any rate resembles the things which do so, more than it 
resembles any other things. In most cases, however, it is unnecessary 
to suppose any such alternative, the latter of the two gi'ounds being 
very seldom that on which the assertion is made : and when it is, there 
is generally some slight difference in the form of the expression, as, 
This species (or genus) is considered, or may he ranked, as belonging 
to such and such a family : we should hardly say positively that it 
does belong to it, unless it possessed unequivocally the properties of 
which the class-name is scientifically significant. 

There is still another exceptional case in which, although the predi- 
cate is a name of a class, yet in predicating it we affirm nothing but 
resemblance, the class being founded not upon resemblance in any 
particular respect, but upon general unanalyzable resemblance. The 
classes in question are those into which our simple sensations, or 
other simple feelings, are divided. Sensations of white, for instance, 
are classed together, not because we can take them to pieces, and say 
they are alike in this, and not alike in that, but because we feel them 
to be alike altogether, although in different degrees. When, there- 
fore, I say. The color I saw yesterday was a white color, or, The 
sensation I feel is one of tightness, in both cases the attribute I affirm 
of the color or of the other sensation is mere resemblance, — simple 
likeness to sensations which I have had before, and which have had 
those names bestowed upon them. The names of feelings, like other 
concrete general names, are connotative ; but they connote a mere 
resemblance. When predicated of any individual feeling, the infor- 
mation they convey is that of its likeness to the other feelings which 
we have been accustomed to call by the same name. And thus much 
may suffice in illustration of the kind of Propositions in which the 
matter-of-fact asserted (or denied) is simple Resemblance. 

Existence, Coexistence, Sequence, Causation, Resemblance : one or 
other of these is asserted (or denied) in every proposition, without ex- 
ception. This five-fold division is an exhaustive classification of mat- 
ters-of-fact ; of all things that can be believed or tendered* for belief; 
of all questions that can be propounded, and all answers that can be 
returned to them. Instead of Coexistence and Sequence, we shall 
sometimes say, for gi-eater particularity, Order in Place, and Order in 
Time : Order in Place being one of the modes of coexistence, not ne- 
cessary to be more particularly analyzed here ; while the mere fact of 
coexistence, or simultaneousness, may be classed, together with Se- 
quence, under the head of Order in Time. 



IMPORT OF PROPOSITIONS. 71. 

§ 7. In the foregoing inquiry into the import of Propositions, we 
have thought it necessary to analyze directly those alone, in which the 
terms of the proposition (or the predicate at least) are concrete terms. 
But, in doing so, we have indirectly analyzed those in which the terms 
are abstract. The distinction between an abstract term and its cor- 
responding concrete, is no difference in what they are appointed to sig- 
nify ; for the real signification of a concrete general name is, as we 
have so often said, its connation ; and what the concrete term con- 
notes, forms the entire meaning of the abstract name. Since there is 
nothing in the import of an abstract name which is not in the import 
of the corresponding concrete, it is natural to suppose that neither can 
there be anything in the import of a proposition of which the terms are 
abstract, but what there is in some proposition which can be framed of 
concrete terms. 

And this presumption a closer examination will conlinii. An ab- 
stract name is the name of an attribute, or combination of attributes. 
The corresponding concrete is a name given to things, because of, and, 
in order to express, their possessing that attribute, or that combination 
of attributes. Wlien, therefore, we predicate of anything a concrete 
name, the attribute is what we in reality predicate of it. But it 
has now been sho\vn that in all propositions of which the predicate is 
a concrete name, what is really predicated is one of five things : Ex- 
istence, Coexistence, Causation, Sequence, or Resemblance. An 
attribute, therefore, is necessarily either an existence, a coexistence, 
a causation, a sequence, or a resemblance. When a proposition con- 
sists of a subject and predicate which are abstract terms, it consists of 
terms which must necessarilly signify one or other of these things. 
When we predicate of any thing an abstract name, we affirm of the 
thing that it is one or other of these five things ; that it is a case of 
Existence, or of Coexistence, or of Causation, or of Sequence, or of 
Resemblance. 

It is impossible to imagine any proposition expressed in abstract 
terms, which cannot be transformed into a precisely equivalent propo- 
sition in which the terms are concrete, namely, either the concrete 
names which connote the attributes themselves, or the names of the 
fundarnenta of those attributes, the facts or phenomena on which they 
are grounded. To illustrate the latter case, let us take this propo- 
sition, of which only the subject is an abstract name, — "■ Thoughtless- 
ness is dangerous." Thoughtlessness is an attribute grounded on the 
facts which we call thoughtless actions ; and the proposition is equiva- 
lent to this. Thoughtless actions are dangerous. In the next example 
the predicate as well as the subject are abstract names : " Whiteness 
is a color;" or " The color of snow is a whiteness." These attributes 
being grounded upon sensations, the equivalent propositions in the 
concrete would be. The sensation of white is one of the sensations 
called those of color, — The sensation of sight, caused by looking at 
snow, is one of the sensations called sensations of white. In these 
propositions, as we have before seen, the matter-of-fact asserted is a 
Resemblance. In the following examples, the concrete terms are 
those which directly coiTespond to the abstract names ; connoting the 
attribute which these denote. "Prudence is a virtue:" this may be 
rendered, " All prudent persons, in so far as prudent, are virtuous :" 
" Courage is deserving of honor" thus, " All courageous persons are 



72 NAMES AND PROPOSITIONS. 

deservino- of honor so far forth as they are courageous;" which is 
equivalent to this — " All courageous persons deserve an addition to the 
honor, or a diminution of the disgrace, which would attach to them on 
other gi'ounds." 

In order to throw still further light upon the import of propositions 
of which the terms are abstract, we wall subject one of the examples 
given above to a minuter analysis. The proposition we shall select is 
the following — *' Prudence is a virtue." Let us substitute for the 
word virtue an equivalent but more definite expression, such as " a 
mental quality beneficial to society," or " a mental quality pleasing to 
Grod," or whichever other of the definitions of virtue we prefer. What 
the proposition asserts is a sequence, accompanied with causation, 
namely, that benefit to society, or that the approval of God, is consequent 
upon, and caused by, prudence. Here is a sequence ; but between 
what % We understand the consequent of the sequence, but we have 
yet to analyze the antecedent. Prudence is an attribute ; and, in con- 
nexion with it, two things besides itself are to be considered ; prudent 
persons, who are the subjects of the attribute, and prudential conduct, 
which may be called \}ciQ foundation of it. Now, is either of these the 
antecedent % and, first, is it meant, that the approval of Grod, or benefit 
to society, is attendant upon all prudent lyersons 1 No ; except in so 
far forth as they are prudent ; for prudent persons who are scoundrels 
can seldom on the whole be beneficial to society, nor acceptable to 
even finite wisdom. Is it upon prudential conduct, then, that divine 
approbation and benefit to mankind are invariably consequent ] Nei- 
ther is this the assertion meant when it is said that prudence is a 
virtue ; except with the same reservation as before, and for the same 
reason, namely, that prudential conduct, although in so far as it is pru- 
dential it is beneficial to society, may yet, by reason of some other of 
its qualities, be productive of an injury outweighing the benefit, and of 
a divine displeasure exceeding the approbation which would be due 
to the prudence. Neither the substance, therefore (viz., the person), 
nor the phenomenon (the conduct), is an antec-edent upon w^hich the 
other term of the sequence is universally consequent. But the propo- 
sition, " Prudence is a virtue," is an universal proposition. What is it, 
then, upon which the proposition afl^irms the effects in question to bo 
universally consequent 1 Upon that in the person, and in the conduct, 
which causes them to be called prudent, and which is equally in them 
when the action, though prudent, is wicked ; namely, a coiTect fore- 
sight of consequences, a just estimation of their importance to the object 
in view, and repression of any unreflecting impulse at vai'iance with 
the deliberate purpose. These, which are states of the person's mind, 
are the real antecedent in the sequence, the real cause in the causation, 
which are asserted by the proposition. But these are also the real 
ground, or foundation, of the attribute Prudence ; since wherever these 
states of mind exiwt we may predicate pi-udence, even before we know 
whether any conduct has followed. And in this manner every asser- 
tion respecting an attiibute may be transformed into an assertion exactly 
equivalent respecting the fact or phenomenon which is the ground of 
the attribute. And no case can be assigned, where that which is pre- 
dicated of the fa(;t or phenomenon, does not belong to one or other of 
the five species formerly enumerated : it is either simple Existence, or 
it is some Sequence, Coexistence, Causation, or Resemblance. 



VERBAL AND REAL PROPOSITIONS. ^S 

And as these five are the only things which can be affirmed, so are 
they the only things which can be denied. " No horses are web- 
footed," denies that the attributes of a horse ever coexist with web-feet. 
It is scarcely necessary to apply the same analysis to Particular affirm- 
ations and negations. " Some birds are web-footed," affirms that, with 
the attributes connoted by bird, the phenomenon web-feet is sometimes 
coexistent: "Some birds are not web-footed," asserts that there are 
other instances in which this coexistence does not have place. Any 
farther explanation of a thing which, if the previous exposition has 
been assented to, is so obvious, may well be spared. 



CHAPTER VI. 

OF PROPOSITIONS MERELY VERBAL. 



§ 1. As a preparation for the inquiry which is the proper object of 
Logic, namely, in what i^anner propositions are to be proved, we have 
found it necessary to inquire what they contain which requires, or is 
susceptible of, proof; or (which is the same thing) what they assert. 
In the course of this preliminary investigation into the import of Prop- 
ositions, we examined the opinion of the Conceptualists, that a propo- 
sition is the expression of a relation between two ideas ; and the doc- 
trine of the Nominalists, that it is the expression of an agreement or 
disagreement between the meanings of two names. We decided that, 
as general theories, both of these are erroneous ; and that, although 
propositions may be made both respecting names and respecting ideas, 
neither the one nor the other are the subject-matter of Propositions 
considered generally. We then examined the different kinds of prop- 
ositions, and we found that, with the exception of those which are 
merely verbal, they assert five different kinds of matters of fact, name- 
ly. Existence, Order in Place, Order in Time, Causation, and Resem- 
blance ; that in every proposition one of these five is either affirmed, or 
denied, of some fact or phenomenon, or of some object the unknown 
source of a fact or phenomenon. 

In distinguishing, however, the different kinds of matters of fact as- 
serted in propositions, we reserved one class of propositions, which do 
not relate to any matter of fact, in the proper sense of the term, at all, 
but to the meaning of names. Since names and their signification are 
entirely arbitrary, such propositions are not, strictly speaking, suscep- 
tible of truth or falsity, but only of conformity or disconformity to usage 
or convention ; and all the proof they are capable of, is proof of usage ; 
proof that the words have been employed by others in the acceptation 
m which the speaker or vsa'iter desires to use them. These propositions 
occupy, however, a conspicuous place in philosophy ; and their nature 
and characteristics are of as much importance in logic, as those of any 
of the other classes of propositions previously adverted to. 

If all propositions respecting the signification of words, were as sim- 
ple and unimportant as those which served us for examples when ex- 
amining Hobbes' theory of predication, viz., those of which the subject 
and predicate are proper names, and which assert only that those names 



74 NAMES AND PEOPOSITIONS. 

have, or that they have not, been conventionally assigned to the same 
individual ; there would be little to attract to such propositions the 
attention of philosophers. But the class of merely verbal propositions 
embraces not only much more than these, but much more than any 
propositions which at first sight present themselves as verbal ; compre- 
hending a kind of assertions which have been regarded not only as 
relating to things, but as having actually a more intimate relation with 
them than any other propositions whatever. The student in philosophy 
will perceive that I allude to the distinction on which so much stress 
was laid by the schoolmen, and which has been retained either under 
the same or under other names by most metaphysicians to the present 
day, viz., between what were called essential, and what were called 
accidental propositions, and between essential and accidental properties 
or attributes. 

§ 2. Almost all metaphysicians prior to Locke, as well as many since 
his time, have made a great mystery of Essential Predication, and of 
predicates which were said to be of the essence of the subject. The 
essence of a thing, they said, was that without which the thing could 
neither be, nor be conceived to be. Thus, rationality was of the es- 
sence of man, because without rationality, man could not be conceived 
to exist. The different attributes which made up the essence of the 
thing, were called its essential properties ; and a proposition in which 
any of these were predicated of it, was called an Essential Proposi- 
tion, and was considered to go deeper into the nature of the thing, and 
to convey more important information respecting it, than any other 
proposition could do. All properties, not of the essence of the thing, 
were called its accidents ; were supposed to have nothing at all, or 
nothing comparatively, to do with its inmost nature ; and the proposi- 
tions in which any of these were predicated of it were called Acciden- 
tal Propositions, A connexion may be traced between this distinction, 
which originated with the schoolmen, and the well known dogmas of 
suhstanticB secundce, or general substances, and substantial forms, doc- 
trines which under varieties of language pervaded alike the Aristote- 
lian and the Platonic schools, and of which more of the spirit has come 
down to modern times than might be conjectured from the disuse of 
the phraseology. The false views of the nature of classification and 
generalization which prevailed among the schoolmen, and of which 
these dogmas were the technical expression, afford the only explanation 
which can be given of their having misunderstood the real nature of 
those Essences which held so conspicuous a place in their philosophy. 
They said, truly, that man cannot be conceived without rationality. 
But though man cannot, a being may be conceived exactly like a man 
in all points except that one quality, and those others which are the 
conditions or consequences of it. All therefore which is really true in 
the assertion that man cannot be conceived without rationality, is only, 
that if he had not rationality, he would not be reputed a man. There 
is no impossibility ifi conceiving the thing, nor, for aught we know, in 
its existing : the impossibility is in the conventions of language, which 
will not allow the thing, even if it exist, to be called by the name which 
is reserved for rational beings. Rationality, in short, is involved in the 
meaning of the word man ; it is one of the attributes connoted by the 
name. The essence of man, simply means the whole of the attributes 



VERBAL AND REAL PROPOSITIONS. 75 

connoted by the word ; and any one of those attributes taken singly, is 
an essential property of man. 

The doctrines which prevented the real meaning of Essences from 
being understood, not having assumed so settled a shape in the time of 
Aristotle and his immediate followers as was afterwards given to them 
by the Realists of the middle ages, we find a nearer approach to true 
views of the subject in the writings of the ancient Aristotelians than in 
their more modem followers. Porphyry, in his Isagoge, approached so 
near to the true conception of essences, that only one step remained to 
be taken, but this step, so easy in appearance, was reserved for the 
Nominalists of modern times. By altering any property, not of the 
essence of the thing, you merely, according to Porphyry, made a differ- 
ence in it; you made it aXXolov : but by altering any property which 
was of its essence, you made it another thing, aXXo* To a modern it 
is obvious that between the change which only makes a thing different, 
and the change which makes it another thing, the only distinction is 
that in the one case, though changed, it is still called by the same name. 
Thus, pound ice in a mortar, and being still called ice, it is only made 
aXkolov : melt it, and it becomes dXXo, another thing, namely, water. 
Now it is really the same thing, i. e., the same particles of matter, in 
both cases; and you cannot so change anything that it shall cease to be 
the same thing in this sense. The identity which it can be deprived 
of is merely that of the name : when the thing ceases to be called ice, 
it becomes another thing, its essence, what constitutes it ice, is gone ; 
while, so long as it continues to be so called, nothing is gone except 
some of its accidents. But these reflections, so easy to us, would have 
been difficult to persons who thought, as most of the Aristotelians did, 
that objects were made what they were called, that ice (for instance) 
was made ice, not by the possession of certain properties to which 
mankind have chosen to attach that name, but by participation in the 
nature of a certain general substance, called Ice in general, which sub- 
stance, together with all the properties that belonged to it, inhered in 
every individual piece of ice. As they did not consider these universal 
substances to be attached to all general names but only to some, they 
thought that an object borrowed only a part of its properties from an 
universal substance, and that the rest belonged to it individually : the 
foiTner they called its essence, and the latter its accidents. The scho- 
lastic doctrine of essences long survived the theory on which it rested, 
that of the existence of real entities corresponding to general terms ; 
and it was reserved for Locke, at the end of the seventeenth century, 
to convince philosophers that the supposed essences of classes were 
merely the signification of their names; nor, among the signal services 
which that great man rendered to philosophy, was there one more 
needful or more valuable.! 

* 'Kad67\.ov jiiev ovv Tvaaa 6La<popa Trpoayivofiivr] tlvI ^repniov ttoleV lih.V at jitv kolvQq 
Ts Kat ISltog (differences in the accidental properties) u/.?,olov rroLovaiV at de idLacrara, 
(differences in the essential properties) aAAo. — Porph.,7s«^.. cap. iii. 

t Few among the great names m philosophy have met with a harder measure of justice 
from the present generation than Locke ; the unquestioned founder of the analytic philos- 
ophy of mind, but whose doctrines were first caricatured, then, when the reaction arrived, 
cast off" by the prevailing school even with contumely, and who is now regarded by one of 
the conflicting parties in philosophy as an apostle of heresy and sophistry, while among 
those who still adhere to the standard which he raised, there has been a disposition in later 
times to sacrifice his reputation in favor of Hobbes ; a great writer, and a great thinker for 
his time, but inferior to Locke not only in sober judgment but even in profundity and origi- 



76 NAMES AND PROPOSITIONS. 

Now, as the most familiar of the general names predicable of an 
object usually connotes not one only, but several attributes of the object, 
each of which attributes separately fOrms also the bond of union of some 
class, and the meaning of some general name ; we may predicate of a 
name which connotes a variety of attributes, another name which con- 
notes only one of these attributes, or some smaller number of them than 
all. In such cases, the universal affirmative proposition will be true ; 
since whatever possesses the whole of any set of attributes, must pos- 
sess any part of that same set. A proposition of this sort, however, 
conveys no information to any one who previously understood the whole 
meaning of the terms. The propositions. Every man is a corporeal 
being. Every man is a living creature. Every man is rational, convey 
no knowledge to any one who was already aware of the entire meaning 
of- the word man, for the meaning of the word includes all this: and, 
that every man has the attributes connoted by all these predicates, is 
already asserted when he is called a man. Now, of this nature are all 
the propositions which have been called essential ; they are, in fact, 
identical propositions. 

It is true that a proposition which predicates any attribute, even 
though it be one implied in the name, is in most cases understood to 
involve a tacit assertion that there exists a thing corresponding to the 
name, and possessing the attributes connoted by it ; and this implied 
assertion may convey information, even to those who understood the 
meaning of the name. But all information of this sort, conveyed by 
all the essential propositions of which man can be made the subject, is 
included in the assertion. Men exist. And this assumption of real ex- 
istence is after all only the result of an imperfection of language. It 
arises fi'om the ambiguity of the copula, which, in addition to its proper 
office of a mark to show that an assertion is made, is also, as we have 
formerly remarked, a concrete word connoting existence. The actual 
existence of the subject of the proposition is therefore only apparently, 
not really, implied in the predication, if an essential one: we may 
say, A ghost is a disembodied spirit, without believing in ghosts. But 
an accidental, or non-essential, affirmation, does imply the real exist- 
ence of the subject, because in the case of a non-existent subject there 
is nothing for the proposition to assert. Such a proposition as, The 
ghost of a murdered person haunts the couch of the murderer, can 
only have a meaning if understood as implying a belief in ghosts; for 
since the signification of the word ghost implies nothing of the kind, 
the speaker either means nothing, or means to assert a thing which 
he wishes to be believed really to have taken place. 

It will be hereafter seen that when any important consequences 
seem to follow, as in mathematics, from an essential proposition, or, in 
other words, from a proposition involved in the meaning of a name, 
what they really flow from is the tacit assumption of the real existence 

nal genius. Locke, the most candid of philosophers, and one whose speculations bear on 
every subject the strongest marks of having been wrought out from the materials of his 
own mind, has been mistaken for an unworthy plagiarist, while Hobbes has been extolled 
as having anticipated many of his leading doctrines. He did anticipate many of them, and 
the present is an instance in what manner it was generally done. They both rejected the 
scholastic doctrme of essences ; but Locke understood and explained what these supposed 
essences really were ; Hobl)es, instead of explaining the distinction between essential and 
accidental properties, and between essential and accidental propositions. jumpc<l over it, 
and gave a definition which suits at most only essential propositions, and scarcely those, as 
the dcilinition of Proposition in general. 



VERBAL AND REAL TROPOSITIONS. 77 

of the object so named. Apart from this assumption of real existence, 
the class of propositions in which the predicate is of the essence of the 
subject (that is, in which the predicate connotes the whole or part of 
what the subject connotes, but nothing besides), answers no purpose 
but that of unfolding the whole or some part of the meaning of the 
name, to those who did not previously know it. Accordingly, the most 
useful, and in strictness the only useful, kind of essential propositions, 
are Definitions : which, to be complete, should unfold the whole of 
what is involved in the meaning of the word defined ; that is (when it 
is a connotative word), the whole of what it connotes. In defining a 
name, however, it is not usual to specify its entire connotation, but so 
much only as is sufficient to mark out the objects usually denoted by 
it from all other known objects. And sometimes a merely accidental 
property, not involved in the meaning of the name, answers this pur- 
pose equally well. The various kinds of definition which these dis- 
tinctions give rise to, and the purposes to which they are respectively 
subservient, will be minutely considered in the proper place. 

§ 3. According to the above view of essential propositions, no prop- 
osition can be reckoned such which relates to an individual by name, 
that is, in which the subject is a proper name. Individuals have no 
essences. When the schoolmen talked of the essence of an individual, 
they did not mean the properties implied in its name, for the names 
of individuals imply no properties. They regarded as of the essence of 
an individual whatever was of the essence of the species in which they 
were accustomed to place that individual ; i. e., of the class to which 
it was most familiarly referred, and to which, therefore, they conceived 
that it by nature belonged. Thus, because the proposition, Man is a 
rational being, was an essential proposition, they affirmed the same 
thing of the proposition, Julius Caesar is a rational being. This fol- 
lowed very naturally if genera and species were to be considered as 
entities, distinct from, but inhering in, the individuals composing them. 
If man was a substance inhering in each individual man, the essence of 
man (whatever that might mean), was naturally supposed to accom- 
pany it ; to inhere in John Thompson, and form the coimnon essence 
of Thompson and Julius Cassar. It might then be fairly said, that ra- 
tionality, being of the essence of Man, was of the essence also of 
Thompson. But if Man altogether be only the indi^ddual men and a 
name bestowed upon them in consequence of certain common proper- 
ties, what becomes of John Thompson's essence % 

A fimdamental error is seldom expelled from philosophy by a single 
victory. It retreats slowly, defends every inch of ground, and often 
retains a footing in some remote fastness after it has been driven from 
the open country. The essences of individuals were an unmeaning 
figment arising from a misapprehension of the essences of classes, yet 
even Locke, when he extii-pated the parent error, could not shake 
himself free from that which was its fruit. He distinguished two sorts 
of essences, Real and Nominal. His nominal essences were the es- 
sences of classes, explained nearly as we have now explained them. 
Nor is anything wanting to render the third book of Locke's Essay a 
nearly perfect treatise on the connotation of names, except to free its 
language from the assumption of what are called Abstract Ideas, which 
unfortunately is involved in the phraseology, although not necessarily 



78 NAMES AND PROPOSITIONS. 

connected with the thoughts, contained in that immortal Third Book.* 
But, besides nominal essences, he admitted real essences, or essences 
of hidividual objects, which he supposed to be the causes of the sensi- 
ble properties of those objects. We know not (said he), what these 
are (and this acknowledgment rendered the fiction comparatively in- 
nocuous) ; but if we did, we could, from them alone, demonstrate the 
sensible properties of the object, as the properties of the triangle are 
demonstrated from the definition of the triangle. I shall have occasion 
to revert to this theory in treating of Demonstration, and of the con- 
ditions under which one property of a thing admits of being demon- 
strated from another property. It is enough here to remark that 
according to this definition, the real essence of an object has, in the 
progress of physics, come to be conceived as nearly equivalent, in the 
case of bodies, to their corpuscular structure : what it is now supposed 
to mean in the case of any other entities, I would not take upon my- 
self to define. 

§ 4. An essential proposition, then, is one which is purely verbal ; 
which asserts of a thing under a particular name, only what is asserted 
of it in the fact of calling it by that name ; and which therefore either 
gives no information, or gives it respecting the name, not the thing. 
Non-essential, or accidental propositions, on the contrary, may be called 
Keal Propositions, in opposition to Verbal. They predicate of a thing, 
some fact not involved in the signification of the name by which the 
proposition speaks of it ; some attribute not connoted by that name. 
Such are all propositions concerning things individually designated, 
and all general or particular propositions in which the predicate con- 
notes any attribute not connoted by the subject. All these, if true, add 
to our knowledge : they convey information not already involved in the 
names employed. When I am told that all, or even that some objects, 
which have certain qualities, or which stand in certain relations, have 
also certain other qualities, or stand in certain other relations, I leani 
from this proposition a new fact ; a fact not included in my knowledge 
of the meaning of the words, nor even of the existence of Things 
answering to the signification of those words. It is this class of propo- 
sitions only which are in themselves instructive, or from which any 
instructive propositions can be infeiTed. 

Nothing has probably contiibuted more to the opinion so commonly 
prevalent of the futility of the school logic, than the circumstance that 
almost all the examples used in the common school books to illustrate 
the doctrines of predication and of the syllogism, consist of essential 
propositions. They were usually taken either from the branches or 
from the main trunk of the Predicamental Tree, which included nothing 
but what was of the essence of the species : Omne corfus est substantia^ 
Onme animal est corpses, Omiiis Itoino est corpus^ Om7iis homo est ani- 
mal, Omnis homo est rationalis, and so forth. It is far from wonderfiil 

* The always acute and often profound author of Tire Outline of Sematohgy (Mr. B. H. 
Smart) justly says, " Locke will be much more intelligible if, in the majority of places, we 
substitute ' the knowledge of for what he calls, ' the idea of " (p. 10). Among the many 
criticisms upon Locke's use of the word Idea, this is the only one which, as it appears to 
me, precisely Kits the mark ; and I quote it for the additional reason that it precisely ex- 
presses the pouit (jf (iin'crenco respecting the import of Propositions, between my view and 
what I have called tlio ('onco])tuu!ist view of them. Where a Concoptualist says that a 
name or a proposition expresses our Idea of a thing, I should generally say (instead of our 
Idea) our Knowledge, or Belief, concerning the thing itself. 



VERBAL AND REAL PROPOSITIONS. 79 

tliat the syllogistic art should have been thought to be of no use in 
assisting correct reasoning, when almost the only propositions which, 
in the hands of its professed teachers, it was employed to prove, were 
such as every one assented to without proof the moment he compre- 
hended the meaning of the words : and stood exactly on a level, in 
point of evidence, with the premises from which they were drawn. I 
have, therefore, throughout this work, studiously avoided the employ- 
ment of essential propositions as examples, except where the nature of 
the principle to be illustrated specifically required them. 

§ 5. With respect to propositions which do convey information, 
which assert something of a Thing, under a name that does not already 
presuppose what is about to be asserted, there are two different aspects 
in which these, or rather such of them as are general propositions, may 
be considered : we may either look at them as portions of specula- 
tive truth, or as memoranda for practical use. According as we con- 
sider propositions in one or the other of these lights, their import may 
be conveniently expressed in one or in the other of two formulas. 

According to the formula which we have hitherto employed, and 
which is best adapted to express the import of the proposition as a 
portion of our theoretical knowledge. All men are mortal, means that 
the attributes of man are always accompanied by the attribute mor- 
tality : No men are gods, means that the attributes of man are never 
accompanied by the attributes, or at least never by all the attributes, 
of a god. But when the proposition is considered as a inemorandum 
for practical use, we shall find a different mode of expressing the same 
meaning better adapted to indicate the office which the proposition 
performs. The practical use of a proposition is to apprise or remind 
us what we have to expect in any individual case which comes within 
the assertion contained in the proposition. In reference to this pur- 
pose, the proposition, All men are mortal, means that the attributes of 
man are evidence of^ are a mark of, mortality ; an indication by which 
the presence of that attribute is made manifest. No men are gods, 
means that the attributes of man are a mark or evidence that some or 
all of the attributes of a god are not there ; that where the former are, 
we need not expect to find the latter. 

These two forms of expression are at bottom equivalent ; but the 
one points the attention inore directly to what a proposition means, the 
latter to the manner in which it is to be used. 

Now it is to be observed that Reasoning (the subject to which we 
are next to proceed) is a process into which propositions enter not as 
ultimate results, but as means to the establishment of other proposi- 
tions. We may expect, therefore, that the mode of exhibiting the 
import of a general proposition which shows it in its application to 
practical use, will best express the function which propositions per- 
form in Reasoning. And accordingly, in the theory of Reasoning, the 
mode of viewing the subject which considers a Proposition as asserting 
that one fact or phenomenon is a maTk or evidence of another fact or 
phenomenon, will be found almost indispensable. For the purposes 
of tliat Theory, the best mode of defining the import of a proposition 
is not the mode which shows the most clearly what it is in itself, but 
that which most distinctly suggests the manner in which it may be 
made available for advancing from it to other propositions. 



80 NAMES AND PROPOSITIONS. 

CHAPTER VII. 

OF THE NATURE OF CLASSIFICATION, AND THE FIVE PREDICABLES. 

§ 1. In examining into the nature of general propositions, we havo 
adverted much less than is usual with Logicians, to the ideas of a 
Class, and Classification; ideas which, since the Realist doctrine of 
General Substances went out of vogue, have formed the basis of almost 
every attempt at a philosophical theory of general terms and general 
propositions. We have considered general names as having a mean- 
ing, quite independently of their being the names of classes. That 
circumstance is in truth accidental, it being wholly immaterial to the 
signification of the name whether there are many objects or only one 
to which it happens to be applicable, or whether there be any at all. 
God is as much a general term to the Christian or the Jew as to the 
Polytheist; and dragon, hippogiiff, chimera, mermaid, ghost, are as 
much so as if real objects existed, corresponding to those names. 
Every name the signification of which is constituted by attributes, is 
potentially a name of an indefinite number of objects ; but it needs 
not be actually the name of any; and if of any, it may be the name of 
only one. As soon as we employ a name to connote attributes, the 
things, be they more or fewer, which happen to possess those attri- 
butes, are constituted, ipso facto, a class. But in predicating the name 
we predicate only the attributes ; and the fact of belonging to a class 
does not, in ordinary cases, come into view at all. 

Although, however. Predication does not presuppose Classification, 
and although the theory of Names and of Propositions is not cleared 
up, but only encumbered, by intruding the idea of classification into 
it, there is nevertheless a close connexion between Classification, and 
the employment of General Names. By every general name which 
we introduce, we create a class, if there be any existing things to 
compose it ; that is, any Things corresponding to the signification of 
the name. Classes, therefore, mostly owe their existence to general 
language. But general language, also, though that is not the most 
common case, sometimes owes its existence to classes. A general, 
which is as much as to say a significant, name, is indeed mostly intro- 
duced because we have a signification to express by it ; because we 
need a word by means of which to predicate the attributes which it 
connotes. But it is also true that a name is sometimes introduced be- 
cause we have found it convenient to create a class ; because we have 
thought it useful for the regulation of our mental operations, that a 
certain group of objects should be thought of together. A naturalist, 
for purposes connected with his particular science, sees reason to dis- 
tribute the animal or vegetable creation into certain groups rather 
than into any others, and he requires a name to bind, as it were, each 
of his groups together. It must not, however, be supposed that such 
names, wlicn introduced, differ in any respect, as to their mode of sig- 
nification, from other connotative names. The classes which they de- 
note are, as much as any other classes, constituted by certain common 
attributes ; and tlieir names are significant of those attributes, and of 
nothing else. The names of Cuvier's classes and orders, 'Planti- 
grades, Digitigradcs, &c., are as much the expression of attiibutos, aa 



CLASSIFICATION AND THE PREDICABLES. 81 

if those names had preceded, instead of growing out of, his Classifica- 
tion of Animals. The only peculiarity of the case is, that the conve- 
nience of classification was here the primary motive for introducing the 
names ; while in other cases the name is inti-oduced as a means of 
predication, and the formation of a class denoted by it is only an indi- 
rect consequence. , - . 

The principles which ought to regulate Classification as a logical 
process subservient to the investigation of ti^uth, cannot be discussed to 
any purpose until a much later stage of our inquiiy. But, of classifi- 
cation as resulting from, and implied in, the fact of employing general 
language, we cannot forbear to treat here, without leaving the theory 
of general names, and of their employment in predication, njutilated 
and formless. . ,. >.. ^ ■ \ .^ . 

§ 2. This portion of the theory of general language is the subject of 
what is termed the doctrine of the Predicables ; — a set of distinctions 
handed down from^ Aristotle and his follower. Porphyry, many of 
which have taken a firm root in scientific, and some of them even in 
popular, phraseology. The Predicables are a five-fold division of Gen- 
eral Names, not grounded as usual upon a difference in their mean- 
ing, that is, in the attribute which they connote, but upon a difference 
in the kind of class which they denote. We may predicate of a thing 
five different varieties of class-name :— 

A genm of the thing [ysvog). 

K species .. /j.^-'-^ (sldog). 

A differentia.. ' - /- (dia^opd). 

A proprmm {J,6i6v). 

An accidens {ovfi(3e(37}K6g). 

It is to be remarked of these distinctions, that they express, not 
what the predicate is in its own meaning, but what relation it bears to 
the subject of which it happens on the particular occasion to be predi- 
cated. There are not some names which are exclusively genera, and 
others which are exclusively species, or differentiae : but the same 
name is referred to one or another Predicable, according to the sub- 
ject of which it is predicated on the particular occasion. Animal, for = 
instance, is a genus with respect to Man, or John ; a species vdth re- 
spect to Substance or Being. Rectangular is one of the Differentia of 
a geometrical square : it is merely one of the Accidentia of the table 
on which I am writing. The words, genus, species, &c., are therefore 
relative terms ; they are names applied to certain predicates, to ex- 
press the relation between them and some given subject : a relation 
grounded, as we shall see, not upon what the predicate connotes, but 
upon the class which it (denotes, and upon the place which, in some 
given classification, that class occupies relatively to tlie particular 
subject. 

§ 3. Of these five names, two, Genus and Species, are not only used 
by naturalists in a technical acceptation not precisely agreeing with 
their philosophical meaning, but have also acquired a popular accep- 
tation, much more general than either. In this popular sense any ',two 
classes, one of which includes the whole of the other and more, may 
be called a Genus and a Species. Such, for instance, are Animal and 
Man ; Man and Mathematician. Animal is a genus ; Man and Brute 



82 NAMES AND PROPOSITIONS. 

are its two species ; or we may divide it into a greater number of 
species, sis man, horse, dog, &c. Biped, or two-footed animal^ may 
,also be considered a genus, of whicli man and bird are two species. 
Taste is a genus, of wbich sweet taste, sour taste, salt taste, &c., are 
species. Virtue is a geiius ; justice, prudence, courage, fortitude, 
generosity, &;c., are its species. 

The same class which is a genus with reference to the sub-clsLsses 
or species included in it; may be itself a species 'witb reference to a 
,more comprehensive, or,' as it is often called, ,a superior, genus. Man 
is a species with , reference to animal, but , -a -genus w^ith reference to 
the species mathematician^ Animal is, a genus, di^dded into two 
species, vman and brute ; but animal is also a species, which, with 
• another species, vegetable,- makes up the genus, organized being. 
Biped is a genus with reference to man and bird, but a species with 
respect to the superior genus; animal. Taste is a genus divided into 
species, but also a species of the genus sensation. Virtue, a genus 
with reference to justice, teldp^:ance, &c., is one of the species of the 
genus, mental quality. .^^ ^'. '-^ 

In this popular sense the words Genus and Species have passed 
into common discourse. And it should be obser\^ed that, in ordinary 
parlance, not the name of the class, but the class itself, is said to be 
the genus or species; not, of course, the class in the sense of each 
individual of that class, but the individuals collectively, considered as 
an aggregate whole ; the naine.s' by which the class is designated being 
then called not the genus or species, but the generic or specific name. 
And this is an admissible'form of expression ,•• nor is it of any import- 
ance which of the twtt niodes of speakii^g'we adopt, provided the rest 
of our language is consistent with it; but if we' call the class itself the 
genus,, ;vve must not talk of predicating tile genus. We predicate of 
man the naw.e mortal; and by predicating tire -name, we may be said, 
in an. intelligible sense, to predicate what-, the' name expresses, thfe 
attribute mortality; but in no allowable seitse of the word predication 
do we predicate of man,)-tlie .c?<2.s* mortal.' We predicate of him the 
i^ct'o^helongingX^'lh.Q class, -"i^", '' '..'•;••*' 

By the Aristotelian l0giciatis,'-tlie terms vgenuB £i,nd sl)"^cies were, 
used in a more restricted sei^. ' They dia ' npt adm'it eveiy class 
which could be divided into other classes to be a genus, or every class 
which' could be incKided in a larger class to be a species. Animal 
was by them considered a genus :'. and man 'a,nd brute co-ordinate 
species 'nnd"er that genufS-:- ^if/^ecZ vVduld not have been admitted to be 
a genus wi^h reference 'to maii, but ^ jptojrrium o^ dccidens only. It 
was requisite, according .'to their theory, that genus and species should 
be 'of the ensencb bf t^ie subject. ' Ammdl \Yn^ q? ihe essence of man; 
hiped was not. And in evety ^classification the^^ considered some one 
class as the lowesi o'r infimu species; man, for instance, w^as a lowest 
species. Any further divisions into which the class might be capable 
of being broken down^ as tnan; inter <white', b]ack, and red man, or into 
priest and kyman,'they. did' not admit to be species. 
^ It'hris bcQn scejfi, however, in the preceding chapter, that the dis- 
tinction between the essence, of a class, and the attributes or properties 
which arc not of it*;^ eKsetrr.e, — ^adigtinctaon which has given occasion 
to so miich abstruse speculation, and to which §o- mysterious a charac- 
ter was formerly, and by tnany -vyrrtersis still, attached^— amounts' to 



CLASSIFICATION AND Tllti PRKDICAJiLEH. 88 

nothing more than t}ic dii^cnmca bctwccji those attriljutes of the class 
which are, and those which are not, involved in the signification of the 
class-name. As applied to individuals, the word Essence, we found, 
has no nleaning, except in corniexion with the exploded tenets of the 
Kealists ; aTid what the schoolmen chose to cajl the essence of an indi- 
vidual, was simply the esBence of the class- to ^ieh that inidividual 
was most familiarly i^eferred. ' - . '. 

Is there.no difference, then, ex:cept't;his ^merely veo-balbne, between 
the classes which the schoolmen admittwl to be genera- or species, and 
those to which they refused the title 1 Is it an error to regard some of 
the differences which exist among objects as differences in kind (genere 
or s2>ecie), and others- only as differences in the accidents'? Were the 
Hchoolmen right or wrong in giving to some of the classes into which 
things may be divided, the name o^ kinds, and considering othors as 
secondary divisions, grounded upon differences .of -a comparatively 
superficial natuie 1 Kxamination will show that the Aristotelians did 
mean something by this distinction, and something important ; but 
which, being but imlistinctly conceived, was -inadequately expressed 
by the phraseology of essences, and by -^e various other modes of 
speech to wliich they had recourse. '' ' ' ^ ". 

§;4. It is a fundamental principle in logic, that the power of framing 
classes is unlimited; as long as thei'e is any (even the smallest) differ- 
ence to found a distinction upon; Tak,e any /attribute whatever, and 
if some things have.it, anil others have not, we may ground upon the 
Htfribute a division of all thiiigs intQ-tvvo classes; and wc actually do 
so, the .moment wb create a ]p.amc v/hlch conn bte's the. attribute./ The 
irumber of possible classes, therefore, is boundles's j and' there are as 
many actual classes (either'-of real or -of imagiriary things) as' there are 
general names, positive and negative together. 

But if we contemplate any one of the classes so formed, such as the 
class animal or plant, or the class sulphur fjr phosphorus, or the class 
white or red, ;y:id consider in what, particulars the individuals included 
in the class differ from those v/hich do not- come within it, we find a 
yery'rern;irkciJ:)le diversity in tlris respect between some dasses and 
othore. There are some classes, the things contained in which differ 
from :othei,Mhlngs only in certain particulars which may be numbered ; 
while others differ in more than can be numbered, mora even than wc 
need ever expect to know. Some classes have little or nothing in 
Cf>mmon to characterize them .'by^. except,' precisely what is connoted 
by the name : white things, for exarnplo, arc not distinguished by any 
common properties exfcept wliit^ness ';• or if they arc, it is only by such 
as are in some way dependent upon, or crjTAriected with^^ v/hiteness. 
But a hundred gencrations-haye not cxhaus^x^d the common properties 
of animals or of plants, of sulphxir or of phosphorus ; nor do we suppose 
them to be exhaustible,. but proc^eed to- new observations and experi- 
ments, jnr the full confidence of discovering new properties which were 
by no means implied in those we previously knew. While, if any one 
v/ere to p^opofic for investigation the common properties of all things 
which are of the sarhc color, the 'iame shjipe, or the same specific 
gravity; tljc absurdity would be palpable.,. We have no gi-ound to 
believe that any such common properties -exist, oxcept such as maybe 
shown to be involved in the supposition itself, or to be derivable from 



84 NAMES AND PROPOSITIONS. 

it by some law of causation. It appears, therefore, that the properties, 
on which we gi'ound our classes, sometimes exhaust, all that the class 
has in common, or contain it all by some mode of implication ; but in 
other instances we make a selection of a few properties from among 
not only a greater number, but a number inexhaustible by us, and to 
which as we know no bounds, they may, so far as we are concernedj, 
be regarded as infinite. 

There is no impropriety in saying that of these two classifications, 
the one answers to a much more radical distinction in the things them- 
selves, than the other does. And if any one even chooses to say that 
the one classification is made by nature, the other by us for our conve- 
nience, he will be right ; provided he means no more than this- — that 
where a certain apparent difference between things (although perhaps 
in itself of little moment) answers to we know not what number of 
other differences, pervading not only their known properties but prop- 
erties yet undiscovered, it is not optional but imperative to recognize 
this difference as the foundation of a specific distinction : while, oil the 
contrary, differences that are merely finite and determinate, like those 
designated by the words white, black, or red, may be disregarded if 
the purpose for which the classification is made does not require atten- 
tion to those particular properties. The differences, however, are made 
by nature, in both cases; while the recognition of those differences as 
grounds of classification and of naming, is, equally in both cases, the act 
of man : only in the one case, the ends of language and of classification 
would be subverted if no notice were taken of the difference, while in 
the other case, the necessity of taking notice of it depends upon the 
importance or unimportance of the particular qualities in which the 
difference happens to consist. 

Now, these classes, distinguished by unknown multitudes of prop- 
erties, and not solely by a few determinate ones, are the only classes 
which, by the Aristotelian logicians, were considered as genera or 
species. Differences which extended to a certain property or proper- 
ties, and there terminated, they considered as differences only in the. 
accidents of things ; but where any class differed from other things by 
an infinite series of differences, known and unknown, they considered 
the distinction as one of kind, and spoke of it as being an essential 
difference, which is al«o one of the usual meanings of that vague ex-^ 
pression at the present day. ■ ^ 

Conceiving the schoolmen to have been justified in.dra'wing a bi-oad 
line of separation between these two kinds of classes arid of class-dis-, 
tinctions, I shall not only retain the division itself, but continue to 
express it in their language. According to that language, the proxi- 
mate (or lowest) Kind to which any individual is referable, is called 
Its species. ' Conformably, to this. Sir Isaac Newton would he said to 
be of the species man. There are indeed numerous sub-classes in- 
cluded in the class man, to which Sir Isaac Newton also belongs; as, 
for example, Clnistian, and Englishman, and Mathematician. But 
these, though distinct classes, are not, in our sense of the term, distinct 
Kinds of men. A Christian, for example, differs from other human 
beings ; but ho diffoi's only in the attribute which the word expresses, > 
namely, belief in Christianity, and whatever else that imphes, either as 
involved in the fact itself, or connected with it through some law of 
cauac and effect. We should never think of inquiring what properties, 



CLASSIFICATION AND THE rREDI€ABLES« 85 

unconnected with Christianity, are common to all Christians and pe- 
culiar to them ; while in regard to all Men, physiologists are perpetu- 
ally carrying on such an inquiry ; nor is the answer ever likely to be 
completed. Man, therefore, we may be peiTnitted to call a species ; 
Christian, or Mathematician, we cannot. 

Note here, that it is by no means intended to imply that there may 
not be different Kinds, or logical species, of man. The various races 
and temperaments, the two sexes, and even the various ages, may be 
differences of kind, within our meaning of the term. I say, they may 
be ; I do not say, they are. For in the progress of physiology it may 
be made out, that the differences which distinguisn different races, 
sexes, &c., from one another, follow as consequences, under laws of 
nature, from some one or a few primary differences which can be pre- 
cisely determined, and which, as the phrase is, account for all the rest. 
If this be so, these are not distinctions in kind ; no more than Chris- 
tian, Jew, Mussulman, and Pagan, a difference which also carries 
many consequences along with it. And in this way classes are often 
mistaken for real kinds, which are afterwards proved not to be so. 
But if it shall turn out, that the differences are not capable of being 
accounted for, then man and woman, Caucasian, Mongolian, and Ne- 
gi'o, &c., are really different Kinds of human beings, and entitled to 
be ranked as species by the logician ; though not by the naturalist. 
For (as already hinted) the word species is used in a very different 
signification in logic and in natural history. By the naturalist, organ- 
ized beings are never said to be of different species, if it is supposed 
that they could possibly have descended from the same stock. That, 
however, is a sense artificially given to the word, for the technical pur- 
poses of a particular science. To the logician, if a negro and a white 
man differ in the same manner (however less in degree), as a horse 
and a camel do; that is, if their differences are inexhaustible, and not 
referrible to any common cause, they are different species, whether 
they are both descended from Noah or not. But if their differences 
can all be traced to climate and habits, they are not, in the logician's 
view, specifically distinct. 

When the injima species, or proximate Kind, to w^hich an indi\'idual 
belongs, has been ascertained, the properties common to that Kind 
include necessarily the whole of the common properties of every other 
real Kind to which the individual can be referrible. Let the indi\dd- 
ual, for example, be Socrates, and the proximate Kind, man. Animal, 
or living creature, is also a real Kind, and includes Socrates ; but since 
it likewise includes man, or in other words, since all men are animals, 
the properties common to animals forai a portion of the common prop- 
erties of the sub-class, man : and if there be any class which includes 
Socrates without including man, that class is not a real Kind. Let the 
class, for example, be j?<2^-7eo5e<^ ; that being a class which includes 
Socrates, without including- all men. To deteiinine whether it is a 
real Kind, we must ask ourselves this question : Have all flat-nosed 
animals, in addition to whatever is implied in their flat noses, any 
common properties, other than those which are common to all animals 
whatever % If they had ; if a flat nose were a mark or index to an in- 
definite number of other peculiarities, not deducible fi'om the fonner 
by any ascertainable law ; then out of the class man we might cut an- 
other class, flat-nosed man, which,- according to our definition, woill^' 



80 - NAMES AND PROPOSITIONS. 

be a Kind. But if we could do this, man would not be, as it was as- 
sumed to be, the proximate Kind. Therefore the properties of the 
proximate Kind do comprehend those (whether known or unknown) 
of all other Kinds to which the individual belongs ; which was the 
point we undertook to prove. And hence, every other Kind which is 
predicable of the individual, will be to the proximate Kind in the re- 
lation of a genus, according to even the popular acceptation of the 
terms genus and species; that is, it will be a larger class, including it 
and more. 

We are now able to fix also the logical meaning of these terms.^ 
Every class which is a real Kind, that is, which is distinguished fi'om 
all other classes by an indeterminate multitude of properties not deriv- 
able from another, is either a genus or a species. A Kind which is not 
divisible into other Kinds, cannot be a genus, because it has no species 
under it; but it is itself a species, both with reference to the indi- 
viduals below and to the genera above (Species Prsedicabilis and Species 
Subjicibilis). But every Kind which admits of division into real Kinds 
(as animal into quadruped, bird, &c., or quadruped into various species 
of quadrupeds) is a genus to all below it, a species to all genera in 
which it is itself included. And here we may close this part of the 
discussion, and pass to the three remaining predicables, Differentia, 
Proprium, and Accidens. . 

J ■ : 

§ 5. To begin with Differentia. This word is correlative with the 
words genus and species, and as all agree, it signifies the attribute 
which distinguishes a given species from every other species of the 
same genus. This is so far clear: but which of the distinguishing 
attributes does it signify? For we have seen that every Kind (and a 
species must be a Kind) is distinguished fi-om other Kinds not by any 
one attribute, but by an indefinite number. Man, for instance, is a 
species of the genus animal ; Rational (or rationality, for it is of no 
consequence whether w'e use the concrete or the abstract fonn) is gen- 
erally assigned by logicians as the Differentia; and doubtless this 
attribute serves tlie purpose of distinction : but it has also been re- 
marked of man, that he is a cooking animal; the only animal that 
dresses its food. This, therefore, is another of the attributes by which 
the species man is distinguished from other species of the same genus; 
would this attribute serve equally well for a differentia ? The Aristo- 
telians say No ; having laid it down that the differentia must, like the 
genus and species, be of the essence of the subject. 
■' And he^-e we lose even that vestige of a meaning grounded in the 
nature of the things themselves, which may be supposed to be attached 
to the word essence when it is said that genus and species must be of 
the essence of the thing. There can be no doubt that when the school- 
men talked of the essences of things as opposed to theii' accidents, they 
had confusedly in view the distinction between differences of kind, and 
the difTereiices which are not of kind; they meant to intimate that 
genera and species must be Kinds. Their notion of the essence of a 
thnig was a vague notion of a something which makes it what it is, ^. c.» 
which rnakos it the Kind of thing that it is- — which causes it to. have all 
that variety of propertios which distinguish its Kind. But when the 
matter came to ho looked at more, closely, nobody could discover what 
cua-jcd the tiling to have all those pxppcrties, ppj-. even that there waa 



CLASSIFICATION AND THE PREDICABLES. 87 

anything wliicli caused it to have them. Logicians, however, not liking 
to admit this, and being unable to detect what made the thing to be 
what it was, satisfied themselves with what made it to be what it was 
called. Of the innumerable properties, known and unknown, that are 
common to the class man, a portion only, and of course a very small 
portion, are connoted by its name : these few, lioWever, will naturally 
have been thus distingui3hed fi-om the rest either for their greater 
obviousness, or for gi'eater supposed importance. These properties, 
then, which were connoted by the name, logicians seized upon, and 
called them the essence of the species ; and not stopping there, they 
affirmed them, in the case of the infiina species, to be the essence of the 
iuvxividual too ; for it was their maxim, that the species contained the 
" whole essence" of the thing. Metaphysics, that fertile field of delu- 
sion propagated by language, does not afford a more signal instance of 
such delusion. On this account it was that rationality, being connoted 
by the name man, was allowed to be a differentia of the class ; but the 
peculiarity of cooking their food, not being connoted, was relegated to 
the class of accidental properties. 

The distinction, therefore, between Differentia, Proprium, and Acci- 
dens, is not founded in the nature of things, but in the connotation of 
names ; and we must seek it there if we wish to find what it is. 

Fromthe fact that the genus includes the species, in other words, 
denotes more than the species, or is predicable of a greater number of 
individuals, it follows that the species must, connote more than the 
genus. It must connote all the attributes v^^hich the genus connotes, 
or there would be nothing to prevent it from denoting individuals not 
included in the genus. And it must connote something besides, other- 
wise it would include the whole genus. Animal denotes all the indi- 
viduals denoted by man,, and many more. Man, therefore, must con- 
note all that animal connotes, otherwise there might be men who were 
not animals ; and it must connote something more than animal connotes, 
otherwise all animals would be men. This surplus of connotation — this 
which the species connotes over and above the connotation of the genus 
^ — is the Differentia, or specific difference; or, to state the same prop- 
osition in other words, the Differentia is that which must be added 
to the connotation of the genus, to complete the connotation of the 
species. . 

The word man, for instance, exclusively of what it connotes in com- 
mon with animal, also connotes rationality, and at least some approxi-- 
mation to that external form, which we all know, but which, as we 
have no name for it considered in itself, we are content to call the 
human. The differentia, or specific difference, therefore, of man, as 
referred to the genus animal, is that outward form and the possession 
of reason. The Aristotelians said, the possession of reason, without 
the outward foiTn. But if they adhered to this, they would have been 
obliged to call the Houyhnhms men. The question never arose, and 
they were never called upon to decide how such, a case would have 
affected their notion of essentiality. But, so far. as it is possible to 
determine how language would be used in a case which is purely 
imaginary, we may say that the Houyhnhms would not be called men, 
and that the terra man, therefore, requires other conditions besides 
rationality. The schoolmen, however, were satisfied with taking such 
a portion of the differentia as sufficed to distinguish the species fi'ora 



88 NAMES AND PROPOSITIONS. 

all Other existing thirigs, although by so doing they might not exhaust 
the connotation of the name. 

§ 6. And here, to prevent the notion of differentia from being 
restricted within too narrow limits, it is necessary to remark, that a 
species, even as refen'ed to the same genus, will not always have the 
same differentia, but a different one, according to the principle and 
purpose which presides over the particular classification. For ex- 
ample, a naturalist surveys the various kinds of animals, and looks out 
for the classification of them most in accordance with the order in 
which, for zoological purposes, it is desirable that his ideas should 
arrange themselves. With this view he finds it advisable that one of 
his fundamental divisions should be into warm-blooded and cold-blood- 
ed animals ; or into animals which breathe with lungs and those which 
breathe with gills ; or into carnivorous, and frugivorous or graminivor- 
ous ; or into those which walk on the flat part and those which walk on 
the extremity of the foot, a distinction on which some of Cuvier's fami- 
lies are founded. In doing this, the naturalist creates as many new 
classes, which are by no means those to which the individual animal- is 
familiarly and spontaneously referred ; nor should we ever think of 
assigning to them so prominent a position, in our arrangement of the. 
animal kingdom, unless for a preconcerted purpose of scientific con- 
venience. And to the liberty of doing this there is no limit. In the 
examples we have given, the new classes are real Kinds, since each 
of the peculiarities is an index to a multitude of properties belonging 
to the class which it characterizes; but even if the case were other- 
wise — if the other properties of those classes could all be deiived, by 
any process known to us, from the one peculiarity on which the class 
is founded — even then, if those derivative properties were of primary 
importance for the purposes of the naturalist, he would be wari'anted 
in founding his primary division upon them. 

If, however, practical convenience is a sufficient warrant for making 
the main demarcations in our arrangement of objects run in lines nOt 
coinciding with any distinction of Kind, and so creating genera and 
species in the popular sense which are not genera or species in the 
rigorous sense at all ; a fortiori must we be warranted, when our 
genera and species are real genera and species, in marking the distinc- 
tion between them by those of their properties which considerations 
of practical convenience most strongly recommend. If we cut a 
species out of a given genus — the species man, for instance, out of the 
genus animal — with an intention on our part that the peculiarity by 
which we are to be guided in the application of the name man should- 
be rationality, then rationality is the differentia of the species mkn. 
Suppose, however, that, being naturalists, we, for the purposes of our 
particular study, cut out of the genus animal the same species man^ 
but with an intention that the distinction between man and all other 
species of animal should be, not rationality, but the possession of *' four 
incisors in each jaw, Uisks solitary, and erect posture." It is evident 
that the word man, when used by us as naturalists, no longer connotes 
rationality, but connotes the three other properties specified; for that 
whicli we have expressly in view when we impose a name, assuredly 
forms part of the meaning of that name. We may, therefore, lay it 
down as a maxim, that wherever there is a Genus, and a Species 



CLAF?HIFIC!ATI0N AMI) THE I'KEDICAIll.K.S. 89 

marked out from tliuf, givuns by ;in {issioTiiihlc! iliflijfcntin,, tli(^ mnrui of 
the spocioH must be connotati'vc!, and must CDnriyt^^ the dlffcreutia; 
but ttie connotation may l)o .sjHu-ia], not invfJved in tlic-Higijilicatioii of 
the term as ordinarily used, ])ut frivtm to it when en;i'ploycd as a term of 
art or science. The word Man, in common oise, connotes Tationality 
and a certain ^form, but does not connote the liumiKjr or character of 
the te(!th ; hi the Linnaoan flystoni it connotes the number of incisor 
and canine teeth, but docs liot connote rationality nor any particular 
form. The word man has, therefore, two different meanings; al- 
though not commonly considered as ambiguous, because it hap])cn» in 
both cnses to dcjutUi the same individual obj(;cts. But a case is con- 
ceivable in whi(ili tlie aml)iguity would become (;vident : we have only 
to imagine; that sonu; new kind of animal were discovered, having 
Linnanis's three characteristics of humanity, but not rational, or not 
of the human form. In ordinary p;irlance these animals woidd not be 
called men; but in natural history, they must still be called so by 
those, if any there be, who adhere to the Litmfean classification ; and 
the question w.otild arise, whether the word should continue to be used 
in two senses, or the cliissihcation be given up, and. the technical 
sense of the term be abandoned along witU it. 

Worcjs not otherwise connotativt; may,"in the mode just adverted to, 
actjuire a special or technical connotation. ' Thus the word whiteness, 
as we have so often remarked, connotes nothiirg, it merely d^^note^s the 
attribute con'osponding to a ^e^rtain sensation; but if vve are making 
a classification of colors, and desire to justify, or even merely to point 
out, tin; particular place assigned to w^hiteness in bur arrangement, we 
may df;fme it, *'tho ^olor produced by the mixturt) of all the simple 
rays;" and this fact, though by no means implied in the meaning of 
the word whiteness as ordinarily used, but only known by fivdjse(pjent 
scientific investigation, is part of its meaning in the particular essay or 
treatise, and becomes- the diflerentia of the species.* 

The diff(;rentia, therefore, of a fipecies, may be defined to be, that 
part of th(5 connotaticm of the sj)ecific name, whether ordinary, or 
special and tet^hnical, which distinguishes the 8pf;cies in question from 
all other sptjcic^s of the genus to which on the ])articulur occasion wo 
are referring it. 

§ 7. Having disposed of Gcmus, Species, and DifT'ei'entia, we shall 
not find much difficulty in attaining a clear crmception of the distinction 
between the other two predicables. 

In the Aristotelian phraseology. Genus and Bifferontia are of the 
essence of the subject;^ by which; as wo have seen, is rcAlly meant that 
the properties signified by the genus and those signified by the differ- 
entia, form part of the connotation of the name denoting the sj)ccies. 
Proprium and Accidens, on the other hand, form no part of the essence; 
but are predicated of the species only accKhiUaUy. Btrth are Acci- 
dents in the wider sense, ih which the accidents of a thing are opposed 
tQ it8 essence ; although, in the doctrine of the. Predicables, Accidens 
is used for one sort of accident only, Proprium being another sort. 

* If wo allow a diflnrontia to wliat is not roally a species. For the distinction of Kinds, 
in the sense explnined by vis, not hoing jn any way applicable to attributes, it of course fol- 
lows, that althougii attributes may be put into classes, those classes can be admitted to be 
genera or species only 1/y courtesy. 

M 



90 NAMES AND PROPOSITIONS. 

Propriumj continue the sclioolmen, is predicated accidentally, indeed, 
but necessarily ; or, as they further explain it, signifies an attribute 
which is not indeed part of the essence, but which flows ii"oni, or is a 
consequence of, the essence, and is, therefore, inseparably attached to 
the species ; e. g., the various properties of a triangle, which, though 
no part of its definition, must necessarily be possessed by whatever 
comes under that definition. Accidens, on the contrary, has no con- 
nexion whatever with the essence, but may come and go, and the 
species still remain what it was before. If a species could exist 
without its Propria, it must be capable of existing without that upon 
which its Propria are necessarily consequent, and therefore without its . 
essence, without that which constitutes it a species. But an Accidens, 
whether separable or inseparable from the species in actual experience, 
may be supposed-separated, without the necessity of supposing any 
other alteration; or at; least, without supposing any of the, essential 
properties of the- Species altei^ed/sinGe with them an Accidens' Isja^'liO' 
connexion. , ; ,: ' \ . > ' , ■ 

A Proprium, therefore, of the species, "may be defined, any attribute 
which belongs to all the individuals included in the species, and which, 
although not connoted by the specific name (either ordinarily if the 
classification we are considering be for ordinary purposes, or specially 
if it be for a special purpose), yet follows from some attribute which 
the name either ordinarily or specially connotes. 

One attribute may follow from another in two ways ; and there are 
consequently two kinds of Proprium. It may follow as a conclusion 
follows premisses, or it may follow as an effect follows a cause. Thus, 
the attribute of having the opposite sides equal, which is not one of 
those connoted by the word Parallelogram, nevertheless follows from- 
those connoted by it, namely, from having the opposite sides sti-aight 
lines, and parallel, and the number of sides four. The attribute, • 
therefore, of having the opposite sides equal, is a Proprium of the 
class parallelogram ; and a Proprium of the first kind, which follows 
from the connoted attributes by way of demonstration. The attribute 
of being capable of understanding language is a Proprium of the 
species vian, since, without being connoted by the word, it follows 
from an attribute' which the word does connote, viz., fi'ora the attribute 
of rationality. But this is a Proprium of the second kind, which fol- 
lows by way of causation. How it is that one property of a thing 
follows, or can be inferred from another; under what conditions this 
is possible, and what is the exact meaning of the phrase; are among 
the questions which will occupy us in. the two succefeding Books. At 
present it needs only b6 said, that whether a Proprium follows by 
demonstration or by causation, it follows necessarily ; that is to say, it 
cannot hut follow, consistently with some law which we regard as a 
2)art of the constitution either of our thinking faculty or of the universe. 

§ 8. XJTuler the terrlainingpredieabl^, Accidens, are included all 
attributes of a thing which are neither involved in the signification of 
the name (whether ordinarily or as a term of art), nor have, so far as 
we know, any necessary connexion with attributes which are so in- 
volved. Thqy arc commonly divided into Separable and Inseparable 
Accidents.; Inseparable accidents arc those which — although we knovv 
of no connexion between them and the attributes constitutive of the 



DEFINITION. 91 

species, and although, therefore, so far as we are aware, they might 
be absent without making the name inapplicable and the species a 
different species — are yet never, in fact, known to be absent. A con- 
cise mode of expressing the same meaning is, that inseparable acci- 
dents are properties which are universal to the species but not neces- 
sary to it. . Thus, blackness is an' attribute of a crow, and, asfar as we 
know, an universal one. But if we were to discover a race of white 
birds, in other respects resembling crows, we should not say. These 
are not crows ; we should say, These are white crows. Crow, there- 
fore, does not connote blackness ; nor, from any of the attributes which 
it does connote, whether as a word in popular use or as a term of art, 
could blackness be inferred. Not only, therefore, can we conceive a 
white crow, but we know of no reason why such an animal should not 
exist. Since, however, none butf black crows are known to exist, 
blackness, in the present state of our knowledge, ranks as an accident, 
but an inseparable accident, of the species crow. 

Separable Accidents are those which are found, in point of fact, to 
be sometimes absent j&om the species ; which are not only not neces- 
sary, but not even universal. They are such as do not belong to every 
individual of the species, but only to some individuals; or if to all, not 
at all times. Thus, the color of an European is one of the separable 
accidents of the species man, because it is not an attribute of all human 
creatures. Being born, is also a separable accident of the species 
man, because although an attribute of all human beings, it is so only 
at one particular time. A fortiori those attributes which are not 
constant even in the same individual, as, to be in one or in another, 
place, to be hot or cold, sitting or walking, must be ranked as sepa- 
rable accidents. 



• V .CHAPTER VIII. 

\ - :•*/ ' #' .';, OF. DEFINITION. . '* \ ^-'C ? ; •. • '•• 

' § 1. One. necessary part of the theory of NaineS; arid of Propositions 
remains to be treated of in this place ; the theory of Definitions. As 
being the most important of the class of propositions which we havfe 
characterized as purely verbal, they have already received some notice 
in the chap ter.^ preceding the last. But their fuller treatment was at 
that time postponed, because definition is so closely connected with 
classification, that, until the nature of the latter process is in some 
measure understood, the former cannot be discussed to much purpose. 

§ 2. The simplest and most coiTect notion of a Definition is, a prop- 
osition declaratory of the meaning of a word; namely, either the 
meaning which it bears in, common acceptation, or that which the 
speaker or writer, for the particular purposes of his discourse, intends 
to annex to it. 

The definition of a word being tlie proposition which enunciates its 
meaning, words which have no meaning are unsusceptible of definition. 
Proper names, therefore, cannot be defined. A proper name being a 
mere mark put upon an individual, and of which it is the characteristic 



92 NAMES AND rROPOSITIONS. 

property to be destitute of meaning, its meaning cannot of course be 
declared ; though we may indicate by language, as we might indicate 
still more conveniently by pointing with the finger, upon what individ- 
ual that particular mark has been, or is intended to be, put. It is no 
definition of " John Thomson" to say he is " the son of Gen-eral 
Thomson;" for the name John Thomson does not express this. Nei- 
ther is it any definition of " John Thomson" to say he is " the man 
now crossing the street." These propositions may serve to make 
known who is the particular man to whom the name belongs ; but 
that may be done still more unambiguously by pointing to him, which, 
however, has not usually been esteemed one of the modes of definition. 
In the case of connotative names, the meaning, as has been so often 
observed, is the connotation; and the definition of a connotative name 
i& the proposition which declares its' connotation. This may be done 
either directly or indirectly. The direct mode would be by a propo- 
sition in this form : " Man" (or whatsoever the word may be) " is a 
name connoting such and such attributes," or *' is a name which, when 
predicated of anything, signifies the possession of such and such attri- 
butes by that thing." Or thus : Man is everything which possesses 
such and such attributes : Man is 'everything which possesses corpo- 
reity, organization, life,- rationality, and a form resembling that of the 
descendants of Adam. 

, This form of definition is the most precise and least equivocal of 
any ; but it is not brief enough, and is besides too technical and pe- 
• dantic for common discourse. The more usual mode of declaring the 
connotation of a name, is to predicate of it another name or names of 
known signification, which connote the same aggregation of attributes. 
This may be done either by predicating of the name intended to be 
defined, another connotative name exactly synonymous, as, " Man is a 
human being," which is not commonly accounted a definition at all; 
or by predicating two or more connotative names, which make up 
among them the whole connotation of the name to be defined. In this 
last case, again, we may either compose our definition of as many con- 
notative names as there are attributes, each attribute being connoted 
by one; as, Man is a corporeal, organized, animated, rational being, 
shaped so and so; or we may employ names which connote several of 
. the attributes at once, as, Man is a rational animal, shaped so and so. 
The definition of a name, according to this view of it, is the sum 
total of all the essential propositions which can be framed with that 
name for their subject. All propositions the truth of which is implied 
in the name, all those which we are made aware of by merely hearing 
the name, are included in the definition if complete, and may be 
evolved from it- without the aid of any other premisses ; whether the 
definition expresses them in two or three words, or in a larger num- 
bei\ It is, therefore, not without reason that Condillac and other wri- 
ters have affirmed a definition to be an analysis,. To resolve any 
complex whole into the elements of which it is compounded, is the 
meaning of analysis ; and this we do when we replace one word which 
connotes a set of attributes collectively, by two or more which connote 
the same attributes singly, or in smaller gtoups. 

§ 3. From this, however, the question naturally arises, in what man- 
ner are we to define a name which connotes onlj a single attribute % 



DEFINITION. ..-.*' ( 93 

for instance, " white," which connotes nothing but whiteness ; "ra- 
tional," which connotes nothing but the possession of reason. It might 
seem that the meaning of such names could only be. declared in two 
ways ; by a synonymous term, if any such can be found ;, or in the 
direct way already alluded to : " White is a name connoting the attri- 
bute whiteness." Let us see, however, whether the analysis of the 
meaning of the name, that is, the breaking down of that meaning into 
separate parts, admits of being earned further. Without at present 
deciding this question as to the word white, it is obvious that in the 
case Q)i rational some further explanation may be given of its meaning 
than is contained in the proposition, " Rational is that which possesses 
the attribute of reason ;" since the attribute reason itself admits of be- 
ing defined. And here we must turn our attention to the definitions 
of attributes, or rather of., the names of attributes, that is, of abstract 
names. 

In regard to such names of attributes as are connotativoj and! ex- 
press attributes of those attributes, there is no difficulty : like other 
connotative names, they are defined by declaring then- connotation. 
Thus, the yvordi fault may be defined, " a quality productive of evil or 
inconvenience." Sometimes, again, the attribute to be defined is not, 
one attribute, but an union of several : we have only, therefore, to put 
together the names of all the attributes taken separately, and we ob^ 
tain the definition of the names which belong to them all taken together ; 
a definition which will correspond exactly to that of the corresponding 
concrete name. For, as we define a concrete name by enumerating 
the attributes which it connotes, and as the attributes connoted by a 
concrete name form the entire signification of the corresponding ab- 
stract one, the same enumeration will serve for the definition of both. 
Thus, if the definition of a human heing be this, "A being, corporeal, 
animated, rational, and shaped so and so," the definition of humanity ^^ 
will be, corporeity and animal life, combined with rationa,lity, and with' 
5uch and such a shape. • - • . 

■_ When, on the other hand, the abstract name does not express a 
complication of attributes, but a single attribute, we must remembe'r 
that every attribute is grounded upon some fact or phenomenon, from 
which and which alone it derives its meaning. To that fact or phe- 
nomenon, called in a former chapter the foundation of the attribute, 
we must, therefore, have recourse for its definition. Now, the foun- 
dation of the attribute may be a phenomenon of any degree of com- 
plexity, consisting of many different parts, either coexistent or in 
succession. To obtain a definition of the attribute, we must analyze 
the phenomenon into these parts. Eloquence, for example, is the 
name of one attribute only ; but this attribute is grounded upon exter^ 
lial effects of a complicated nature, flowing fi'om acts of the person to 
whom we ascribe the attribute ; and by resolving this phenomenon of 
causation into its two parts, the cause and the effect, we obtain a defi- 
nition of eloquence, viz., the power of influencing the affections of hu- 
man beings by means of speech or wTiting. 

A name, therefore, whether concrete or abstract, admits of defini- 
tion, provided we are able to analyze, that is, to distinguish into parts, 
the attribute or set of attributes which constitute the meaning both of 
the concrete name and of the- corresponding abstract : if a set of attri- 
butes, by enumerating them ; if a single attribute, by dissecting the 



94 - NAMES AND PROPOSITIONS. 

fact or phenomenon whether of perception or of internal consciousness, 
which is the foundation of the attribute. But, further, even when the 
fact is one of our simple feelings or states of consciousness, and there- 
fore unsusceptible of analysis, the names both of the object and of the 
attribute still admit of definition ; or, rather, would do so if all our 
simple feelings had names. Whiteness may be defined, the property 
or power of exciting the sensation of white. A white object may be 

■ defined an object which excites the sensation of white. The only, 
names which are unsusceptible of definition, becausetheir meaning is 
unsusceptible of analysis, are the names of the simple feelings them- 
selves. These are in the same condition as proper names. They are 
not, indeed, like proper names, unmeaning; for the words sensation 
of white signify, that the sensation which I so denominate resembles 
other sensations which I remember to have had before, and to have 
called -by that name. But as we have no words by which to recall 

'those former sensations, except the very, word, which we seek to de- 

■ fine, or some -other which, being exactly synonymous with it, requires 
definition as much,, words cannot unfold the signification of this class 
of names ; and we are obliged to make a direct appeal to the personal 
experience of the individual whom we address. ' , 

§ 4. Having stqite'd what seems to be the trueidfiia of-aOefitiition, we 
proceed to examine some opinions of philosophers, and some popular 
conceptions on the subject, which conflict more or less with the above." 

The only adequate definition of a name is, as already remarked, one 
which declares the facts, and the whole of the facts, which the name 
involves in its signification. But with most persons, the object of a 
definition does not embrace so much; they look for nothing more, in 
a definition; than ^guide^to the correct use of the term— a protection- 
against applying it in a manner inconsistent- with custom and conven- 
tion. Anything, therefore, is to them a sufficient definition of a term, 
which will serve as a- correct index to wjiat the term denotes ; although 
not embracing the .'whole, and sometimes, perhaps, not even any part, 
.of what it conhoteg. This gives rise to two sorts of imperfect, or un- 
scientific definitions ; namely, Essential but incomplete Definitions, and 
Accidental Definitions, or Descriptions. In the former, a connotative 
name is defined by a part only , of its ' connotation ; in the latter, by 
something which. forms no part of the connotation at all. : : , 

An example of the first kind of imperfect definitions is thip follow- 
ing : Man is a rational animd;!. , If is impossible to consider this as.. a 
conjiplete definition of the Xvord Man, &ince (as before remai'ked) if we 
adhered to it we should be ol)liged- to call the Plouyhnhmsinen; but 
as there happen to be no Houyhnhms, this imperfect definition is suf- 
n'cient to mark out and distinguish from all other things, the objects at 
' present denoted by "man;" all the beings actually known t^o exist, of 
whom the name is predicable. Though the word is defined by some 
only- among the attributes which it connotes, not by all, it happens that 
all known objects which possess, the enumerated attidbutes, possess 
also' those \'fhich are omitted; so that tlie field of predication which the 
word covers,, and the ernploytoent of it which is conformable to usage, 
are as well indicated by the .inadequate- definition as by an adequate 
one. Such definitions, ho Wever, -are always liable to be overthrowri 
>>y tl)e discovery of new objects in n^iture. ' ' 



..N.\- DEFINITION. •.. rrr,.'-" --95 

Definitions of this kind are what logicians have had in view "vv^^n 
thej laid down the rule, that the definition of a s|)ecies should be\^er 
genus et differentiam. Differentia being seldom, taken to mean the 
whole of the peculiarities constitutive of the species, but some one of. 
those peculiarities only, a complete definition would be jper genus tt 
differentias, rather than differentiam. It would include, with the name 
of the superior genus, not merely, -some attribute which distinguishes' 
the species intended to be defined fi'om all other species of the same 
g-enus, but all the attributes implied in the name of the species, which 
the name of the superior genus has n,ot already implied. The asser- 
tion, however, that a definition must 'of necessity consist, of a genua •. 
and differentiae, is not tenable. It was early remarked by logicians,, 
that the sutmnum genus in any classification, having no genus superior 
to, itself, could not be defined in this manner. Yet we have seen that 
all names, except those of our elementai-y feelings, are susceptible of 
definition in the strictest sense ;' by setting forth in words the constit- 
uent parts of the fact or phenomenon, of which the connotation of every 
word is ultimately composed. '" .' , 

§ 5. Althou'gfb the first kind of imperfect definition (which defines a 
connotative term by a part only of what it connotes, but a part sufficient 
to mark out correctly the boundaries of its denotation), has been con- 
sidered by the ancients, and by logicians- in general, as a complete 
definition ; it has always been deemed necessary that the attributes 
employed should really form part of the connotation; for the rule was 
that the definition mufet be draw^n from ihe essence oi \\iq class ; and this 
would notjiave been the case if it had been in any degree made up of 
attributes not connoted by the name. .The second kind of imperfect 
definition, therefore, in which tUe name of a class is defined by any of 
its accidents — -that is, by attributes which are not included in its conno- 
tation — has been, rejected from the rank' of genuine Definition -by all 
philosophers, and has been termed Description. ' - ' , / '■■'■:' 

This kind of imperfect' definition,, however, takes its^ ia^e» froift'.tK'e 
same cause as the other, namely, the willingness to accept as a defini- 
tion anything which, whether it expounds the meaning of the name or 
•not, enables us to discriminate the things denoted by the name from all 
other things, and consequently to employ the term' in predication with- 
out deviating from established usage. This purpose is duly answered 
by stating any (no matter what) of the' attributes which are common to 
the whole of the class, and peculiar to, it- or*: any combination of attri- 
butes which may happen to be peculiar' to- it, although separately each 
ofthoae attributes, may be common to it with, some other things. It js 
only necessary that the definition (or description) thus formed, should 
be convertible with the name which it professes to define ; that is, should 
"be exactly co-extensive with it, being predicable of. everything of whicli- 
it is predicable, and of nothing of which it is not predicable : although 
the atti'ibutes specifi.ed may have no connexion with, those which men ■ 
had in view when they formed or recognized the class, and gave it.-.a 
name. The following are con-ect definitions of Mail, according to i}(A^ 
test: Man is a mammiferous animal, ha\ing (by nature) two hands 
(for the human. species answerg,to this description,. and no other animal 
does) : Man .is ' an. animal -who cooks 'his food": Man is a featherless 
biped. /.< ' . ^" -' '■ ^ ' •' " . • ' ., ■ ..^ . J 



96 NAMES AND PROPOSITIONS,' 

What would otKerwise-Jbe a mere d^rscription, may b^fatised to the 
rank of a real definition by the peculiar purpose which thfe speaker or 
writer has in view. As was seen in the preceding chapter, it may, for 
the ends of a particular art or science, or for the more convenient 
statement of an author's particular views, be advisable to give to some 
general name, without altering its denotation, a special connotation, " 
difierent from its otdinary one. When this is done, a definition of the 
name by means of the attributes which make up the special connota- 
tion, though in general a mere accidental definition, or description, 
becomes on the particular occasion and for the particular purpose, a 
complete and genuine definition. This actually occurs with respect 
to one of the preceding examples, " Man. is a mammiferous animal 
having two hands," which, is the scientific definition of man con- 
sidered as one of th,e species in Cuvier's distribution of the ajiimal 
kingdom. ' - 

In cases of this sort, although the definition is still a declaration of 
the meaning which in the particular instance the name is appointed to 
convey, it cannot be said that to state the meaning of the word is the 
purpose of the definition. • The purpose is not to expound a name, but 
to help to expound a classification. The special meaning which Cuvier 
assigned to the word Man (quite foreign to its ordinary meaning,'-, 
though involving no change in the denotation of the word), was inci- • 
dental to a plan of arranging animals into classes on a certain principle, 
that is, according to a certain set of distinctions. -And since the defi- 
nition of Man according to the ordinary connotation of the word, though,' 
it would have answered every other purpose of a definition, would not 
have pointed out the place which the species ought to occupy in that 
particular classification ; he gave the word a special connotation, that 
he might be able to define it by the kind of attributes upon which, for 
reasons of scientific convenience, he had resolved to found his division. < 
of animated nature. ,*/'«,'. .•'•..'»■ 

Scientific definitions, whetb'ef they are definitions of scientific terms', 
or of common terms used in a scientific sense, are almost always of the 
kind last spoken of: their main purpose is to serve as the landmarks .-. 
of scientific classification. And since the classifications in any science 
are continually modified as scientific knowledge advances, the defi-- 
nitions in the sciences are also constantly varying. A striking instance 
is afforded by the words Acid and Alkali, especially the fonner. As '. 
experimental discovery advanced, the substances classed with acids 
have beeri constantly multiplying, and by a natural consequence the - 
attributes connoted by the word have receded and hecome fewer. At 
first it connoted the attributes, of combining with an alkali to form a- 
neutral substance (called a Salt); being compounded of a base and-^ 
oxygen ; causticity to the taste and touch; fluidity, &c. The true , 
analysis of muriatic acid, into chlorine and hydrogen, caused the second'" 
-property, composition from a base and oxygen, to be excluded from 
the connotation. The sam.c discovery fixed the attention of chemists 
upon hydrogen as an imp<n-tant element in acids ; and more recent 
discoveries having led to the recognition of its presence in sulphuric, 
nitri(',"'and many other acids, where its existence was not previously 
suspected, there is now a tendency to include the presence of this ele- 
ment in^ the connotation of the word. But carbonic acid, sihca, sulphu- 
rous acid, have no hydrogen in their composition j that property cap- 



DEFINITION. 97 

not therefore be connoted by the term, unless tbose substances are no 
longer to- be considered acids. Causticity and fluidity have long since 
been excluded from the characteristics of the class, by the inclusion of 
silica and many other substances in it ; and the formation of neutral 
bodies by combination with alkalis, together with such electro-chemi- 
cal peculiarities as this is supposed to imply, are now the only differ- 
enticB which form the fixed connotation of the word Acid, as a term of 
chemical science. 

Scientific men are still seeking, and may be long ere they find, a 
suitable definition of one of the earliest words in the vocabulary of the 
human race, and one of those of which the popular sense is plainest 
and best understood. The word I mean is Heat; and the source of 
the difficulty is the imperfect state of our scientific knowledge, which 
has shown to us multitudes of phenomena certainly connected with the 
same power which is the cause of what our senses recognize as heat, 
but has not yet taught us the laws of those phenomena with suflficient 
accuracy to admit of our determining under what characteristics the 
whole of those phenomena shall ultimately be embodied as a class : 
which characteristics would of course be so many differentiae for the 
definition of the power itself. We have advanced far enough to know 
that one of the attributes connoted must be that of operating as a 
repulsive force : but this is certainly not all which must ultimately be 
included in the scientific definition of heat. 

What is true of the definition of any term of science, is of course 
true of the definition of a science itself: and accordingly, we showed 
in the Introductory Chapter of this work, that the definition of a science 
must necessarily be progressive and provisional. Any extension of 
knowledge, or alteration in the current opinions respecting the subject 
matter,, inay lead to a change more or less extensive in the particulars 
included in the science ; and its composition being thus altered, it may 
easily happen that a different set of characteristics will be found better 
adapted as differentite for defining its name. 

In the same manner in which, as we have now shown, a special or 
technical definition has for its object to expound the artificial classi- 
fication out of which it grows; the Aristotelian logicians seem to have 
imagined that it was also the business of ordinary definition to expound 
the ordinary, and what they deemed the natural, classification of things, 
namely, the division of them into Kinds ; and to show the place which 
each Kind occupies, as superior, collateral, or subordinate, among 
other Kinds. This notion would account for the rule that all defi- 
nition must necessarily be per genus et differentuirn, and would also 
explain why any one differentia was deemed sufficient. But to 
expound, or express in Vv'ords, a distinction of Kind, has already been 
shown to be an impossibility : the very meaiiing of a Kind is, that the 
properties w^hich distinguish it do not grow out of one another, and 
cannot therefore be set forth in words, even by implication, otherwise 
than by enumerating them all : and all are not known, nor ever will be 
so. It is idle, therefore, to look"^ to this as one of the purposes of a 
definition : while, if it be only required that the definition of a Kind 
should indicate what Kinds include it or are included by it, any defi- 
nitions which expound the connotation of the names will do this : for 
the name of each class must necessarily connote enough of its proper- 
ties to fix the boundaries of the class. If the definition, therefore, is 
N 



98 NAMES AND PROPOSITIONS. 

a full statement of the connotation it is all that a definition can be 
required to be. 

§ 6. Of the two incomplete or unscientific modes of definition, and 
in what they differ from the complete or scientific mode, enough has 
now been said. We shall next examine an ancient doctrine, once 
generally prevalent and still by no means exploded, which I regard as 
the source of a great part of the obscurity hanging over some of the 
most important processes of the understanding in the pursuit of truth. 
According to this, the definitions of which we have now treated are 
only one of two sorts into which definitions may be divided, viz., 
definitions of names, and definitions of things. The former are intended 
to explain the meaning of a term ; the latter, the nature of a thing ; the 
last being incomparably the most important. 

This opinion was held by the ancient philosophers, and by their fol- 
lowers, with the exception of the Nominalists; but as the spirit of 
modern metaphysics, until a recent period, has been on the whole a 
Nominalist spirit, the notion of definitions of things has been to a cer- 
tain extent in abeyance, still continuing, however, to breed confusion 
in logic, by its consequences indeed rather than by itself. Yet the 
doctrine in its own proper form now and then breaks out, and has ap- 
peared (among other places) where it was scarcely to be expected, in 
a deservedly popular work. Archbishop Whately's Logic. In a re- 
view of that work published by me in the Westminster Preview for 
January 1828, and containing some opinions which I no longer enter- 
tain, I find the following observations on the question now before us ; 
observations with which my present views on that question are still 
sufficiently in accordance. 

"The distinction between nominal and real definitions, between 
definitions of words and what are called definitions of things, though 
conformable to -the ideas of most of the Aristotelian logicians, cannot, 
as it appears to us, be maintained. We apprehend that no definition 
is ever intended -to ' explain and' unfold the nature of the thing.' It is 
some confirmation of our opinion, that none of those writers' who have 
thought that there were definitions of things, have ever succeeded in 
discovering any criterion by which the definition of a thing can be dis- 
tinguished from any other proposition relating to the thing. The 
definition, they gay, unfolds the nature of the thing : but no definition 
can unfold its whole nature ; and every proposition in which any qual- 
ity whatever is predicated of the thing, unfolds some part of its nature. 
The true state of tke case we take to be this. All definitions are of 
names, and of names only : but, in some definitions, it is clearly ap- 
parent, that nothing is intended except to explain the meaning of the 
word ; while in .others, besides explaining the meaning of the word, it 
is intended to be implied that there exists a thing, corresponding to 
the word. Whether this be or be not implied in any given case, 
cannot be collected from the mere form of the expression. ' A cen- 
taur is an animal with the upper parts of a man and the lower parts of 
a horse,' and ' A triangle is a rectilineal figure with three sides,' are, 
in form, expressions precisely similar ; although in the former it is not 
implied that any thing, conformable to the term, really exists, while in 
the latter it is ; as may be seen by substituting, in both definitions, the 
word means iovis. In the first expression, ' A centaur means an an- 



DEFINITION. 99 

imal,' &c., the sense would remain unchanged : in the second, ' A tri- 
ano-le means,' &c., the meaning would be altered, since it would be 
obviously impossible to deduce any of the truths of geometry from a 
proposition expressive only of the manner in which we intend to em- 
ploy a particular sign. 

" There are, therefore, expressions, commonly passing for definitions, 
which include in themselves more than the mere explanation of the 
meaning of a term. But it is not correct to call an expression of this 
sort a peculiar kind of definition. Its difference from the other kind 
<ionsists in this, that it is not a definition, but a definition and something 
more. The definition above given of a triangle, obviously comprises 
not one, but two propositions, perfectly distinguishable. The one is, 
* There may exist a figure, bounded by three straight lines :' the other, 
•' And this figure may be termed a triangle.' The former of these pro- 
positions is not a definition at all : the latter is a mere nominal defini- 
tion, or explanation of the use and application of a term. The first is 
susceptible of truth or falsehood, and may therefore be made the foun- 
dation of a train of reasoning. The latter can neither be true nor false ; 
the only character it is susceptible of is that of conformity or discon- 
formity to the ordinary usage of language." 

There is a real distinction, then, between definitions of names, and 
what are erroneously called definitions of things ; but it is, that the 
latter, along with the meaning of a name, covertly asserts a matter of 
fact. This covert assertion is not a definition, but a postulate. The 
definition is a mere identical proposition, which gives information only 
about the use of language, and from which no conclusions affecting 
matters of fact can possibly be drawn. The accompanying postulate, 
on the other hand, afiarms a fact, which may lead to consequences of 
every degree of importance. It aflSrms the real existence of Things 
possessing the combination of attributes set forth in the definition ; and 
this, if true, may be foundation suflScient on which to build a whole 
fabric of scientific truth. 

We have already made, and shall often have to repeat, the remark, 
that the philosophers who overthrew Realism by no means got rid of 
the consequences of Realism, but retained long afterwards, in their 
own philosophy, numerous propositions which could only have a ra- 
tional meaning as part of a Realistic system. It had been handed down 
from Aristotle, and probably from earlier times, as an obvious truth, 
that the science of Geometry is deduced from definitions. This, so 
long as a definition was considered to be a proposition " unfolding the 
nature of the thing," did well enough. But Hobbes camfe, and re- 
jected utterly the notion that a definition declares the nature of the 
thing, or does anything but state the meaning of a name ; yet he con- 
tinued to afiirm as broadly as any of his predecessors, that the dpxat, 
princijna, or original premisses of mathematics, and even of all science, 
are definitions ; producing the singular paradox, that systems of scien- 
tific truth, nay, all truths whatever at which we amve by reasonino-, 
are deduced from the arbitrary conventions of mankind concerning the 
signification of words. 

To save the credit of the doctrine, that definitions are the premisses 
of scientific knowledge, the proviso is sometimes added, that they are 
so only under a certain condition, namely, that they be framed' con- 
formably to the phenomena of nature j that is, that they ascribe such 



100 NAMES AND PROPOSITIONS. 

meanings to terms as shall suit objects actually existing. But this is 
only an instance of the attempt, too often made, to escape from the 
necessity of abandoning old language after the ideas which it expresses 
have been exchanged for contrary ones. From the meaning of a name 
(we are told) it is possible to infer physical facts, provided the name 
has, corresponding to it, an existing thing. But if this proviso be ne- 
cessary, from which of the two is the inference really drawn 1 fi'om the 
existence of a thing having the properties 1 or from the existence of a 
name meaning them 1 

Take, for instance, any of the definitions laid down as premisses in 
Euclid's Elements ; the definition, let us say, of a circle. This, being 
analyzed, consists of two propositions ; the one an assumption with 
respect to a matter of fact, the other a genuine definition. " A figure 
may exist, having all the points in the line which bounds it equally 
distant from a single point within it:" "Any figure possessing this 
property is called a circle," Let us look at one of the demonstrations 
which are said to depend on this definition, and observe to which of 
the two propositions contained in it the demonstration really appeals. 
*' About the centre A, describe the circle B C D." Here is an assump- 
tion, that a figure, such as the definition expresses, may be described : 
which is no other than the postulate, or covert assumption, involved in 
the so-called definition. But whether that figure be called a circle or 
not is quite immaterial. The purpose would be as well answered, in 
all respects except brevity, were we to say, " Tlirough the point B^ 
draw a line returning into itself, of which every point shall be at an 
equal distance from the point A." By this the definition of a circle 
would be got rid of, and rendered needless, but not the postulate im- 
plied in it ; without that the demonstration could not stand. The circle 
being now described, let us proceed to the consequence, " Since 
B C D is a circle, the radius B A is equal to the radius C A." B A is 
equal to C A, not because B C D is a circle, but because B C D is a 
figure with the radii equal. Our waiTant for assuming that such a 
figure about the centre A, with the radius B A, may be made to exist, 
is the postulate.— The admissibility of these assumptions may be 
intuitive, or may admit of proof; but in either case they are the 
premisses on which the theorems depend ; and while these are retained 
it would make no diflference in the certainty of geometrical truths, 
though every definition in Euclid, and every technical term therein 
defined, were laid aside. 

It is, perhaps, superfluous to dwell at so much length upon what is 
so nearly self-evident; but when a distinction, obvious as it may 
appear, has been confounded, and by men of the most powerful intel- 
'lect, it is better to say too much than too little for the purpose of 
rendering such mistakes impossible in future. We will, therefore, 
detain the reader while we point out one of the absurd consequences 
flowing from the supposition that definitions, as such, are the premisses 
in any of our reasonings, except such as relate to words only. If this 
supposition were true, we might argue coiTectly from true premisses, 
and an-ive at a false conclusion. We should only have to assume as a 
premiss the definition of a non-entity : or rather of a name which har. 
no entity corresponding to it. Let this, for instance, be our definition : 
A dragon is a serpent breathing flame. 

This proposition, considered only as a definition, is indisputably 



DEFINITION. 101 

coiTCCt. A dragon is a serpent breathing flame : the word means that. 
The tacit assumption, indeed (if there were any such understood 
assertion), of the existence of an object with properties con-espondirig 
to the definition, would, in the present instance, be false. Out of this 
definition we may carve the premisses of the following syllogism : 

A dragon is a thing which breathes flame : 

But a dragon is a serpent : 
From which the conclusion is, 

Therefore some serpent or serpents breathe flame : — 
an unexceptionable syllogism, in the first mode of the third figure, in 
which both premisses are true and yet the conclusion false ; which 
every logician knows to be an absurdity. The conclusion being false 
and the syllogism correct, the premisses cannot be true. But the 
premisses, considered as parts of a definition, are true : there is no 
possibility of controverting them. Therefore, the premisses considered 
as parts of a definition cannot be the real ones. The real premisses 
must be : 

A dragon is a really existing thing which breathes flame : 

A dragon is a 7'eaUy existing serpent : 
which implied premisses being false, the falsity of the conclusion pre- 
sents no absurdity. If we would determine what conclusion follows 
from the same ostensible premisses when the tacit assumption of real 
existence is left out, let us, according to the recommendation in the 
Westminster Review, substitute means for is. We then have : 

A dragon is a word meaning a thing which breathes flame : 

A dragon is a word meaning a serpent : 
From which the conclusion is. 

Some word or words ivliich mean a serpent, also mean a thing 
which breathes flame : 
where the conclusion (as well as the premisses) is true, and is the only 
kind of conclusion which can ever follow from a definition, namely, a 
proposition relating to the meaning of words. If it relate to anything 
else, we may know that it does not follow from the definition, but from 
the tacit assumption of a matter of fact. 

It is only necessary further to inquire, in what cases that tacit as- 
sumption is really made, and in what cases not. Unless we declare 
the contrary, we always convey the impression that we intend to make 
the assumption, when we profess to define any name which is already 
known to be a name of really existing objects. On this account it is, 
that the assumption was not necessarily implied in the definition of a 
dragon, while there was no doubt of its being included in the defini- 
tion of a cii'cle. 

§ 7. One of the circumstances which have contributed to keep up 
the notion, that demonstrative truths follow from definitions rather 
than from the postulates implied in those definitions, is, that the pos- 
tulates, even in those sciences which are considered to sui-pass all 
others in demonstrative certainty, are not always exactly true. It is 
not true that a circle exists, or can be described, which has all its radii 
exactly equal. Such accuracy is ideal only ; it is not found in nature, 
still less can it be realized by art. People had a difficulty, therefore, 
in conceiving that the most certain of all conclusions could rest upon 
premisses which, instead of being certainly true, are certainly not true 



102 NAMES AND PROPOSITIONS. 

to the whole extent asserted. This apparent paradox will be examined 
when we come to treat of Demonstration ; where we shall be able to 
show that as much of the postulate is true, as is required to support as 
much as is true of the conclusion. Philosophers, however, to whom 
this view had not occurred, or whom it did not satisfy, have thought it 
indispensable that there should be found in definitions something more 
certain, or at least more accurately true, than the implied postulate of 
the real existence of a corresponding object. And this something 
they flattered themselves they had found, when they laid it down that 
a definition is a statement and analysis not of the mere meaning of a 
word, nor yet of the nature of a thing, but of an idea. Thus, the 
proposition, " A circle is a plane figure bounded by a line all the points 
of which are at an equal distance from a given point within it," was 
considered by them, not as an assertion that any real circle has that 
property (which would not be exactly true), but that we conceive a 
circle as having it : that our abstract idea of a circle is an idea of a 
figure with its radii exactly equal. 

Conformably to this it is said, that the subject matter of mathemat- 
ics, and of every other demonstrative science, is not things as they 
really exist, but abstractions of the mind. A geometrical line is a line 
without breadth ; but no such line exists in nature ; it is a mere notion 
made up by the mind, out of the materials in nature. The definition 
(it is said) is a definition of this mental line, not of any actual line : 
and it is only of the mental line, not of any line existing in nature, that 
the theorems of geometry are accurately true. 

Allowing this doctrine respecting tlje nature of demonstrative truth 
to be correct (which, in a subsequent place, I shall endeavor to prove 
that it is not) ; even on that supposition, the conclusions which seem 
to follow from a definition, do not follow from the definition as such, 
but from an implied postulate. Even if it be true that there is no 
object in nature answering to the definition of a line, and that the 
geometrical properties of lines are not true of any lines in nature, but 
only of the idea of a line ; the definition, at all events, postulates the 
real existence of such an idea : it assumes that the mind can frame, or 
rather has framed, the notion of length without breadth, and without 
any other sensible property whatever. According to what appears to 
me the sounder opinion, the mind cannot form any such notion; it 
cannot conceive length without breadth : it can only, in contemplating 
objects, attend to their length exclusively of their other sensible quali- 
ties, and so determine what properties may be predicated of them in 
virtue of their length alone. If this be true, the postulate involved in 
the geometrical definition of a line, is the real existence, not of length 
without breadth, but merely of length, that is, of long objects. This 
is quite enough to support all the truths of geometry, since every 
property of a geometrical line is really a property of all physical 
objects possessing length. But even what I hold to be the false doc- 
trine on the subject, leaves the conclusion that our reasonings are 
grounded upon the matters of fact postulated in definitions, and not 
upon the definitions themselves, entirely imaffected ; and accordingly 
I am able to appeal in confirmation of this conclusion, to the authority 
of Mr. Whewoll, in his recent treatise on The PhilosopJiy of the In- 
ductive Sciences. On the nature of demonstrative truth, Mr. Whewell's 
opinions are greatly at variance with mine, but on the particular point 



DEFINITIONS. 103 

in question it gives me great pleasure to observe, that tliere is a com- 
plete agreement between us. And here, as in many other instances, 
I gladly acknowledge that his writings are eminently serviceable in 
clearing fi-om confusion the initial steps in the analysis of the mental 
processes, even where his views respecting the ultimate analysis (a 
matter generally of far less importance) are such as (though with un- 
feigned respect) I cannot but regard as fundamentally erroneous. 

§ 8. Although, according to the views here presented. Definitions 
are properly of names only, and not of things, it does not follow that 
definition is an easy matter. How to define a name, may not only be 
an inquiry of considerable difiiculty and intricacy, but may turn upon 
considerations going deep into the nature of the things which are 
denoted by the name. Such, for instance, are the inquiries which 
form the subjects of the most important of Plato's Dialogues; as, 
" What is rhetoric 1" the topic of the Gorgias, or " What is justice V 
that of the Republic. Such, also, is the question scornfully asked by 
Pilate, " What is truth "?" and the fundamental question with specula- 
tive moralists in all ages, " What is virtue V 

It would be a mistake to represent these difficult and noble in- 
quiries as having nothing in view beyond ascertaining the conven- 
tional meaning of a name. They are inquiries not so much to 
determine what is, as what should be, the meaning of a name ; which, 
like other practical questions of terminology, requires for its solution 
that we should enter, and sometimes enter very deeply, into the prop- 
erties not merely of names but of the things named. 

Although the meaning of every concrete general name resides in 
the attributes which it connotes, the objects were named before the 
attributes ; as appears from the fact that in all languages, abstract 
names are mostly compounds or derivatives of the concrete names 
which con-espond to them. Connotative names, therefore, were, after 
proper names, the first which were used : and in the simpler cases, 
no doubt, a distinct connotation was present to the minds of those who 
first used the name, and was distinctly intended by them to be conveyed 
by it. The first person who used the word white, as applied to snow 
or to any other object, knew, no doubt, very well what quality he in- 
tended to predicate, and had a perfectly distinct conception in his mind 
of the attribute signified by the name. 

But where the resemblances and difierences on which our classifi- 
cations are founded are not of this palpable and easily determinable 
kind; especially where they consist not in any one quality but in a 
number of qualities, the effects of which being blended together are not 
very easily discriminated and referred each to its true source ; it often 
happens that names are applied to nameable objects, with no distinct 
connotation present to the minds of those who apply them. They are 
only influenced by a general resemblance between the new object and 
all or some of the old familiar objects which they have been accustom- 
ed to call by that name. This, as we have seen, is the law which even 
the mind of the philosopher must follow, in giving names to the simple 
elementary feelings of our nature : bat, where the things to be named 
are complex wholes, a philosopher is not content with noticing a gen- 
eral resemblance ; he examines what the resemblance consists in ; and 
he only gives the same name to things which resemble one another in 



104 NAMES AND PROPOSITIONS. 

the same definite particulars. The philosopher, therefore, habitually 
employs his general names with a definite connotation. But language 
was not made, and can only in some small degree be mended, by 
philosophers. In the minds of the real arbiters of language, general 
names, especially where the classes they denote cannot be brought 
before the tribunal of the outward senses to be identified and discrim- 
inated, connote little more than, a vague gross resemblance to the 
things which they were earliest, or have been most, accustomed to call 
by those names. When, for instance, ordinary persons predicate the 
words just or unjust of any action, nohle or Tnean of any sentiment, 
expression, or demeanor, statesman or charlatan of any personage 
figuring in politics, do they mean to affirm of those various subjects, 
any determinate attributes, of whatever kind % No ; they merely 
recognize, as they think, some likeness, more or less' vague and loose, 
between them and some other things which they have been accustomed 
to denominate or to hear denominated by those appellations. 

Language, as Sir James Mackintosh used to say of governments, 
" is not made, but grows." A name is not imposed at once and by 
previous purpose upon a class of objects, but is first applied to one 
thing, and then extended by a series of transitions to another and 
another. By this process (as has been remarked by several writers, 
and illustrated with great force and clearness by Dugald Stewart, in 
his Philosophical Essays), a name, not unfrequently ' .passes by suc- 
cessive links of resemblance from one object to,, another, until it 
becomes applied to things having nothing in common with the first 
things to which the name was given; which, however, do not, for that 
reason, drop the name ; so that it at last denotes a confused huddle, of 
objects, having nothing whatever in common ; and connotes nothing, 
not eveji a vague and general resemblance. When a name has fallen 
into this state, in which by predicating it of any object we assert 
literally nothing about the object, it has become unfit for the purposes 
either of thought or of the communication of thought ; and can only 
be made serviceable by stripping it of some part of its multifarious 
denotation, and confining it to. objects possessed of some attributes in 
common, which it may be made to connote. Such are the inconve- 
niences of a language which " is not made, but grows." Like a road 
which is not made but has made itself, it requires continual mending 
in order to be passable. 

From this it is already evident, why the question respecting the 
definition of an abstract name is often one bf so much difficulty. The 
question. What is justice 1 is, in other words, What is the attribute 
which mankind mean to predicate when they call, an action just % To. 
which the first answer is, that having come to no precise agreement on • 
the point, they do not mean to predicate distinctly any attribute at all. 
Nevertheless, all believe that there is some common attribute belonging 
to all the actions which they are in the habit of calling just. The 
question then must be, whether there is any such common attribute 1 
and, in the first place, whether mankind agree sufficiently with one 
another as to the particular actions which they do or do ^ot call just, 
to render the inquiry, what quality those actions have in common, a 
possible one : if so, whether the actions really have any quality in 
common ; and if they have, what it is. Of these three, the first alone 
is an inquiry into usage and convention ; the other two are inquiries 



DEFINITION. 105 

into matters of fact. And if the second question (whether the actions 
form a class at all), has been answered negatively, there remains a 
fourth, often more arduous than all the rest, namely, how best to form 
a class artificially, which the name may denote. 

Arid here it is fitting to remark, that the study of the spontaneous 
growth of languages is of the utmost importance to the philosopher 
who would logically remodel them. The classifications rudely made 
by established language, when retouched, as they almost always require 
to be, by the hands of the logician, are often in themselves excellently 
suited to many of his purposes. When compared with the classifica- 
tions of a philosopher, they are like the customary law of a country, 
which has gi'own up as it were spontaneously, compared with laws 
methodized and digested into a code : the former are a far less perfect 
instrument than the latter ; but being the result of a long, though 
unscientific, course of experience, they contain the greater part of the 
materials out of which the systematic body of written law may and 
ought to be formed. In like manner, the established grouping of 
objects under a common name, though it may be founded only upon a 
gross and general resemblance, is evidence, in the first place, that the 
resemblance is obvious, and therefore considerable ; and, in the next 
place, that it is a resemblance which has struck great numbers of 
persons during a series of years and ages. Even when a name, by 
successive extensions, has come to be applied to things among which 
there does not exist even a gross resemblance common to them all, 
still at every step in its progress we shall find such a resemblance. 
And these transitions of the meaning of words are often an index to 
real connexions between the things denoted by them, which might 
otherwise escape the notice even of philosophers ; of those at least 
who, from using a difierent language, or from any difference in their 
habitual associations, have fixed their attention in preference upon 
some other aspect of the things. The history of philosophy abounds 
in examples of such oversights, which would not have been committed 
if a philosopher had seen the hidden link that connected together the 
seemingly disparate meanings of some ambiguous word.* 

Whenever the inquiry into the definition of the name of any real ob- 
ject consists of anything else than a mere comparison of authorities, 
we tacitly assume that a meaning must be found for the name, com- 
patible with its continuing to denote, if possible all, but at any rate the 
greater or the more important part, of the things of which it is com- 
monly predicated. The inquiry, therefore, into the definition, is an 
inquiry into the resemblances and differences among those things : 
whether there be any resemblance running though them all ; if not, 
through what portion of them such a general resemblance can be traced : 

* " Few people" (I have said in another place) " have reflected how great a knowledge 
of Things is required to enable a man to affirm that any given argument turns wholly upon 
words. There is, perhaps, not one of the leading terms of philosophy which is not used 
in almost innumerable shades of meaning, to express ideas more or less widely different 
from one another. Between two of these ideas a sagacious and penetrating mind will 
discern, as it were intuitively, an unobvious link of connexion, upon which, though per- 
haps unable to give a logical account of it, he will found a perfectly valid argument, which 
his critic, not having so keen an insight into the Things, will mistake for a fallacy turning 
on the double meaning of a term. And the greater the genius of him who thus safely leaps 
over the chasm, the greater will probably be the crowing and vain-glory of the mere 
logician, who, hobbling after him, evinces his own superior wisdom by pausing on its brink, 
and giving up as desperate his proper business of bridging it over." 



106 NAMES AND PROPOSITIONS. 

and finally, wliat are the common attributes, the possession of which 
gives to them all, or to that portion of them, the character of resem- 
blance which has led to their being classed together. When these 
common attributes have been ascertained and specified, the name 
which belongs in common to the resembling objects, acquires a dis- 
tinct instead of a vague connotation ; and by possessing this distinct 
connotation, becomes susceptible of definition. 

In giving a distinct connotation to the general name, the philosopher 
will endeavor to fix upon such atti'ibutes as, while they are common to 
all the things usually denoted by the name, are also of greatest impor- 
tance in themselves, either directly, or from the number, the conspic- 
uousness, or the interesting character, of the consequences to which 
they lead. He will select, as far as possible, such differenticE as lead 
to the greatest nuii^ber of interesting propria. For these, rather than 
the more obscure and recondite qualities on which they often depend, 
give that general character and aspect to a set of objects, which deter- 
mine the groups into which they naturally fall. But to mount up to 
the more hidden agreement upon which these obvious and superficial 
agi'eements depend, is often one of the most difiicult of scientific prob- 
lems. As it is among the most difiicult, so it seldom fails to be among 
the most important. And since upon the result of this inquiry respect- 
ing the causes of the properties of a class of things, there incidentally 
depends the question what shall be the meaning of a word ; some of 
the most profound and most valuable investigations which philosophy 
presents to us, have been introduced by, and have offered themselyes 
under the guise of, inquiries into the definition of a name. 



BOOK II. 

OF REASONING. 



Atuptafzivcov de tovtuv, My^iiev ridrj, dia rtvuv, koI ttote, kol Trcjf yivETat, nag crvXXo- 
yta/iog' voTEpov 6^ Xekteov ixEpl unodEL^eoyg. UpoTEpov yap izEpl GvkXoyLai.LOv Tiekteov, tj 
TTEpl uTTodEi^ECjg, 6ia to KaOoXov judXXov Etval tov avWoyiajxbv. 'H [itv yap aTrodEi^cg, 
cvlTioycaixbg rig- 6 cvTJkoyLGjxbg 6i ov 7rag,.uTTu6ei^ig. 

Arist. Analyt. Prior., 1. i. cap. 4. 



* CHAPTER L 

OF INFERENCE, OR REASONING, IN GENERAL. 

§ 1. In the preceding Book, we have been occupied not with the 
nature of Proof, but with the nature of Assertion : the import conveyed 
by a Proposition, whether that Proposition be true or false ; not the 
means by which to discriminate true from false Propositions. The 
proper subject, however, of Logic is Proof. Before we could under- 
stand what Proof is, it was necessary to understand what that is to 
which proof is applicable ; what that is which can be a subject of be- 
lief or disbelief, of affirmation or denial ; what, in short, the different 
kinds of Propositions assert. 

This preliminary inquiry we have prosecuted to a ijdefinite result. 
Assertion, in the first place, relates either to the meaning of words, or 
to some j)roperty of the things which words signify. Assertions re- 
specting the meaning of words, arnong which definitions are the most 
important, hold a place, and an indispensable one, in philosophy ; but 
as the meaning of words is essentially arbitrary, this class of assertions 
is not susceptible of truth or falsity, nor therefore of proof or dis- 
proof Assertions respecting Things, or what may be called Real 
Propositions in contradistinction to verbal ones, are of various sorts. 
We have analyzed the import of each sort, and have ascertained the 
nature of the things they relate to, and the nature of what they sever- 
ally assert respecting those things. We found that whatever be the 
form of the proposition, and whatever its nominal subject or predicate, 
the real subject of every proposition is some one or more facts or phe- 
nomena of consciousness, or some one or more of the hidden causes or 
powers to which we ascribe those facts ; and that what is predicated 
or asserted, either in the affirmative or negative, of those phenomena 
or those powers, is always either Existence, Order in Place, Order in 
Time, Causation, or Resemblance. This, then, is the theory of the 
Import of Propositions, reduced to its ultimate elements : but there is 
another and a less abstruse expression for it, which though stopping 
short in an earlier stage of the analysis, is sufficiently scientific for 
many of the purposes for which such a general expression is required. 



108 REASONING. 

This expression recognizes the commonly received distinction between 
Subject and Attiibute, and gives the following as the analysis of the 
meaning of propositions : — Every Proposition asserts, that some given 
subject does or does not possess some attribute ; or that some attribute 
is or is not (either in all or in some portion of the subjects in which it 
is met with) conjoined with some other attribute. 

We shall now for the present take our leave of this portion of our 
inquiry, and proceed to the peculiar problem of the Science of Logic, 
namely, how the assertions, of which we have analyzed the import, 
are proved, or disproved : such of them, at least, as, not being amena- 
ble to direct consciousness or intuition, are appropriate subjects of 
proof 

We say of a fact or statement, that it is proved, when we be- 
lieve its truth by reason of some other fact or statement from which 
it is said to follow. Most of the propositions, whether affirmative or 
negative, universal, particular, or singular, which we believe, are not 
believed on their own evidence, but on the ground of something pre- 
viously assented to, and from which they are said to be inferred. To 
infer a proposition from a previous proposition or propositions ; to 
give credence to it, or claim credence for it, as a conclusion from 
something else ; is to reason, in the most extensive sense of the term. 
There is a narrower sense, in which the name reasoning is confined to 
the form of inference which is termed ratiocination, and of which the 
syllogism is the general type. The reasons for not conforming to this 
restricted use of the term were stated in an early stage of our inquiry, 
and additional motives will be suggested by the considerations on 
which we are now about to enter. 

§ 2. In proceeding to take into consideration the cases in which 
inferences can legitimately be drawn, we shall first mention some cases 
in which the inference is apparent, not real ; and which require notice 
chiefly that they may not be confounded with cases of inference prop- 
erly so called. This occurs when the proposition ostensibly inferred 
from another, appears on analysis to be merely a repetition of the same, 
or part of the same, assertion, which was contained in the first. All 
the ca^es mentioned in books of Logic, as examples of Jj]quipollency 
or equivalence of propositions, are of this nature. Thus, if we were 
to argue, No man is incapable of reason, for every man is rational ; . 
or. All men are mortal, for no man is exempt from death ; it would 
be plain that we Were not proving the proposition, but only appealing 
to another mode of wording it, which may or may not be more readily 
comprehensible by the hearer, or better adapted to suggest the real 
proof, but v/hich contains in itself no shadow of proof 

Another case is where, from an universal proposition, we affect to 
infer another which differs from it only in being particular : as, All A 
is B, therefore Some A is B : No A is B, therefore Some A is not B. 
This, too, is not to conclude one proposition fi-om another, but to 
repeat a second time something which had been asserted at fii'st ; with 
the difference, that wo do not here repeat the whole of the previous 
assertion, but only an indefinite part of it. 

A third case is where, the antecedent having affinned a predicate 
of a given subject, the consequent affiiins of the same subject some- 
thing already connoted by the former predicate : as, Socrates is a 



INFERENCE IN GENERAL. 109 

man, therefore Socrates is a living creature ; where all that is connoted 
by living creature v\^as affirmed of Socrates when he was asserted to 
be a man. If the propositions are negative, we must invert their 
order, thus : Socrates is not a living creature, therefore he is not a 
man ; for if we deny the less, the greater, which includes it, is already 
denied by implication. These, therefore, are not really cases of infer- 
ence ; and yet the trivial examples by which, in manuals of Logic, the 
rules of the syllogism are illustrated, are often of this ill- chosen kind ; 
demonstrations in form, of conclusions to which whoever understands 
the terms used in the statement of the data, has already, and con- 
sciously, assented. 

The most complex case of this sort of apparent inference is what is 
called the Conversion of Propositions ; which consists in making the 
predicate become a subject, and the subject become a predicate, and 
framing out of the same terms, thus reversed, another proposition, 
which must be true if the former is true. Thus, from the particular 
affirmative proposition, Some A is B, we may infer that Some B is A. 
From the universal negative, No A is B, we may Conclude that No 
B is A. From the universal affirmative proposition. All A is B, it 
cannot be inferred that All B is A ; though all water is liquid, it is not 
implied that all liquid is water ; but it is implied that some liquid is 
so ; and hence the proposition, All A is B, is legitimately convertible 
into Some B is A. This process, which converts an universal propo- 
sition into a particular, is termed conversion jper accidens. From the 
proposition, Some A is not B,, we cannot even infer that Some B is 
not A : though some men are not Englishmen, it does not follow that 
some Englishmen are not men. The only legitimate conversion, if 
such it can be called, of a particular negative proposition, is in the 
form. Some A is not ^, therefore,^ something which is not B is A ; and 
this is termed conversion by contraposition. In this case, however, 
the predicate and subject are not merely reversed, but one of them is 
altered. Instead of [A] .and [B], the terms of the new' proposition 
are [a thing which is not Bj, and [A]. The original proposition, 
Some A is not B, is first changed into a proposition gequipollent with 
it, Some A is " a thing which is not B ;" and the proposition, being 
now no longer a particular negative, but a particular affirmative, admits 
©f conversion in the first mode, or, as it is called, simple conversion. 

In all these cases there is not really any inference ; there is in the 
conclusion no new truth, nothing but what was already asserted in the 
■ premisses, and obvious to whoever apprehends them. The fact as- 
serted in the conclusion is either the very same fact, or part of the fact, 
asserted in the original proposition. This follows fi^om our previous 
analysis of the Import of Propositions. When we say, for example, 
that some lawful sovereigns are tyrants, what is the meaning of the 
assertion % That the attributes connoted by the term " lawful sover- 
eign," and the attributes connoted by the term "tyrant," sometimes 
coexist in the same individual. Now this is also precisely what we 
mean, when we say that some tyrants are lawful sovereigns ; which, 
therefore, is not a second proposition inferred from the first, any more 
than the English ti'anslation of Euclid's Elements is a collection of 
theorems different from, and consequences of, those contained in the 
Greek original. Again, if we assert that no gi'eat general is a fool, we 
mean that the attributes connoted by " great general," and those con- 



110 REASONING. 

noted by "fool," never coexist in the same subject; which is also the 
exact meaning which we express when we say, that no fool is a great 
general. Wlien we say that all quadrupeds are warm-blooded, we as- 
sert, not only that the attributes connoted by " quadruped" and those 
connoted by " warm-blooded" sometimes coexist, but that the former 
never exist vdthout the latter : now the proposition. Some wann- 
blooded creatures are quadrupeds, expresses the first half of this mean- 
ing, dropping the latter half; and, therefore, has been already affirmed 
in the antecedent proposition. All quadrupeds are warm-blooded. But 
that all warm-blooded creatures are quadrupeds, or, in other words, 
that the attributes connoted by ''warm-blooded" never exist without 
those connoted by " quadruped," has not been asserted, and cannot be 
infeiTed. In order to reassert, in an inverted form, the whole of what 
was affirmed in the proposition, All quadrupeds are warm-blooded, we 
must convert it by contraposition, thus. Nothing which is not warm- 
blooded is a quadruped.* This proposition, and the one from which it 
is derived, are exactly equivalent, and either of them may be substitu- 
ted for the other; for, to say that when the attributes of a quadruped 
are present, those of a warm-blooded creature are present, is to say, 
that when the latter are absent the former are absent. 

In a manual for young students, it would be proper to dwell at 
gi'eater length upon the conversion and sequipollency of propositions. 
For, although that cannot be called reasoning or inference which is a 
mere reassertion in different words of what had been asserted before, 
there is no more important intellectual habit, nor any the cultivation 
of which falls more strictly within the province of the art of logic, than 
that of discerning rapidly and surely the identity of an assertion when 
disguised under diversity of language. That important chapter in 
logical treatises which relates to the Opposition of Propositions, and 
the excellent technical language which logic provides for distinguishing 
the different kinds or modes of opposition, are of use chiefly for this 
purpose. Such considerations as these, that conti^ary propositions may 
both be false, but cannot both be true ; that sub-contrary propositions 
may both be true, but cannot both be lahe; that of two contradictory 
propositions one must be true and the other false; that of two subal- 
ternate propositions the truth of the universal proves the truth of the 
particular, and the falsity of the particular proves the falsity of the 
universal, but not vice versd;* are apt to appear, at first sight, very 
technical and mysterious, but when explained, seem almost too obvious 
to require so formal a statement, since the same amount of explanation 
which is necessary to make the principles intelligible, would enable 
the truths which they convey to be apprehended in any particular case 
which can occur. In this respect, however, these axioms of logic are 
on a level with those of mathematics. That things which are equal to 
the same thing are equal to one another, is as obvious in any particular 

* All A is B ) 
No A is B J contraries. . . 

Some A is B ) , , . 

Some A is not B < s^bcontranes. 

All AisB ) , ,., . 

Some A ie not B \ contradictories. 

No A is B ) , . V • 

Some A is B ( ^^^° contradictories. 

All A Ik B ) ,No AisB ) • , , ix 

Some A is li } ^"^ Some A is not B \ respectively subaltemate. 



INFERENCE IN GENERAL. Ill 

case as it is in the general statement : and if no such general maxim 
had ever been laid down, the demonstrations in Euclid would never 
have halted for any difficulty in stepping across the gap which this 
axiom at present serves to bridge over. Yet no one has ever censured 
writers on geometry, for placing a list of these elementary generaliza- 
tions at the head of their treatises, as a first exercise to the learner of 
the faculty which will be required in him at every step, that of appre- 
hending a general truth. And the student of logic, in the discussion 
even of such tmths as we have cited above, acquires habits of circum- 
spect interpretation of words, and of exactly measuring the length and 
breadth of his assertions, which are among the most indispensable con- 
ditions of any considerable attainment in science, and which it is one 
of the primary objects of logical discipline to cultivate. 

§ 3. Having noticed, in order to exclude from the province of Rea- 
soning or Inference properly so called, the cases in which the progress 
from one truth to another is only apparent, the logical consequent being 
a mere repetition of the logical antecedent ; we now pass to those 
which are cases of inference in the proper acceptation of the term, 
those in which we set out from known truths, to airive at others really 
distinct from them. 

Reasoning, in the extended sense in which I use the term, and in 
which it is synonymous with Inference, is popularly said to be of two 
kinds : reasoning from particulars to generals, and reasoning from gen- 
erals to particulars; the former being called Induction, the latter 
Ratiocination or Syllogism. It will presently be shown that there is 
a third species of reasoning, which falls under neither of these descrip- 
tions, and which, nevertheless, is not only valid, but the foundation of 
both the others. , 

It is necessary to observe, that the expressions, reasoning from par- 
ticulars to generals, and reasoning from generals to particulars, are 
recommended by brevity rather than by precision, and do not ade- 
quately mark, without the aid of a commentary, the distinction between 
Induction and Ratiocination. The meaning intended by these expres- 
sions is, that Induction is infemng a proposition from propositions less 
general than itself, and Ratiocination is inferring a proposition from 
propositions equally or more general. When, from the observation of 
a number of individual instances, we ascend to a general proposition, 
or when, by combining a number of general propositions, we conclude 
from them another proposition still more general, the process, which is 
substantially the same in both instances, is called Induction. When 
from a general proposition, not alone- (for fi'om a single proposition 
nothing can be concluded which is not involved in the terms), but by 
combining it with other propositions, ,we infer a proposition of the 
same degree of generality wiih itself, or a less general proposition, or 
a proposition merely individual, the process is Ratiocination. Wlien, 
in short, the conclusion is more general than the largest of the prem- 
isses, the argument is commonly called Induction ; when less general, 
or equally general, it is Ratiocination. 

As all experience begins ^vith individual cases, and proceeds from 
them to generals, it might seem most conformable to the natural order 
of thought that Induction should be treated of before we touch upon 
Ratiocination. It will, however, be advantageous, iii a science which 



112 REASONING. 

aims at tracing our acquired knowledge to its sources, that the inquirer 
should commence with the later rather than with the earlier stages of 
the process of constructing our knowledge ; and should trace deriva- 
tive truths backward to the truths from which they are deduced, and 
upon which they depend for their evidence, before attempting to point 
out the original spring from which both ultimately take their rise. 
The advantages of this order of proceeding in the present instance will 
manifest themselves as we advance, in a manner superseding the ne- 
cessity of any further justification or explanation. 

Of Induction, therefore, we shall say no more at present, than that 
it at least is, without doubt, a process of real inference. The conclu- 
sion in an induction embraces more than is contained in the premisses. 
The principle or law collected from particular instances, the general 
proposition in which we embody the result of our experience, covers 
a much larger extent of ground than the individual experiments which 
are said to form its basis. A principle ascertained by experience, is 
more than a mere summing Up of what we have specifically observed 
in the individual cases that we have examined ; it is a generalization 
grounded on those cases, and expressive of our belief, that what we 
there found true is true in an indefinite number of cases which we have 
not examined, and are never likely to examine. The nature and 
grounds of this inference, and the conditions necessary to make it 
legitimate, will be the subject of discussion in the Third Book: but 
that such inference really takes place is not susceptible of question. 
In every induction we proceed from truths which we knew, to truths 
which we did not know : from facts certified by observation, to facts 
which we have not observed, and even to facts not capable of being 
now obsei-ved ; future facts, for example : but which we do not hesitate 
to believe upon the sole evidence of the induction itself 

Induction, then, is a real process of Reasoning or Inference. 
Whether, and in what sense, so much can be said of the Syllogism, 
remains to be determined by the examination. into which we are about 
to enter. 



CHAPTER II. 

OF RATIOCINATION, OR SYLLOGISM. 



§ 1. The analysis of the Syllogism has been so accurately and fully 
performed in the common manuals of Logic, that in the present work, 
which is not designed as a manual, it is suflficient to recapitulate, me- 
morioi causd, the leading results of that analysis, as a foundation for 
the remarks to be afterwards made upon the functions of the syllogism, 
and the place which it holds in philosophy. 

To a legitimate syllogism it is essential that there should be three, 
and no more than three, propositions, namely, the conclusion, or propo- 
sition to be proved, and two other propositions which together prove 
it, and which are called the premisses. It is essential that there should 
be three, and no more than three terms, namely, the subject and pred- 
icate of the conclusion, and another called the middleterm, which must 



RATIOCINATION, OR SYLLOGISM. 



118 



be found in both premisses, since it is by means of it that the other 
two terms are to be connected together. The predicate of the conclu- 
sion is called the major term of the syllogism; the subject of the con- 
clusion is called the minor term. As there can be but three terms, 
the major and minor terms must each be found in one, and only one, 
of the premisses, together with the middleterm which is in them both. 
The premiss which contains the middleterm and the major term is 
called the major premiss ; that which contains the middleterm and the 
minor term is called the minor premiss of the syllogism. 

Syllogisms are divided by some logicians into xhree figures , by oth- 
ers into four, according to the position of the middleterm, which may 
either be the subject in both premisses, the predicate in both, or the 
subject in one and the predicate in the other. The most common 
case is that in which the middleterm is the subject of the major prem- 
iss and the predicate of the minor. This is reckoned as the first figure. 
When the middleterm is the predicate in both premisses, the syllogism 
belongs to the second figure ; when it is the subject in both, to the 
third. In the fourth figure the middleterm is the subject of the minor 
premiss and the predicate of the major. Those writers who reckon 
no more than three figures, include this case in the first. 

Each figure is subdivided into modes^ according to what are called 
the quantity and quality of the propositions, that is, according as they 
are universal or particular, aflBrmative or negative. The following are 
examples of all the legitimate modes, that is, all those in which the 
conclusion correctly follows from the premissess A is the minor term, 
G the jnaj or, B the middleterm. • '' 



First Figure. 



M B is C 
All A is B 
theriefore 
AH A is a 



No B is C 
All A is B 
therefore 
No A is C 



All B is C 
Some A is B 

therefore 
Some A is C 



NoBisC 
Some A is B ' 

therefore 
Some A is not C 



No C is B 
All A is B 
- therefore 
No A is C 



Second Figure.' 



All C is B 
No A is B 

therefore 
No A is C 



No C is B 
Some A is B 

therefore 
Some A is not C 



All C is B 
Some A is not B 

therefore 
Some A is not C 



Third Figure. 



AlIBi^C ^BisC " 
All Bis A All Bis A 
therefore therefore 
Some A is C Some A is not C 



Some B is C 

All B is A 

therefore 

.Some A is C 



All B is C 
Some B i^ A 

therefore 
Some A is C, 



Some Bis note 
All B is A 
therefore • 
Some A is note 



No B is C 
Some B is A 

therefore 
Some A is note 



I ..".- ;. ' ■- »" Fourth Figure. \'. . , ; 

All C is B ' ■ ' AUG is*B = ' Some C is B No C is B 

All B is A No B is A ' All B is A All B is A 

therefore therefore therefore, therefore^ 

Some A is C Some A is C Some/A•'itg^?^,■_ Some A is not C 



NoC isB 
Some B is A 

therefore 
Some A is not C 



In these exemplars, or blank forms for making syllogisms, no place 
is assigned to singular propositions ; not, of course, because such pro- 
positions are not used in ratiocination, but because, their predicate 
being affirmed or denied of the whole of the subject, they are ranked, 
for the purposes of the, syllogism, with universal propogitions. Thus, 
thege two syllogisms— ■ - " : _ • . ^ '•.' /'- ^ ■ 



114 <' REASONING. ^ 

. ' AH men sxe mott^X^ •_ ^' ^ ♦'^All'fneii.alife mortal, ' ' •• 
All kings are men, " Socrates is a man, 

therefore therefore 

All kings are mortal, Socrates is mortal, 

are arguments precisely similar, and are both ranked in the first mode' 
of the first figure. y i ^, • * ' 

■ The reasons why syllogisms in any of ihe". above forms are legitimate, 
that is, why, if the premisses be true, the conclusion must necessarily be 
so, and why this is not the case in any other possible mode, that is, in 
any other combination of universal and particular, affirmative and 
negative propositions, any person taking interest in these inquiries may 
be presumed to have either learnt from the common school books of 
the syllogistic logic, or to be capable of divining for himself The 
reader may, however, ^)e referred, for every needful explanation, to 
Archbishop Whately's 'Elements of Logic, where he will find stated with 
philosophical precision, and explained with peculiar perspicuity, the 
whole of the common doctrine of the syllogism. ' ' *^.^ . / .« ." " 

All valid ratiocination ; all reasoning by which, from general ptop^o- 
sitions previously admitted, other propositions equally or .less general 
are inferred ;' may be exhibited in some of the above forms. The whole 
of Euclid, for example, might be thrown without difficulty into a series 
pf syllogism-s, regular in mode and figure. 

Although a syllogism framed according to any of these formulse is a 
valid argument, all correct ratiocination admits of being stated in syllo- 
gisms of the first figure alone; The rules for throwing an argument in 
any of the other figures into the iirst figure, are called rules for the re- 
duction of syllogisms. It is done by the conversion of one or other, or 
both, of the pre^iissQ5^.. '. Thus, an. argument in, the first rgbde of the 
second figiire, as-*-* ,%".*.■ -.-'.- ' • r- ' . . •' '' '-C 

■•'• ^/v* -"' = -NoCis-B' • -\ '^ •' -■*'■■.-. • 
All A is B .; * . .^ " '* ■• ■ V 
.> ' ''./-. - therefore . H' * •. . * ; ' . 

■•,.■. ^. ■-.«;,* ; -.NoAisC, / *: ,, ■ ' •' - ^' -:; 

may be reduced as follows. The proposition. No G is B, being an uni- 
versal negative, admits of simple conversion, and may be changed into 
No B is C, which, as we showed, is the very same assertion in other 
words — the same fact dilferently expressed. This transformation hav-- 
ing been effected, the argumejit assumes th^ follbwing.fQrm:;*.--^- 
' ■ ''NoB.isG" ■■ -^.^ • .. ^> '''.^' 

All A is B .""■*,• ■ ' ■- .'*' 

^ th'erefi^re 

^' • ' ■ No.AisC, ^ ,; .. ■;'•;■•'.'. • 

which is a good syllogism in the second ode of the first figiiVe. Agaiil, * 
an argument in the first mode of the third figure must resemble th© 
following:— ; ;•_,;, ■ - ,- ,. ..iv.- ^ .^ ' <.>...;••• < 

.' . . All B IS 0. .', •••.', •, ' , • ■", 

.All B is Av--^ .^^."" '■-. ^ ■ 7>'v''- <:';• ;^ ;. 
therefore- ' •'■ ..'•.;.'", . ^ .,, '' ; - 
• . . , Some A is C, ' •' . •'"*'.' " . 

where thq ihiilor premiss, All B is A, conformably fo wKat was' laid 
down in the last chapter respecting universal affirmatives, does not ad- 
mit of simple conversion, but may bo convertcd^er •([Xc^cz^e^.*?, thus, >^ome . 



RATIOCINATION, OR SYLLOGISM. 115 

A is B ; which, though it does not express the whole of what is assert- 
ed in the proposition, All B is A, expresses, as was formerly shown, part 
of it, and must- therefore be true if the whole is true. We have, then, 
as the result of the reduction, the following syllogism in the third mode 
of the first figure :— 

All Bis C 

Some A is B, 
from -which it obviously follows, that 

Some A is C. > 
In the same manner, or in, a manner on which, after these examples, 
it is not necessary to enlarge, every mode of the second, third, and 
fourth figures may be reduced to some one of the four modes of the 
first. In other words, every conclusion which can be proved in any of' 
the last three figures, may be proved in the first figure from the same 
premisses, with a slight alteration in the mere manner of expressing 
them. ,■ Every valid ratiocination, therefore, may be stated in the first 
figure, that is,iil one of the following forms : — . ■ . . ■ 



' Every B' is C 


No B is C 


All A 1 . -R 


All A ' ) . 
^•^SpmeA y ^ 


■ . "• therefore ■■. " 


"' " • therefor^ 


^••&omeA" 1, ^^^• 


■ "No A.is' ■ > 
Some A is not y 



IOC 5 ' 

Or, if more significant symbols, .are preferred, — 

To prove" an affirmative, the argument must admit of being stated 
in this form:— 

,', All animals are mortal : . .■•:.■. 
All men ^ ' ., .^y« ...» 

V , .. i .,' '. .t'Some men > are animals' j" , •; *%.'.•.".' 
"' ,'.V.' ' .r ., 't '.^Socrates ) •', ' "^ ••', • -" .■'^,, < 

>. ' '.'•'* ".. %\ < therefore • ;,' '. 

..',:\.' .'v ' ■ '--.^^'jAllmen ^ " .' V , , 

, ■ ^ ' Some men > are mortal. 

. ,' . . ,. f /.^ ■ . Socrates ) - 

/to pr.d:vj@ a" negative; the argument must be capable of being 
expressed in this form :— ' 

No one who is capable of self-control is necessarily vicious; 
All negi-oes V > . . 

■ Some negi'oes . ^ > are.capable of self-contr.oT,-' 

^ Mr. A's ilfegrO .* j ;.."''. . • ■; 
■ / " ^. ' \ therefotie ( -" . 

No negroes are • : ^ ' . / 

Some negroes are not > necessarily \dcious. 
. , Mr, A's negro is- not , ) 

Althoiigh all ratiocination admits of being thrown into one or the, 
ot^ier of 'these forms, arid sometimes gains considerably by the trans- 
formation, both in clearness and in the obviousness of its consequence ; 
there a,re, no doubt," cases in, which the argument falls more naturally 
into one of the other three figures, and in which its conclusiveness is 
more apparent at the first glance in thesis. figures, than when reduced 
into the first. Thus, if the proposition were that pagans may be vir- 



116 ' REASONING. ' 

tuous, and the evidence to prove it were the example of Aristides ; a 
syllogism in the third figure, . 

Aristides was virtuous, ' -^ 

Aristides was a pagan, 

therefore 
Some pagan was ■virttiou;s^ 

would be a more natural mode of stating the argiirrient, and would 
carry conviction more instantly home, than the same ratiocination 
sti-ained into the first figure, thus — • 

- , , Aristides was virtuous, 

'v « . • ' ■ Some pagan was Aristides, 

■ ' ' ; • '. therefore ;• 

- Some pagan was virtuous. . ' • ■ 

A German philosopher, Lambert, whose Neues Organon (published- 
in the year 1764) contains among other things the most elaborate and- 
complete exposition of the syllogistic doctrine which I have happened 
to meet with, has expressly examined what sorts of arguments fall 
most naturally and suitably into each of the four figures ; and his solu- 
tion is characterized by great ingenuity and clearness of thought.^ 
The argument, however, is one arid the same, in whichever figure it is 
expressed ; since, as We have already seen, the premisses of a syllo- 
' gism in the second, third, or fourth figure, and those of the syllogism 
in the first figure to which it may be reduced, are the same premisses, 
in everything except language, or, at least, as much of them as con- 
. tributes to the proof of the conclusion is the same. We are therefore 
at liberty, in conformity with the general opinion of logicians, to con- 
sider the two elementary forms of the ^first figure as the universal 
types of all correct ratiocination; the one, when the conclusion to be 
proved is affirmative, the other, when it is negative ; even though cer- 
tain arguments may have a tendency to clothe themselves in the forms 
of the second, third, and fourth figures ; which, however, cannot possi- 
bly happen with the only class of arguments which are odf first-rate 
scientific importance, those in which the conclusion is an universal 
affirmative, such conclusions being susceptible of proof in the first 
figure alone. ■ ^ .;.'- ■ ' 

§ 2. On examining, then, these two general formulae, we find that in 
both of them one premiss, the major, is an universal proposition; ,and 

* His conclusions are, " Tiie first figure is suited to the discovery or proof of the proper- 
tie^ of a thing; the second to 'the discovery or proof of the distinctions between things; 
the third to the discovery or proof of instances and exceptions ; the fourth to the discovery, ■ 
or exclusion, of the different species of a genus." The reference of syllogisms in the last 
three figures to the dictum de omni ct nulla is, -in Lambert's view, strained and unnatural : 
to each of the three belongs, according to him, a separate axiom, coordinate and of equal 
authority with that dictum, and to which he gives the names of dictum de divers'o for the 
second figure, dictum de exemplo for the third, and dictum de reciproco -for the foutth. Seo 
part i. or Dianoiologie, chap. iv. § 229 et seqq. 

Were it not that the views I am about to propound on the functions and iiltimate foun- 
dation of the syllogism render such distinctions as these of very subordinate importance, I 
should have availed myself largely of this and other speculations of Lambert ; who has 
displayed, within the limits of the received theory of the syllogism, an originaUty for which 
it was scarcely to bo supposed that there could still have been room on so exhausted a 
subject, and whose book may be strongly recommended to those who may attempt still 
furllicr to improve the excellent manuals we already possess of this elementary portion '• 
the Art of Reasoiring .^ 



RATIOCINATION, OR SYLLOGISM. 117 

according as this is affirmative or negative, the conclusion is so too. 
All ratiocination, therefore, starts from a general proposition, principle, 
or assumption : a proposition in w^hich a predicate is affirmed or denied 
of an entire class ; that is, in which some attribute, or the negation of 
some attribute, is asserted of an indeffiiite number of objects, distin- 
guished by a common characteristic, and designated, in consequence, 
by a common name. 

The other premiss is ahvays affirmative, and asserts- that something 
(which may be either an individual, a class, or part of a class), belongs 
to, or is included in, the class, respecting which something was affirmed 
or denied in the major premiss. It follows that the attribute affirmed 
or denied of the entire class may (if there was truth in that affirmation 
or denial) be affirmed or denied of the object or objects alleged to be 
included in the class : and this is precisely the assertion made in the 
conclusion. 

Whether or not the foregoing is an adequate account of the con- 
stituent parts of the syllogism, will be presently considered ; but as 
far as it goes it is a true account. It has accordingly been generalized 
and erected in^o a logical maxim, on which all ratiocination is said to 
be founded, insomuch that to reason and to apply the maxim are 
supposed to be one and the same thing. The maxim is, That what- 
ever can be affirmed (or denied) of a class, may be affirmed (or denied) 
of everything included in the class. This axiom, supposed to be the 
basis of the syllogistic theory, is termed by logicians the dicUim de 
omni et nullo. — 

This maxim, however, when considered as a principle of reasoning, 
appears suited to a system of metaphysics once indeed generally 
received, but which for the last two centuries has been considered as 
finally abandoned, though there have not been wanting, in our own 
day, attempts at its revival. So long as what were termed Universals 
were regarded as a peculiar kind of substances, having an objective 
existence distinct from the individual objects classed under them, the 
dictum de omni conveyed an important meaning ; because it expressed 
the intercommunity of nature, which it was necessary upon that theory 
that we should suppose to exist between those general substances and 
the particular substances which were subordinated to them. That 
everything predicable of the universal was predicable of the various 
individuals contained under it, was then no identical proposition, but 
a statement of what was conceived as a fundamental law of the uni- 
verse. The assertion that' the entire nature and properties of the 
suhstantia secunda formed part of the properties of each of the 
individual substances called by the same name ; that the properties of 
Man, for example, were properties of all men ; was a proposition of 
real significance when Man did not mean all men, but something 
inherent in men, and vastly superior to them in dignity. Now, how- 
ever, when it is known that a class, an universal, a genus or species, is 
not an entity per se, but neither more nor less than the individual 
substances themselves which are placed in the class, and that there is 
nothing real in the matter except those objects, a common name given 
to them, and common attributes indicated by the name ; what, I should 
he glad to know, do we learn by being told, that whatever can be 
affirmed of a class, may be affirmed of every object contained in the 
dass 1 The class is nothing but the objects' contained in it : and the 



118 REASONING. 

dictum de omni nieorely amounts to the identical proposition, tliat what- 
ever is true of certain objects, is true of each of those objects. If aH' 
ratiocination were no more than the apphcation of this maxim to 
particular cases, the syllogism would indeed be, what it has so often 
been declared to be, solemn trifling. The dictum de omni is on a par 
with another truth, which in its time was also reckoned of great 
importance, "Whatever is, is;" and not to be compared in point of 
sioiiificance to the cognate aphorism, " It is impossible for the same 
thino- to be and not to be ;" since this is, at ~the lowest, equivalent to 
the loo-ical axiom that contradictory propositions cannot both be true. 
To give any real meaning to the dictum de omni, w^e must consider it 
not as an axiom but as a definition ; we must look upon it as intended 
to explain, in a circuitous and paraphrastic manner, the meaning of 
the word class. 

An error which seemed finally refuted and dislodged from science, 
often needs only put on a new suit of phrases, to be welcomed back to 
its old quarters, and allowed, to repose unquestioned for another cycle 
of ages. Modern philosophers have not been sparing in their contempt 
for the scholastic dogma that genera and species are a peculiar kind of 
substances, which general substances being the only peiTuanent things, 
while the individual substances comprehended under them are in a 
perpetual flux, knovv^ledge, which necessarily imports stability, can only 
have relation to those general substances or universals, and not to the 
facts or particulars included under them. Yet, though nominally re- 
jected, this very doctrine, whether disguised under the Abstract Ideas of 
Locke (whose speculations, however, it has less vitiated than those of 
perhaps any other writer who has been infected with it), under the 
ultra-nominalism of Hobbes and Condillac, or the ontology of the later 
Kantians, has never ceased to poison philosophy. Once accustomed- 
to consider scientific investigation as essentially consisting in the study 
of universals, men did not drop this habit of thought when they ceased 
to regard uniVersals as possessing an independent existence : and even 
those who went the length of considering them as mere names, could 
not free themselves from the notion that the investigation of ti'uth con- 
sisted entirely or partly in some kind of conjuration or juggle with 
those names. When a philosopher adopted fully the Nominalist view . 
of the signification of general language, retaining along with it the. 
dictum de omni as the foundation of all reasoning, two such premisses 
fairly put together were likely, if he was a consistent thinker, to land 
him in rather startling conclusions. Accordingly it has been seriously 
held by writers of deserved celebrity, that the process of an-iving at 
new truths by reasoning consists in the mere substitution of one set of 
arbitrary signs for another; a doctrine which they supposed to dorive 
iiTesistible confirmation from the example of algebra. If there were ' 
any process in sorcery or necromancy more preternatural than this, I 
should be much surprised. The culminating point of this philosophy 
is the noted aphorism of Condillac, that a science is nothing, or scarcely 
anything, but ime langue hienfaite : in other words, that the one suflB- 
cient rule for discovering the nature and properties of objects is to 
name them properly : as if the reverse were not the truth, that it is im- , 
possible to name them properly except in proportion as we are already 
acquainted witli their nature, and properties. Can it be necessary to 
say, that none, not even the most trivial knowledge with respect to 



RATIOCINATION, OR SYLLOGISM. 119 

Things, ever was or could be originally got at by any conceivable, 
manipulation of mere names : and that vv^hat can be learnt from names, 
is only what somebody who used the namos, knew before ? Philoso- 
phical analysis confirms the indication of common sense, that the func- 
tion of names is but that of enabling us to rememler and to communi- 
cate our thoughts.. That they also strengthen, even to an incalculable 
extent, the power of tliought itself, is most true : but they do this by ~ 
no intrinsic, and peculiar virtue : they do it by the power inherent in 
an artificial memory, an instrument of which few have adequately con- 
sidered the immense potency. As an artificial memory, language truly 
is, what it has so often been called, an instrument of thought : but it is 
one tiling to be the instrument, and another to be the exclusive subject 
upon which the instrument is exercised. We think, indeed, to a con- 
siderable extent, by means of names, but what we think of, are the 
things called by those names ; and there cannot be a greater error than 
to imagine that thought can be carried on with nothing in our mind 
but names, or that we can make the names think for us. 

§ 3. Those who considered the dictum de omni as the foundation of 
the syllogism, looked upon arguments in a manner corresponding to 
the en^oneous view which Hobbes took of propositions. Because there 
are some propositions which are merely verbal, Hobbes, in order (ap- 
parently) that his definition might be rigorously universal, defined a 
proposition as if no propositions declared anything except the meaning 
of words. If Hobbes was right ; if no further account than this could 
'be given of the import of propositions ; no theory could be given but 
the commonly received one, of the combination of propositions in a 
syllogism. If the minor premiss asserted nothing rhore than that some- 
thing belongs to a claSvS, and if, as consistency would require us to 
suppose, the major premiss asserted nothing of that class except that 
it is included in another class, the conclusion would only be, that what 
was included in the lower class is included in the higher, and the result, 
therefore, nothing except that the classification is consistent with itself. 
But we have seen that it is no suflnicient account of the meaning of a 
proposition, to say that it refers something to, or excludes something 
from, a class. Every proposition which conveys real information 
asserts a matter of fact, dependent upon the laws of nature and not 
upon artificial classification. It asserts that -a given object does or 
'does not possess a given attribute-;' or it asserts' that two attributes, or 
sets of attributes, do or do not (constantly or occa:sionally) coex- 
ist. Since such is the- purport of all propositions which convey 
any real knowledge, and since ratiocination is a mode of acquir- . 
ing real knowledge, any theory of ratiocination which does not re- 
cognize this import of propositions, cannot, we may be sure, be the 
true one. 

Applying this view of propositions to the two premisses of a syllo- 
gism, we obtain the following results. The major premiss, which, as 
already remarked, is always universal, asserts, that all things which have 
a certain attribute (or attributes) have or have not along with it, a cer- 
tain other attribute (or attributes). The minor premiss asserts that the 
thing or set of things which are the subject of that premiss, have the 
first-mentioned attribute ; and the conclusion is, that they have (or that 
thev have not) the second. "Thus in our former example, 



120 REASONING. 

All men are mortal, . * ' . 

Socrates is a man, ' v « - 
therefore 

Socrates is mortal, 
tlie subject and predicate of tlie major premiss are connotative tetms, 
denotino- objects and connoting attributes. The assertion in the major 
premiss is, that along with one of the two sets of attributes, we always 
lind the other : that the attributes connoted by '* man" never exist un- 
less conjoined with the attribute called mortality. The assertion in the 
minor premiss is that the individual named Socrates possesses the 
former attributes; and it is concluded that he possesses also the attri- 
bute mortality. Or, if both the premisses are general propositions, as 

All men are mortal, ' 

All kings are, men, 

therefore ' \ ■ ' 

All kings are mortal, • 

the minor premiss asserts that the attributes denoted by kingship only 
exist in conjunction with those signified by the word man. The major 
asserts as before, that the last-mentioned attributes are never found 
without the attribute of mortality. The conclusion is, that wherever 
the attributes of kingship are found, that of mortality is found also. 

If the major premiss were negative, as. No men are gods,, it would 
assert, not that the attributes connoted by '' Man" never exist without, 
but that they never exist with, those connoted by " God :" from which, 
together with the minor premiss, it is concluded, that the same incom- . 
patibility exists between the attributes constituting a god and those con- 
stituting a king. In a similar manner we might analyze any other ex- 
ample of the syllogism. 

If we generalize this process, and look out for the principle or law 
involved in every such inference, and presupposed in every syllogism 
the propositions of which are anything more than merely verbal ; we 
•find, not the unmeaning dictum de o?mii et nullo, but a fundamental 
principle, or rather two principles, strikingly resembling the axioms of 
mathematics. The first, which is the principle of affirmative syllo- 
-gisms,, is, that things which coexist with the same thing, coexist v/ith 
one another. , The second is the principle of negative syllogisms, and 
is to this effect : that a thing which coexists with another thing, with 
which other a third thing does not coexist, is not coexistent with tliat 
third thing. These axioms manifestly relate to facts, and not to con- 
ventions : and one or other of them is the ground of the legitimacy of 
every argument in which facts and not conventions are the matter treat- 
ed of. -^ 

§ 4. It only remains to translate this exposition of the syllogism 
from the one into the other of the two languages in which we formerly 
remarked* that all propositions, and of course therefore all combina- 
tions of propositions, might be expressed. We observed that a propo- 
sition might be considered in two different lights ; as a portion of our 
knowledge of nature, or as a memorandum for our guidance. Under 
the former, or speculative aspect, an affirmative general proposition is 
an asaertion of vi spQculatije truth, viz., that whatever has a certain at- 

• ■' ' -^ Supra, p, -157, ' , . ■ ' 



RATIOCINATION, OR SYLLOGISM. 121 

tribute has a certain other attribute. Under the other aspect, it is to 
be regarded not as a part of our knowledge, but as an aid for our prac- 
tical exigencies, by enabling us when we see or learn that an object 
possesses one of the two attributes, to infer that it possesses the other; 
thus employing the first attribute as a mark or evidence of the second.. 
Thus regarded, every . syllogism . comes within the following general 
formula : — 

Attribute A is a mark of attribute B, 
A given object has the mark A, 

therefore 
The given object has the attribute B. 
RefeiTod to this type, the arguments which we have lately cited as 
specimens of the syllogism, will express themselves in the following 
manner : — 

The attributes of man are a mark of the attribute mortality, 
Socrates has the attributes of man, 

tlierefore 
Socrates has the attribute mortality. 
And again. 

The attributes of man are a mark of the attribute mortality. 
The attributes of a king are a mark of the attributes of man, 

therefore 
The attributes of a king are a mark of the attribute mortality. 
And lastly, 

The attributes of man are a mark of the absence of the attributes 
of a god, 
', ; The attributes of a king are a mark of the attributes of man, 

therefore 
The attributes of a king are a mark of the absence of the attributes- 
signified by the word god : 
,^ " ., • (or, are evidence of the absence of those attributes). 

. Ta correspond with this alteration in the form of the, syllogisms^ the 
axioms on' which the syllogistic process is founded must undergo a 
corresponding transformation. In this altered phraseology, both those 
axioms may be brought under one general expression ; namely, that 
"whatever possesses any mark,..possesses that which it is a mark of. 
Or, when the minor premiss as well as the major is universal, we may 
state it thus : whatever is a mark of any mark, is a mark of that which 
this last is a mark of. To trace the identity of these axioms with those 
previously laid down, maybe safely left to the intelligent reader. We 
shall find, as we proceed, the great convenience of the phraseology 
into which we have last thrown them, and which is better adapted than 
any I am acquainted with, to express with precision and force what is 
aimed at, and actually accomplished, in every case of" the ascertain- 
ment of a truth by ratiocination. 



Q, 



122 REASONING. " - ^ * 

CHAPTER III. ~ . 

OF THE FUNCTIONS, AND LOGICAL VALUE, OF THE SYLLOGISM, 

§ 1. We have shown what is the reaJ nature of the truths with 
which the Syllogism is conversant, in contradistinction to the more 
superficial manner in which their import is conceived in the common • 
theory ; and what are the fundamental axioms on which its probative 
force or conclusiveness depends. We have now to inquire, whether 
the syllogistic process, that of reasoning from generals to particulars, , 
is, or is not, a process of inference ; a progress from the known to the 
unknown ; a means of coming to a knowledge Of something which we 
did not know before. 

Logicians have been remarkably unanimous in their mode of an- 
swering this question. It is universally allowed that a syllogism is 
vicious if there be anything more in the conclusion than was assumed 
in the premisses. But this is, in fact, to say, that nothing ever was, or 
can be, proved by syllogism, which was not known, or assumed to be 
known, before. Is ratiocination, then, not a process of inference ? 
And is the syllogism, to which the word reasoning has so often been 
represented to be exclusively appropriate, not really entitled to be 
called reasoning at all 1 This seems an inevitable consequence of the 
doctrine, admitted by all writers on the subject, that a syllogism can 
prove no more than is involved in the premisses.. Yet the acknowl- 
edgment so explicitly made, has not prevented one set of- writers from 
continuing to represent the syllogism as the correct analysis of what 
the mind actually performs in discovering and proving the larger half 
of the truths, whether of science or of daily life, which we believe; 
while those who have avoided this inconsistency, and followed out the 
general theorem respecting the logical value of the syllogism to its 
legitimate corollary, have been led to impute uselessness and frivolity 
to the syllogistic theory itself, on the ground of the petitio principii 
which they allege to be inherent in every syllogism. As I believe 
both these opinions to be fundamentally erroneous, I must request the 
attention of the reader to certain considerations, without which any 
just appreciation of the true character of the syllogism, and the func- 
tions it performs in philosophy, appears to me impossible ; but which 
seem to have been either overlooked, or insufficiently adverted to, 
both by the defenders of the syllogistic theory and by its assailants. 

§ 2. It must be granted that in every syllogism, considered as an 
argument to prove the conclusion, there is a petitio principii. When 
we say, ' 

' All men are mortal, 
Socrates is a man, 

therefore 
Socrates is mortal ;. ' 

it is unanswerably urged by the adversaries of the syllogistic theory, 
that the proposition, Socrates is mortal, is presupposed in the more 
general assumption. All men are mortal : that we cannot be assured 
oi' the mortality of all mqn, unless we were previously certain of the 



FUNCTIONS AND VALUE OF THE SYLLOGISM. 123 

rfiortality of every individual man : tliat if it be still doubtful whether 
Socrates, or any other individual you choose to name, be mortal or 
not, the same degree of uncertainty must hang over the assertion. All 
men are mortal : that the general principle, instead of being given as 
evidence of the particular case, cannot itself be taken for true without 
exception, until every shadow of doubt which could affect any case 
comprised with it, is dispelled by evidence aliunde; and then what 
remains for the syllogism to proved that, in short, no reasoning from 
generals to particulars can, as such, prove^ anything : sincO from a 
general principle you cannot infer any particulars, but tho^e which the 
principle itself assumes as foreknown. ■ 

This doctrine is irrefragable ; and if logicians, though unable to 
dispute it, have usually exhibited a strong disposition to explain it 
away, this was not because they could discover any flaw in the argu- 
ment itself, but because the contrary opinion seemed to rest upon 
arguments equally indisputable. In the syllogism last referred to, for 
example, or in any of those which we previously constructed, is it not 
evident that the conclusion may, to the person to whom the syllogism 
is, presented, be actually and honoL fide a new truth % Is it not matter 
of daily experience that truths previously undreamt of, facts which 
have not been, and cannot be, directly observed, are arrived at by way 
of general reasoning % We believe that the Duke of Wellington is 
mortal. We do not know this by direct observation, since he is not 
yet dead. If we were asked how, this being the case, we know the 
diLke to be mortal, we should probably answer. Because all men are 
so. Here, therefore, we arrive at the knowledge of a truth not (as 
yet) susceptible of observation, by a reasoning which admits of being 
exhibited in the following syllogism : — 

\ "■ ' ■" ' All men are mortal, \ 

- ' . The Duke of Wellington is a man, 
' : therefore 

\ The Duke of Wellington is mortal. 

And since a large portion of our knowledge is thus acqiiired, logicians 
have persisted in representing the syllogism as a procdss of inference 
or proof; although none of them have cleared up the difficulty which 
arises from the inconsistency between that assertion and the principle, 
that if there be anything in the conclusion which was not already as- 
serted in the premisses, the argument is vicious. For it is impossible 
to attach any serious scientific value to such a mere salvo, as the dis- 
tinction drawn between being involved hy implicatwn in the premisses, 
and being directly asserted in them. When Archbishop Whately, for 
example, says,* that the object of reasoning is '' merely to expand and 
unfold the assertions wrapt up, as it were, and implied in those with 
which we set out, and to bring a person to perceive and acknowledge 
the full force of that which he has admitted," he does not, I think, 
meet the real difficulty requiring to be explained, namely, how it hap- 
pens that a science, like, geometry, can be all '• wi'apt up" in a few 
definitions and axioms. Nor does this defence of the syllogism differ 
much from what its assailants urge against it as an accusation, when 
they charge it with, being of no use except to those who seek to press 

■ * iog7c, p. 216. '' ■ . ■ , 



124 EEASONING. ' . 

the Gonsequences of an admission into which a man has be6n entrapped 
without having considered and understood its full force. When you 
admitted the major premiss, you asserted the conclusion ; but, says 
Archbishop Whately, you asserted it by implication merely: this, 
however, can here only mean that you asserted it unconsciously ; that 
you did not know you were asserting it; but, if so, the difficulty re- 
vives in this shape — Ought you not to have known 1 Were you war- 
ranted in asserting the general proposition without having satisfied 
yourself of the truth of everything which it fairly includes *? And if 
not, what then is the syllogistic art but a contrivance for catching you 
in a ti^ap, and holding you fast in it ? 

§ 3. From this difficulty there appears to be but one issue. The 
proposition, that the Duke of Wellington is mortal, is evidently an in- 
ference ; it is got at as a conclusion from something else ; but do we, in 
reality, concltide it from the proposition. All men are mortal] I an- 
swer, no. 

The error committed is, I conpeive, that of overlooking the distinc- 
tion between the two parts of the process of philosophizing, the infer- 
ring part, and the registering part ; and ascribing to the latter the 
functions of the former. The mistake is that of referring a man to his 
own notes for the origin of his knowledge. If a^man is asked a ques-^ 
tion, and is at the moment unable to answer it, he may refresh his 
memory by turning to a memorandum which he carries about with 
him. But if he were asked, how the fact came to his knowledge, he 
.would scarcely answer, because it was s€t down in his note-book: 
unless the book was written, like the Koran, with a quill from the 
wing of the angel Gabriel. 

Assuming that the proposition, The Duke of Wellington is mortal, 
is immediately an inference from the proposition. All men are mortal; 
whence do we derive our knowledge of that general truth ] No super- 
natural aid being supposed, the answer must be, by observation. Now, 
all which man can observe are individual cases. From these all gen- 
eral truths must be drawn, and into these they may be again resolved : 
for a general truth is but an aggregate of particular truths ; a compre- 
hensive expression, by which an indefinite number of individual facts 
are affirmed or denied at once. But a general proposition is not 
merely u compendious form for recording and preserving in the mem-- 
ory a number of particular facts, all of which have been observed. 
Generalization is not a process of mere naming, it is also a process of 
inference. From instances which we have observed, we feel warranted 
in concluding, that what we found true in those instances, holds in all 
similar ones, past, present, and future, however numerous they may be. 
We then, by that valuable contrivance of language which enables us to 
speak of many as if they were one, record all that we have observed, 
together with all that we infer from our observations, in one concise 
expression; and have 'thus only one proposition, instead of an endless 
nurriber, to remember or to communicate. The results of many obser- 
vations and inferences, and instructions for making innumerable infer- 
ences in unforeseen cases, are compressed into one short sentence. 

When, therefore, we conclude from the death of John and Thomsfcs, 
and every other person we ever heard of in whose case the experi- 
ment had been fairly tried, that the Puke gf Wellington is mortal like 



FUNCTIONS AND VALUE Or THE SYLLOGISM. 125 

the rest ; we may, indeed, pass tlirougli the generalization, All men 
are mortal, as an intermediate stage ; but it is not in the latter half of 
the process, the descent from all men to the Duke of Wellington, that 
the inference resides. ■ The inference is finished when we have asserted 
that all men are mortal. What remains to be performed afterwards 
is merely deciphering our own notes. 

Archbishop Whately has contended that syllogizing, or reasoning 
from generals to particulars, is not,^ agreeably to the vulgar idea, a pe- 
culiar mode of reasoning, but the philosophical analysis of tlie mode in 
which all men reason, and must do so if they, reason at all. With the 
deference due to so high an authority, I cannot help thinking that the 
vulgar notion is, in this case, the more correct. If, from our experi- 
ence of John, Thomas, &c., who once were living, but are now dead, 
We are entitled to conclude that all human beings are mortal, we might 
Purely without any logical inconsequence have concluded at once from 
those instances, that the Duke of Wellington is mortal. The mortality 
of John, Thomas, and company is, after all, the whole evidence we 
have for the mortality of the Duke of Wellington. Not one iota is 
added to the proof by interpolating a general proposition. Since the 
individual cases are all the evidence we can possess, evidence which 
no logical form into which we choose to throw it can make greater 
than it is ; and since that evidence is either sufficient in itself, or, if in- 
sufficient for one purpose, cannot be sufficient for the other; I am 
unable to see why we should be forbidden to take the shortest cut 
from these sufficient premisses to the conclusion, and constrained to 
travel the " high priori road" by the arbitrary fiat of logicians. I can- 
not perceive why it should be impossible to journey from one place to 
another unless we " march up a hill, and then march down again." It 
may be the safest road, and there may be a resting place at the top 
of the hill, affi)rding a commanding view of the surrounding country ; 
but for the mere purpose of an^iving at our journey's end, our taking 
that road is perfectly optional ; it is a question of time, trouble, and 
danger. . 

. Not only may we reason from particulars to particulars, without 
passing through generals, but we perpetually do so reason. All our 
-earliest inferences are of this nature. From the first dawn of intelli- 
gence we draw inferences, but years elapse before we learn the use 
of general' language. The child, who, having burnt his fingers, avoids 
to thrust them again into the fire, has reasoned or inferred, though he 
has never- thought of the general maxim. Fire burns. He knows from 
memory that he has been burnt, and on this evidence believes, when 
he sees a candle, that if he puts his finger into the flame of it, he will 
be burnt again. He believes this in every case which happens to 
arise ; but without looking, in each instance, beyond the present case. 
He is not generalizing ; he is inferring a particular from particulars. 
In the same way, also, brutes reason. There is little or no ground for 
attributing to any of the lower animals the use of conventional signs, 
without which general propositions are impossible. But those animals 
profit by experience, and avoid what they have found to cause them pain, 
in the same manner, though not always with the same skill, as a human 
creature. Not only the burnt child, l3ut the burnt dog, dreads the fire. 

I believe that, in point of fact, when drawing inferences from our 
personal experience and not from maxims handed down to us by 



126 REASONING. ,- • / . ' ' ^ 

books or tradition, we mucli oftener conclude from particulars to par- 
ticulars dii-ectly, than through the intermediate agency of any general 
proposition. We are constantly reasoning from ourselves to' other 
people, or from one person to another, without giving ourselves the 
trouble to erect our obsei'vations into general maxims of human or 
external nature. When we conclude that some person will, on some 
given occasion, feel' or act so and so, we sometimes judg;p from an 
enlarged consideration of the manner in which men in general, or men 
of some particular character, are accustomed to feel and act ; but 
much oftener fi-om having known the feelings and conduct of the same 
man in some previous instance, or from considering how we should 
feel or act ourselves. It is not ouly the village matron who, when 
called to a consultation upOn the case of a neighbor's child, proiiouii- 
ces on the evil and its remedy simply on the recollection and authority 
of what she accounts the similar case of her Lucy. We all, where, 
we have no definite m.axims to steer by, guide ourselves in the same 
way; and if we have an extensive experience, and retain its impres- 
sions strongly, we may acquire in this nianner a very considerable 
power of accurate judgiuent, which we may be utterly incapable of 
justifying or of communicating to others. Among the higher order of 
pra-ctical intellects, there have been many of whom it was remarked 
how" admirably they suited their means to their ends, without being 
able to give any sufficient reasons for what they did; and applied, or 
seemed to apply, recondite principles which they were wholly unable 
to state. This is a natural consequence of having a mind stored" 
with appropriate particulars, and having been long accustomed to 
risason at once from these to fresh particulars, without practising the 
habit of stating to oneself or to others the corresponding general prop- 
ositions. An old. ' waiTior, on a rapid glance at the outlines of the 
ground, is able at once to give the necessary orders for a skillful ar- 
rangement of his troops; though if he has received little theoretical 
instruction, and has seldom been called upon to answer to other people 
for his conduct, he may never have had in his mind a single general 
theorem respecting the relation between ground and array. But his 
experience of encampments, under circumstances more or less similar,' 
has left a nlimber of vivid, uwexpressed, ungeneralized analogies in 
his mind, the n:iost appropriate of which, instantly suggesting itself, 
determines him to a judicious an'angement. 

• The skill of an uneducated person in the use of ^V'eapbns, or of tools, 
is of a precisely similar nature. The savage who executes unemngly 
the exact throw which' brings down his game, or his enemy, In the man- 
ner most suited to his purpose, under the operation of all the conditions 
necessarily involved, the weight and form of the weapon, the direction 
and distance of the object, the action of the wind, &c., owes this power 
to a long series of previous' experiments, the^ results of which he cer- 
tainly never fi'amed into any verbal theorems or rules. It is the same 
in all extraordinary manual dexterity. Not long ago a Scotch manufac- 
tu7-er procured frqm England, at a high rate- of wages, a working dyer, 
famous for producing very fine colors', with 'the view of teacl^ing to his 
other workmetrtho same skilL The workman came ; but his mode of 
proportioning the ingredients,, in which lay the secret of the effects he 
produced, was by taldng them up in handftils, while the common method 
was to weigh them. Tlic manufacturer sought to make him turn his 



.FUNCTIONS AND VALUE OF THE SYLLOGISM. 127 

handling systeialmto. an equivalent weighing system, that the general 
principle of his peculiar mode of proceeding might be ascertained. 
This, however^ the man found himself quite unable to do, and therefore 
could impart his skill to. nobody. He had, from the individual cases of 
his own experience, established a connexion in his mind between fine 
effects of color, and tactual perceptions in handling his dyeing materi- 

xals ; and from these perceptions he could, in any particular cases, infer 
the means to be employed, and the effects which would be produced, 
but could not put others in possession of the grounds on which he pro- 
ceeded, from having never generalized them in -his own mind, or ex- 
pressed them in language. 

Almost every one knows Lord Mansfield's advice to a man of prac- 
tical good sense, who, being appointed governor of a colony, had to 

' preside in its court of justice, without previous judicial practice or legal 
education. The advice was, to give his decision boldly, for it would 
probably be right ;' but never to venture on assigning reasons, for they 
would almost infallibly be wrong. In cases like this, which are of no, 
uncommon occurrence, it would be absurd to suppose that the bad 
reason, was the source of the good decision.. Lord Mansfield knew that 
if any reason were assigned it would be necessarily an afterthought, 
the judge being in fact guided by impressions from past experience, 
without the circuitous process of frariiing general principles from them, 
and that if he attempted to frame any such he would assuredly fail. 
Lord Mansfield, however, would not have doubted that a man of equal 

'experience, who had ako a mind stored with general propositions de- 
rived by legitimate induction from that experience, would have been 
greatly preferable as a judge, to one,' however sagacious, who could 
not be trusted with the explanation and justification of his own judg- 
ments. The Cases of-able men performing wonderful things they know 
not how, are examples of the less civilized and most spontaneous form 
of the operations of superior minds. It is a defect in them, and often 
a source of errors, not to have generalized as they went on ; but gen- 
eralization is a heljp; &e jno&t important indeed of all helps, yet not an 
essential. " ' ' • '' ■. . 

". Even philoso;f)hers, who possess', in the form of general propositions, 
a systematic record of the results of the experience of manldnd, need 
not always revert to those .genetal propositions in order to apply that 
experience to a new case. It is justly remarked by Dugald Stewart, 
that though our re,asonings in mathematics, depend entirely upon the 
axioms, it is by no means necessary to our seeing the conclusiveness of 

. the proof, that the axioms should be expressly adverted to. Wlien it 
is inferred that A B is equal to C D because ^acli of them is equal to 

. E. F, the most uncultivated understanding, as soon as the propositions 
were understood, would as'sent to the inference, without having ever 

' heard of the gener ah truth that '' things which are equal to the same 
thing are equal to one another." This- remark of Stewart, consistently 
followed out, goes to the root, as I conceive, of the philosophy of 
ratiocination ; and it is to be regretted that he himself stopped short at 
a much more limited application of it. He saw that the general propo- 
sitions on which a reasoning is said to depend, may, in certain cases, 
be altogether omitted, without impairing its probative force. But he 
imagined this to be a peculiarity belonging to axioms ; and argued from 
it, that axioms are not the foundationg or fii'sf principles of geometiy, 



128 ..REASONING. ^ *•", • 

from wMchall the other truths bf the science are synthetically deduced 
(as the laws of motion and of the composition of forces in mechanics, . 
the equal mobility of fluids in hydrostatics, the laws of reflection and 
refraction in optics, are the first principles of those sciences) ; but are 
merely necessary assumptions, self-evident indeed, and the denial of 
which would annihilate all demonstration, but from which, as premisses, . 
nothing can be demonstrated. In the present, as in many other in- 
stances, this thoughtful and elegant WTiter has perceived an important 
truth, but only by halves. Finding, in the case of geometrical axioms, 
that general names have not any talismanic virtue for conjuring new 
truths out of the pit of darkness, and not seeing that this is equally true 
in every other case of generalization, -he contended that axioms are in 
their nature barren of consequences, and that the really fruitful truths, 
the real first principles of geometry, are the definitions ; that the defi- 
nition, for example, of the circle is to the properties of the circle, what 
the laws of equilibrium and of the pressure of the atmosphere are to the 
rise of the mercury in the Torricellian tube. Yet- all that he had 
asserted respecting the, function to which the ' axioms are confined in 
the demonstrations of geometry, holds equally true of the definitions. 
Every demonstration in Euclid might be carried on without them. 
This is apparent from the ordinary process of proving a proposition of 
geometry by means of a diagram. What assumption, in fact, do we 
set out from, to demonstrate by a diagram any of the properties of the 
circle 1 Not that in all circles the radii are equal, but only that they 
are so in the circle ABC. As our warrant for assuming this, we 
appeal, it is true, to the definition of a circle in general; but it is only 
necessary that you should grant the assumption in the case of the par- 
ticular circle supposed. From this, which is not a general but a sin- 
gular proposition, combined with other propositions of a similar kind, 
some of which tv/ien generalized are called definitions, and others 
axioms, we prove that a certain conclusion is true, not of all circles^ 
but of the particular circle ABC; or at least would be so, if the facts- 
precisely accorded with our assumptions. The enunciation, as it is 
called, that is, the general theorem which stands at the head of the 
demonstration, is not the proposition actually demonstrated. One 
instance only is demonstrated : but the process by which this is done, 
is a process which, when we consider its nature, we perceive might be 
exactly copied in an indefinite number of other instances; in every 
instance which conforms to certain conditions. The contrivance of 
general language furnishing us with tei'ms which connote these con- 
ditions, we are" able to assert this indefinite multitude of truths in a 
single expression, and this expression is the general theorem. By 
di'opping the use of diagi^ams, and substituting, in the demonsti'ations, 
general phrases for the letters of the alphabet, we might prove the 
general theorem directly, that is, we might demonstrate all the cases 
at once; and to do this we must, of course, employ as our premisses, 
the axioms and definitions in their general form. But this only mea-ns, 
that if wc can prove an individual conclusion by assuming an individual 
fact, then in whatever case we are waiTanted in making aji exactly 
similar assumption, we may draw an exactly similar conclusion. The 
definition is a sort of notice to ourselves and others, what assumptions 
we thinl<: ourselves entitled to make. And so in all cases, the general 
propositions^ whether called definitions, axioms, or laws of nature, 



FUNCTIONS AND VALUE OF THE SYLLOGISM. 129 

which we lay down at the beginning of our reasonings, are merely 
abridged statements in a kind of short hand, of the particular facts, 
which, as occasion arises, we either think we may proceed upon as 
proved, or intend to assume. In any one demonstration it is enough 
if we assume for a particular case, suitably selected, what by the state- 
ment of the definition or principle we announce that we intend to 
o,ssume in all cases which may arise. The definition of the circle, 
therefore, is to one of Euclid's demonstrations, exactly what, according 
to Stewart, the axioms are ; that is, the demonstration does not depend 
upon it, but yet if we deny it the demonstration fails. The proof does 
not rest upon the general assumption, but upon a similar assumption 
confined to the particular case : that case, however, being chosen as a 
specimen or paradigm of the whole class of cases included in the theo- 
rem, there can be no ground for making the assumption in that case 
which does not exist in every other ; and if you deny the asstimption as 
a general truth, you deny the right to make it in the particular instance. 
There are, undoubtedly, the most ample reasons for stating both the 
principles and the theorems in their general form, and these will be 
explained presently, so far as explanation is requisite. But, that an 
unpractised learner, even in making use of one theorem to demon- 
strate another, reasons rather from particular to particular than from 
the general proposition,, is manifest from the diflSculty he finds in ap- 
plying a theorem to a case in which the configuration of the diagram 
is extremely unlike that of the diagi'am by which the original theorem 
was demonstrated. A difl[iculty which, except in cases of unusual 
mental power, long practice can alone remove, and removes chiefly by 
rendering us familiar with all the configurations consistent with the 
general conditions of the theorem. 

§ 4. From the considerations now adduced, the following conclu- 
sions seem to be established: All inference is from particulars to par- 
ticulars : Greneral propositions are merely registers of such inferences 
already made, and short formulae for making more : The major premiss 
of a syllogism, consequently, is a formula of this description : and 
the conclusion is not an inference drawn jrro?n the formula, but an in- 
ference drawn according to the formula : the real logical antecedent, 
or premisses, being the particular facts from which the general propo- 
sition, was collected by induction. Those facts, and the individual in- 
stances which supplied them, may have been forgotten ; but a record 
remains, not indeed descriptive of the facts themselves, but showing 
how those cases may be distinguished respecting which the facts, when 
known, were considered to warrant a given inference. According to 
tlie indications of this record, we draw our conclusion ; which is, to all 
intents and purposes, a conclusion from the forgotten facts. For this 
it is essential that we should read the record correctly : and the rules 
of the syllogism are a set of precautions to insure our doing so. 

This view of the functions of the syllogism is confirmed by the con- 
sideration of precisely those cases which might be expected to be least 
favorable to it, namely, those in which ratiocination is independent of 
any previous induction. We have already observed that the syllogism, 
in the ordinary course of our reasoning, is only the latter half of the 
process of ti'avelling from premisses to a conclusion. There are, how- 
ever, some peculiai' cases in which it is the whole process. Particu- 
R 



130 REASONING. 

lars alone are capable of being subjected to observation ; and all knowl- 
edge which is derived from observation, begins, therefore, of necessity, 
in particulars ; , but our knowledge may-, in cases of a certain descrip- 
tion, be conceived as coming to us from other sources than obser\^a- 
tion. It may pz'esent itself as coming from revelation ; and the knowl- 
edge, thus supernaturally communicated, may be conceived to com- 
prise not only particular facts but general propositions, such as occur 
so abundantly in the t\Titings of Solomon and in the apostolic epistles. 
Or the generalization may not be, in the ordinary sense, an assertion at 
all, but a command ; a law, not in the philosophical, but in the moral 
and political sense of the term : an expression of the desire of a supe- 
rior, that we, or any number of other persons, shall conform our con- 
duct to certain general instriictions. So far as this asserts a fact, 
namely, a volition of the legislator, that fact is anindividual fact, and 
the proposition, therefore, is not a general proposition. But the de- 
scription therein contained of the conduct which it is the will of the 
legislator that his subjects should observe, is general. The proposi- 
tion asserts, not that all men a?'e anything, but that all men s?iaU do 
something. These two cases, of a truth revealed in general terms, arid 
a command intimated in the like manner, might be exchanged for the 
more extensive cases, of any general statement received upon testimony, 
and any general practical precept. But the more limited illustrations 
suit us better, being drawn from subjects where long and complicated 
trains of ratiocination have actually been grounded upon premisses 
which came to mankind from the first in. a general form, the subjects 
of ScriptuTal Theology and of positive Law. 

> In both these cases the generalities are given to us, and the partic- 
ulars are ehcited from them by a process which correctly resolves itself 
into a series of syllogisms. The real nature, however, of the supposed 
deductive process, is evident enough. It is a search for truth, no "doubt, 
but through the medium- of an inquiry into the meaning of a form of 
words. The only point to be determined is, whether the authority 
which declared the general proposition, intended to include this case 
in it ; and whether the legislator intended his command to apply to the 
present case among others. Or not. This is a. question, as the Germans 
express it, of hermeneutics ; it relates to the meaning of a certain foiTQ 
of discourse. The operation is not a process of inference, but a pro- 
cess of interpretation. . . 

In this last phrase we have obtained an expression which appears to 
me to characterize, more aptly than any other, the functions of the 
syllogism in all cases. When the premisses are given by authority, 
the function of Reasoning is to ascertain the testimony of a^' witness, 
or the will of a legislator, by interpreting the signs in which the one 
has intimated his assertion and the other his command. In like man- 
ner, when the premisses ai'e derived from observation, the function of 
Reasoning is to ascertain What we (or our predecessors) formerly 
thought might be infen-ed from the observed facts, and to do this by 
intei'prcting a memorandum of ours, or of theirs. The memorandum 
reminds us, that from evidence, more or less carefully weighed, it 
formerly appeared that a certain attribute might be inferred wherever 
wo perceive a certain mark. The proposition. All men are mortal, 
(for instance,) shows that we have had experience from which we 
thought it followed that the attributes connoted by the term man, are 



FUNCTIONS AND VALUE OP THE SYLLOGISM. 131 

a mark of mortality. But when we conclude that the Duke of "Wel- 
lington is mortal, we do not infer this from the memorandum, but from 
the former experience. All that we infer from the memorandum, is 
our own previous belief, (or that of those who transmitted to us the 
proposition,) concerning the inferences which that former experience 
would waiTant. 

This view of the nature of the syllogism renders consistent and 
intelligible what otherwise remains obscure and confused in the theory 
of Archbishop Whately and other enlightened defenders of the 
syllogistic doctrine, respecting the limits to which its functions are 
confined. They all affirm, in as explicit terms as can be used, that 
the sole office of general reasoning is to prevent inconsistency in our 
opinions ; to prevent us from assenting to anything, the truth of which 
would contradict something to which we had previously on good 
grounds given our assent. And they tell us, that the sole ground 
w^hich a syllogism affords for assenting to the conclusion, is that the 
supposition of its being false, combined with the supposition that the 
premisses are true, would lead to a contradiction in terms. Now this 
would be but a lame account of the real grounds which we have for 
believing the facts which we learn from reasoning, in contradistinction 
to observation. The true reason why we believe that the Duke of 
Wellington will die, is that his fathers, and our fathers, and all other 
persons who were contemporary with them, have died. Those facts 
are the real premisses of the reasoning. But we are not led to infer 
the conclusion fi'om those premisses, by the necessity of avoiding any 
verbal inconsistency. There is no contradiction in supposing that all 
those persons have died, and that the Duke of Wellington may, not- 
withstanding, live for ever. But there would be a contradiction if we 
first, on the ground of those same premisses, made a general assertion 
including and covering the case of the. Duke of AVellington, and then 
refused to stand to it in the individual case. There is an inconsistency 
to be avoided between the memorandum we make of the inferences 
which maybe justly drawn in future - cases, and the inferences we 
actually draw in those cases when they arise. With this view we 
intei-pret our ovm formula, precisely as a judge interprets a law: in 
order that we may avoid drawing any inferences not conformable to 
our former intention^ as a judge avoids giving any decision not con- 
formable to the legislator's intention. The rules for this interpretation 
are the rules of the syllogism: and its sole purpose is to maintain 
consistency between the conclusions we draw in every particular case, 
and the previous general directions for drawing them ; whether those 
general directions were framed by ourselves as the result of induction, 
or were received by us from an authority competent to give them. 

§ 5. In the above observations it has, I think, been clearly shown, 
that, although there is always a process of reasoning or inference 
where a syllogism is used, the syllogism is not a connect analysis of 
that process of reasoning or inference; which is, on the contrary,, 
(when not a mere inference from testimony,) an inference fi'om partic- 
ulars to particulars ; authorized by a previous inference from particu- 
lars to generals, and substantially the same vdth it ; of the nature, 
therefore, of Induction. But while these conclusions appear to me 
undeniable, I must yet enter a protest, as strong as that of Archbishop 



132 ' - REASONING. 

Whately himself, against the doctrine that the syllogistic art is useless 
for the purposes of reasoning. The reasoning lies in the act of gen- 
eralization, not in interpreting the record of that act ; but the syllogistic 
form is an indispensable collateral security for the correctness of the 
generalization itself 

It has already been seen, that if we have a collection of particulars 
sufficient for grounding an induction, we need not frame a general 
proposition ; we may reason at once from those particulars to other 
particulars. But it is to be remarked withal, that whenever, from a 
set of particular cases, we can legitimately draw any inference, we/ 
may legitimately make our inference a general one. If, from obser- 
vation and experiment, we can conclude to one new case, so may we 
to an indefinite number. If that which has held true in our past 
experience will therefore hold in time to come, it will hold not merely 
in some individual case, but in all cases of a given description. Every 
induction, therefore, which suffices to prove one fact, proves an indefi- 
nite multitude of facts : the experience which justifies a single predic- 
tion must be such as will suffice to bear out a general theorem. This 
theorem it is extremely important to ascertain and declare, in its 
broadest form of generality ; and thus to place before our minds, in 
its full extent, the whole of what our evidence must prove if it proves 
anything. 

This throwing of the whole body of possible inferences from a given 
set of particulars, into one general expression, operates as a security 
for their being just inferences in more ways than one. First, the gen- 
eral principle presents a. larger object to the imagination than any of 
the singular propositions which it contains. A process of thought which 
leads to a comprehensive generality, is felt as of greater importance 
than one which terminates in an insulated fact ; and the mind is, even 
unconsciously, led to bestow greater attention upon the process, and 
to weigh more carefully the sufficiency of the experience appealed to, 
for supporting the inference grounded upon it. There is another, and 
a more important, advantage. In reasoning from a course of individ- 
ual observations to some new and unobserved case, which we are but 
imperfectly acquainted with (or we should not be inquiring into it), 
and in which, since we are inquiring into it, we probably feel a pecu- 
liar interest ; there is very little to prevent us from giving way to 
negligence, or to any bias which may affect our wishes or our imagina- 
tion, and, under that influence, accepting insufficient evidence as suffi- 
cient. But if, instead of concluding straight to the particular case, we 
place before ourselves an entire class of facts, the whole contents of a 
general proposition, every tittle of which is legitimately inferrible from 
our premisses, if that one particular conclusion is so ; there is then a 
considerable likelihood that if the premisses are insufficient, and the 
general inference, therefore, groundless, it will comprise within it some 
fact or facts the reverse of which we already know to be true ; and 
we shall thus discover the error in our generalization, by what the 
schoolmen termed ^rcduttio ad impossibile. 

Thus if, during the reign of Marcus Aurelius, a subject of the Roman 
empire, under the bias naturally given to the imagination and expec- 
tations by the lives and characters of the Antonines, had been disposed 
to conclude that Commodus would be a just ruler : supposing him to 
stop there, he might only have been undeceived by sad experience. 



FUNCTIONS AND VALUE OF THE SYLLOGISM. 133 

But if he reflected that this conclusion could not be justifiable unless 
fi'om the same evidence he was also warranted in concluding some gen- 
eral proposition, as, for instance, that all Roman emperors are just 
rulers; he would immediately have thought of Nero, Domitian, and 
other instances, which, showing the falsity of the general conclusion, and 
therefore the insufficiency of the premisses, would have warned him 
that those premisses could not prove in the instance of Commodus, 
what they were inadequate to prove in any collection of cases in which 
}i,is was included. 

The advantage, in judging whether any controverted inference is 
legitimate, of referring to a parallel case, is universally acknowledged. 
But by ascending to the general proposition, we bring under our view 
not one parallel case only, but all possible parallel cases at once; all 
cases to which the same set of evidentiary considerations are applicable. 
, When, therefore, we argue from a number of known cases to another 
case supposed to be analogous, it is always possible, and generally ad- 
vantageous, to divert oiir EirgUment into the circuitous channel of an 
induction fi^om those known cases to a general proposition, and a subse- 
quent application of the general proposition to the unknown case. 
This second part of the operation, which, as before observed, is essen- 
tially a process of interpretation, will be resolvable into a syllogism or 
a series of syllogisms, the majors of which will be general propositions 
embracing whole classes of cases; every one of which propositions 
must be true in all its « extent, if our argument is maintainable. If, 
therefore, any fact fairly coming within the range of one of these general 
propositions, and consequently asserted by it, is known or suspected 
to be other than the proposition asserts it to be, this mode of stating 
the argument causes us to know or to suspect that the original obser- 
vations, which are the real grounds of our conclusion, are not sufficient 
to support it. And in proportion to the greater chance of our detecting 
the inconclusiveness of our evidence, will be the increased reliance we 
are entitled to place in it if no such evidence of defect shall appear. 

The value, therefore, of the syllogistic form, and of the rules for 
using it correctly, does not consist in their being the form and the rules 
according to which our reasonings are necessarily, or even usually, 
made ; but in their furnishing us with a mode in which those reason- 
ings may always be represented, and which is admirably calcu- 
lated, if they are inconclusive, to bring their inconclusiveness to light. 
An induction from particulars to generals, followed by a syllogistic 
process frorh those- generals to other particulars, is a form in which we 
may always state our reasonings if we please. It is not a form in 
which we must reason, but it is a form in which we mat/ reason, and 
into which it is indispensable to throw our reasoning, when there is 
any doubt of its validity; though when the case is familiar and little 
complicated, and there is no suspicion of error, we may, and do, reason 
at once from the known particular cases to unknown ones. 
'. These are the uses of the syllogism, as a mode of verifying any 
given argument. Its ulterior uses, as respects the general course of 
our intellectual operations, hardly require illustration, being in fact the 
acknowledged uses of general language. They amount substantially 
to this, that the inductions may be made once for all : a single careful 
interrogation of experience may suffice, and the result may be regis- 
tered in the form of a general proposition, which is committed to 



134 , . . REASONING. 

memory or to writing, and fi'om whicli afterwards we have only to syl- 
logize. The particulars of our experiments may then be dismissed 
from the memory, in which it would be impossible to retain so great 
a multitude of details ; while the knowledge which those details afforded 
for future use, and which would otherwise be lost as soon as the obser- 
vations were forgotten, or as their record became too bulky for refer- 
ence, is retained in a commodious and immediately available shape by 
means of general language. 

Against this advantage is to be set the countervailing inconvenience^ 
that inferences originally made on insufficient evidence, become conse- 
crated, and, as it were, hardened into general maxims ; and the mind 
cleaves to them from habit, after it has outgrown any liability to be 
misled by similar fallacious appearances if they were now for the first 
time presented ; but having forgotten the particulars, it does not think 
of revising its own former decision. An inevitable drawback, which, 
however considerable in itself, forms evidently but a trifling deduction 
from the immense advantages of general language. . 

The use of the syllogism is in truth no other than the use of general 
propositions in reasoning. We can reason without them ; in simple 
and obvious cases we habitually do so ; Ininds of great sagacity can 
do it in cases not simple and obvious, provided their experience 
supplies them with instances essentially similar to every combination 
of circumstances likely to arise. But other men, or the same men 
when without the same preeminent advantages of personal experience, 
are quite helpless without the aid of general propositions, wherever 
the case presents the smallest complication ; and if we made no general 
propositions, few of us would get much beyond those simple infer- 
ences which are drawn by the more intelligent of the brutes. Though 
not necessary to reasoning, general propositions are necessary to any 
considerable progress in reasoning. It is, therefore, natural and 
indispensable to separate the. process of investigation into two parts ; 
and obtain general formulae for determining what inferences may be 
drawn, before the occasion arises for drawing the inferences. The 
work of drawing them is then that of applying the formulas ; and the 
rules of the syllogism are a system of securities for the correctness of 
the application. 

§ 6. To complete the series of considerations connected with the 
pnilosophical character of the syllogism, it is requisite to consider^ 
since the syllogism is not the universal type of the reasoning process, 
what is the real type. This resolves itself into the question, what is 
the nature of the minor premiss, and in what manner it contributes to 
establish the conclusion : for as to the major, we now fully understand, 
that the place which it nominally occupies in oiir reasonings, properly 
belongs to the individual facts or observations of which it expresses 
the general result ; the major itself being no real part of the argument, 
but an intermediate halting place for the mind, interposed by an artifice 
of. language between the real premisses and the conclusion, by way 
, of a security, which it is in a most material degree, for the correctness 
of the process. The minor, however, being an indispensable part of 
the syllogistic expression of an argument, without doubt either is, or 
correspf)nds to, an equally indispensable part of the argument itself* 
and we have only to inquire what part. 



FUNCTIONS AND VALUE OF THE SYLLOGISM. 135 

Jt is perhaps worth while to notice here a speculation of one of the 
philosophers to whom mental science is most indebted, but who, 
thougli a very penetrating, was a very hasty thinker, and whose want 
of due circumspection rendered him fully as remarkable for what he 
did not see, as for what he saw. I allude to Dr. Thomas Brown, 
whose theory of ratiocination is peculiar. He saw the lyetitio principii 
which is inherent in every syllogism, if we consider the major to be 
itself the evidence by which the conclusion is proved, instead of being, 
what in fact it is, an assertion of the existence of evidence sufficient 
to prove any conclusion of a given description. Seeing this, Dr. 
Brown not only failed to see the immense advantage, in point of 
security for coiTectness, which is gained by interposing this step 
between the real evidence and the conclusion ; but he thought it 
incumbent upon him to strike out the major altogether from the reason- 
ing process, without substituting anything else ; and maintained that 
our reasonings consist only of the minor premiss and the conclusion, 
Socrates is a man, therefore Socrates is mortal : thus actually suppress- 
ing, as an unnecessary step in the argument, the appeal to former 
experience. The absurdity of this was disguised from him by the 
opinion he adopted, that reasoning is merely analyzing our own general 
notions, or abstract ideas ; and that the proposition, Socrates is mortal, 
is evolved from the proposition, Socrates is a man, simply by recog- 
nizing the notion of mortality, as already contained in the notion we 
form of a man. 

After- the explanations so fully entered into on the subject of 
propositions, much further discussion cannot be necessary to make the 
radical error of this view of ratiocination apparent. If the word man 
connoted mortality ; if the meaning of " mortal" were involved in the 
meaning of "man;" we might, undoubtedly, evolve the conclusion 
from the minor alone, because the minor would have distinctly asserted 
it. But if, as is in fact the case, the word man does not connote mortality, 
how does it appear that in the mind of every person who admits 
Socrates to be a man, the idea of man must include the idea of mor- 
tality 1 ,. Dr. Brown could not help seeing this difficulty, and in order 
to avoid it, was led, contrary to his intention, to reestablish, under 
another name, that step in the argument which corresponds to the 
major, by affirming the necessity of previously perceiving the relation 
between the idea of man and the idea of mortal. If the reasoner has 
not previously perceived this relation, he will not, says Dr. Brown, 
infer because Socrates is a man, that Socrates is^ mortal. But even 
this admission, though amounting to a surrender of the doctrine that 
an argument consists of the minor and the conclusion alone, will not 
save the remainder of Dr. Brown's theory. The failure of assent to 
the argument does not take place merely because the reasoner, for 
want of due analysis, does not perceive that his idea of man includes 
the idea of mortality ; it takes place, much more commonly, because 
in his mind that relation between the t\YO ideas has never existed. 
And in truth it never does exist, except as the result of experience. 
Consenting, for the sake of the argument, to discuss the question upon 
a supposition of which we have recognized the radical incorrectness, 
namely, that the meaning of a proposition relates to the ideas of the 
things spoken of, and not to the things themselves ; and conceding for 
a moment, the existence of abstract ideas, I must yet observe, that the 



136 REASONING. 

idea of man, as an universal idea, the common property of all rational 
creatures, cannot involve anything but what is strictly implied in the 
name. If any one includes in his ov^n private idea of man, as no 
doubt is almost always the case, some other attributes, such for 
instance as mortality, he does so only as the consequence of experi- 
ence after having satisfied himself that all men possess that attribute: 
so that whatever the idea contains, in any person's mind, beyond what 
is included in the conventional signification of the word, has been added 
to it as the result of assent to a proposition ; while Dr. Brown's theory 
requires us to suppose, on the contrary, that assent to the proposition 
is produced by evolving, through an analytic process, this very el^ement 
out of the idea. This theory, therefore, may be considered as 
sufficiently refuted, and the minor premiss must be regarded as totally 
insufficient to prove the conclusion, except with the assistance of the 
major, or of that which the major represents, namely, the various 
singular propositions expressive of the series of observations, of which 
the generalization called the major premiss is the result. 

In the argument, then, which proves that Socrates is mortal, one 
indispensable part of the premisses will be as follows : " My father, 
and my father's father. A, B, C, and an indefinite number of other 
persons, were mortal;" which is only an expression in different words 
of the observed fact that they have died. This is the major premiss, 
divested of the petitlo princifii, and cut down to as much as is really 
known by direct evidence. 

In order to connect this proposition wdth the conclusion, Socrates is 
mortal, the additional link necessary is such a proposition as -the fol- 
lowing : " Socrates resembles my father, and my father's father, and 
the other individuals specified," This proposition w^e assert when we 
say that Socrates is a man. By saying so we likewise assert in what 
respect he resembles them, namely, in the attributes connoted by the 
word man. And from this we conclude that he further resembles 
them in the attribute mortality. 

§ 7. We have thus obtained what we were seeking, an universal 
type of the reasoning process. We find it resolvable in all cases into 
the following elements : Certain individuals have a given attribute ; 
an individual or individuals resemble the former in certain other attri- 
butes ; therefore they resemble them also in the given attribute. This 
type of ratiocination does not claim, like the syllogism, to be conclu- 
sive from the mere form of the expression ; nor can it possibly be so. 
That one proposition does or does not assert the very fact which was 
already asserted in another, may appear from the form of the expres- 
sion, that is, from a comparison of the language ; but when the two 
propositions assert facts which are hondjlde different, whether the one 
fact proves the other or not can never appear from the language, but 
must depend upon other considerations. Whether, from the attributes 
in which Socrates resembles those men who have heretofore died, it 
is allowable to infer that he resembles them also in being mortal, is a 
question of Induction ; and is to be decided by the principles or canons 
which we shall hereafter recognize as tests of the correct performance 
of that great mental operation. 

Meanwhile, however, it is certain, as before remarked, that if thia 
inference can be drawn as to Socrates, it can be drawn as to all others 



TRAINS OF REASONING. 137 

wlio resemble the observed individuals in the same attributes in which 
he resembles them ; that is (to express the thing concisely), of all men. 
If, therefore, the argument be conclusive in the case of Socrates, we 
are at liberty, once for all, to treat the possession of the attributes of 
man as a mark, or satisfactory evidence, of the attribute of mortality. 
This we do by laying down the universal proposition. All men are 
mortal, and interpreting this, as occasion arises, in its application to 
Socrates and others. By this means we establish a very convenient 
division of the entire logical operation into 'two steps; first, that of 
ascertaining what attributes are marks of mortality ; and, secondly, 
whether any given individuals possess those marks. And it will gener- 
ally be advisable, in our speculations on the reasoning process, to 
consider this double operation as in fact taking place, and all reason- 
ing as carried on in the form into which it must necessarily be thrown 
to enable us to apply to it any test of its correct performance. 

Although, therefore, all processes of thought in which the ultimate 
premisses are particulars, whether we conclude from particulars to a 
general formula, or from particulars to other particulars according to 
that formula, are equally Induction; we shall yet, conformably to 
usage, consider the name Induction as mOre peculiarly belonging to 
the process of establishing the general proposition ; and the remaining 
operation, which is substantially that of interjjreting the general pro- 
position, we shall call by its usual name. Deduction. And we shall 
consider every process by which anything is inferred respecting an 
unobserved case, as consisting of an Induction followed by a Deduc- 
tion; because, although the process needs not necessarily be earned 
on in this form, it is always susceptible of the form, and must be 
thrown into it when assurance of scientific accuracy is needed and 
desired. 



CHAPTER IV. 

OF TRAINS OF REASONING, AND DEDUCTIVE SCIENCES. 

§ 1. In our analysis of the syllogism it appeared that the minor prem- 
iss always affirms a resemblance between a new case, and some cases 
previously known ; while the major premiss asserts something which, 
having been found true of those known cases, we consider ourselves 
warranted in holding true of any other case resembling the former in 
certain given particulars. 

If all ratiocinations resembled, as to the minor premiss, the examples 
which we exclusively employed in the preceding chapter; if the re- 
semblance, which that premiss asserts, were obvious to the senses, as in 
the proposition, " Socrates is a man," or were at once ascertainable by 
direct observation ; there would be no necessity for trains of reasoning, 
and Deductive or Ratiocinative Sciences would not exist. Trahis of 
reasoning exist only for the sake of eiitending an induction, founded as 
all inductions must be upon observed cases, to other cases in which we 
not only cannot directly observe what is to be proved, but cannot di- 
rectly observe even the mark which is to prove it. 
S 



138 . ' . REASONING. 

§ 2. Suppose the syllogism to be, All cows ruminate, the animal which 
is before me is a cow, therefore it ruminates. The minor, if true at all, 
is obviously so : the oiily premiss the establishment of which requires 
any anterior process of inquiry, is the major;, and provided the induc- 
tion of which that premiss is the expression was correctly performed, 
the conclusion respecting the animal now present will be instantly 
drawn; because as soon as she is compared with the formula, she will 
be identified as being included in it. But suppose the syllogism to be 
the following: — All arsenic is poisonous-, the substance which is, before 
me is arsenic, therefore it is poisonous. The truth of the minor may not 
here be obvious at first sight ; it may not be intuitively evident, but may 
itself be known only by inference. It may be the conclusion of another 
argument, which, thrown into the syllogistic form, would stand thus:— 
Whatever forms a compound with hydrogen, which yields a black pre- 
cipitate with nitrate of silver, is arsenic ; the substance before me con- 
forms to this condition ; therefore it is arsenic. To establish, therefore, 
the ultimate conclusion. The substance before me is -poisonous, requires 
a process which, in order to be syllogistically expressed, stands in need 
of two syllogisms : and we have a Train of Reasoning. 

"When, however, we thus add syllogism to syllogism, we are really 
adding induction to induction. Two separate inductions must have ta- 
ken place to render this chain of inference possible ; inductions founded^ 
probably, on different sets of individual instances, but which converge in 
their results, so that the instance which is the subject of inquiry comes 
within the range of them both. The record of these inductions is con- 
tained in the majors of the two syllogisms. First, we, or others before 
us, have examined various objects which yielded under the given cir-. 
cumstances the given precipitate, and found that they possessed the 
properties connoted by the word arsenic ; they were metallic, volatile, 
their vapor had a smell of garlic, and so forth. Next, we, or others be-, 
fore us, have examined various specimens which possessed this metallic 
and volatile character, whose vapor had this smell, &c., and have inva- 
riably found that they were poisonous. The first observation we judge 
that we may extend to all substances whatever which yield the precipi- 
tate : 'the second, to all metallic and volatile substances resembling 
those we examined; and consequently, not to those only which are 
seen to be such, but to those which are concluded to be such by the 
prior induction. The substance before us is only seen to come within 
one of these inductions ; but by means of this one, it is brought within 
the other. We are still, as before, concluding fi'om particulars to par- 
ticulars ; but we are now concluding from particulars observed, to other 
particulars which are not, as in the simple case, seen to resemble them 
in the material points, but inferred to do so, because resembling them 
in something else, which we have been led by quite a different set of 
instances to consider as a mark of the former resemblance. 

This first example of a train of reasoning is still extremely simple, 
the series consisting of only two syllogisms. The following is some- 
what more complicated : — No government, which earnestly seeks the 
good of its subjects, is liable to revolution ; the Prussian government 
earnestly seeks the good of its subjects, therefore it is not in danger 
of revolution. The major premiss in. this argument we shall suppose 
not to be derived from considerations a priori, but to be a generaliza- 
tion from history, which, whether correct or erroneous, must have 



TRAINS OF REASONING. 139 

been founded upon . observation of governments concerning w^hose 
desire of the good of their subjects there: vv^as no doubt. It bas been 
found, or thought to be found, that these were not hable to revolution, 
and it has been deemed that those instances v^arranted an extension 
of the same predicate to any and every government which resembles 
them in the attribute of desiring earnestly the good 'of its subjects. 
But does the Prussian government thus resemble them 1 This may be 
debated pro and con hj many arguments, and must, in any case, be 
proved by another induction ; for we cannot directly observe the sen- 
timents and desires of the persons who conduct the government of 
that country. To prove the minor, therefore, we require an argument 
in this form : Every government which acts in a certain manner, de- 
sires 'the good of its subjects; the Prussian government acts in that 
particular manner, therefore it desires the good of its subjects. But 
is it true that the Prussian government acts in the manner supposed 1 
This minor also may require proof; still another induction, as thus: — 
What is asserted by many disinterested witnesses, must be believed 
to be true ; that the Prussian government acts in this manner, is as- 
serted by many disinterested witnesses, therefore it must be believed 
to be true. The argument hence consists of three steps. Having the 
evidence of our senses tbat the case of the Prussian government re- 
sembles a number of former cases,, in the circumstance of having 
something asserted respecting it by many disinterested witnesses, we 
infer, first, that as in those former instances, so in this instance the asser- 
tion is true. Secondly, what was asserted of the Prussian government 
being that it acts in a particular manner, and other governments or 
persons having been observed to act in the same manner, the Prussian 
government is. brought into known resemblance with those other gov- 
ernments or persons ; and since they were known to desire the good 
of the people, we thereupon, by a second induction, infer that the 
Prussian government desires the good of the people. This brings that 
government into known resemblance with the other governments which 
were observed to escape revolution, and thence, by a third induction, 
we predict that the Prussian government will in like manner escape. 
And thus we are enabled to reason from the well-intentioned govern- 
ments which we historically know as having escaped revolution, to 
other governments which, when we made the induction, we may have 
known nothing about : yet if the induction was good, and therefore 
applicable to all governments of which we know the intentions but do 
not know the fortunes, it must be no less applicable to those whose 
intentions we do not know, but can only infer, provided this inference 
also rests upon a good induction. We are still reasoning from particu- 
lars to particulars, but we now reason to the new instance from three 
distinct sets of former instances : to one only of those sets of instances 
do we directly perceive the new one to be similar ; but from that sim- 
ilarity we inductively infer that it has the attribute by which it is as- 
similated to the next set, and brought within the corresponding induc- 
tion ; when by a repetition of the same operation we infer it to be 
similar to the third set, and hence a, third induction conducts us to the 
ultimate conclusion. 

§ 3, Notwithstanding the superior complication of these examples, 
compared with those by which in the preceding chapter we illustrated 



140 REASONING. - 

the general theory of reasoning, every doctrine which we then laid, 
down holds equally true in these more intricate cases. The succes- 
sive general propositions are not steps in the reasoning, are not inter- 
mediate links in the chain of inference, between the particulars observed, 
and those to which we apply the observation. If we had sufficiently 
capacious memories, and a sufficient power of maintaining order among 
a huge mass of details, the reasoning could go on without any general 
propositions ; they are mere formulae for infemng particulars from 
particulars. The principle of general reasoning is (as before explained), 
that if from observation of certain known particulars, what was seen to 
be true of them can be inferred to be true of any others, it may be in- 
ferred of all others which are of a certain description. And in order 
that we may never fail to draw this conclusion in a new case when it 
can be drawn coiTectly, and may avoid drawing it when it cannot, we 
determine once for all what are the distinguishing marks by which 
such cases may be recognized. The subsequent process is merely 
that of identifying an object, and ascertaining it to have those marks; 
whetlier we identify it by the very marks themselves, or by others 
which we have ascertained (through another and a similar process) to 
be marks of those marks. The real inference is always from particu- 
lars to particulars, from the observed instances to an unobserved one : 
but in drawing this inference, we conform to a formula which we have 
adopted for our guidance in such operations, and which is a record of 
the criteria by which we thought we had. ascertained that we might 
distinguish when the inference could and when it could not be drawn. 
The real premisses are the individual observations, even though they 
may have been forgotten, or being the observations of others and not 
of ourselves, may, to us, never have been known : but we have 
before us proof that we or others once thought them sufficient for an 
induction, and we have marks to show whether any new case is 
one of those to which, if then known, the induction would have been 
deemed to extend. These marks we either recognize at once, or by 
the aid of other marks, which by another previous induction we col- 
lected to be marks of them. Even these marks of marks may only be 
.recognized through a third set of marks ; and we may have a train of 
reasoning, of any length, to bring a new case within the scope of an 
induction grounded on particulars its similarity to which is only ascer- 
tained in this indirect manner. 

Thus, in the argument concerning the Prussian government, the 
ultimate inductive inference was, that it was not liable to revolution : 
this inference was drawn according to a formula in which desire of the 
public good was set down as a mark of not being liable to revolution ; 
a mark of this mark was, acting in a particular manner ; and a mark of 
acting in that manner, was, being asserted to do so by many disinter- 
ested witnesses : this mark, the Prussian government was recognized 
by the senses as possessing. Hence that government fell within the 
last induction, and by it was brought within all the others. The per- 
ceived resemblance of the case to one set of observed particular cases, 
brought it into known resemblance with another set, and that with a 
third. 

In the more complex branches of knowledge, the deductions seldom 
consist, as in the examples hitherto exhibited, of a single chain, a a 
mark o£ b, b of c, c o£ d, therefore a a mark of d. They consist (to 



TRAINS OF REASONING. 141 

carry on the same metaphor) of several chains united at the extremity, 
as thus: a a mark of ^, h oi e, c off, defofn, therefore abc n. mark 
of^. Suppose, for example, the following combination of circum- 
stances : 1st, rays of light impinging on a reflecting surface ; 2d, that 
surface parabolic ; 3d, those rays parallel to each other and to the 
axis of the surface. It is to be proved that the concourse of these 
three circumstances is a mark that the reflected rays w^ill pass through 
the focus of the parabolic surface. Now each of the three circum- 
stances is singly a mark of something material to the case. Rays of 
light impinging on a I'eflecting surface, are a mark that those rays w^ill 
be reflected at an angle equal to the angle of incidence. The para- 
bolic form of the surface is a mark that, from any point of it, a line 
draw^n to the focus and a line parallel to the axis will make equal an- 
gles with the surface. And finally, the parallelism of the rays to the 
axis is a mark that their angle of incidence coincides with one of these 
equal angles. The three marks taken together are therefore a, mark 
of all these three things united. .But the three united are evidently a 
mark that the angle of reflection must coincide with the other of the 
two equal angles, that formed by a line drawn to the focus ; and this 
again, by the fundamental axiom concerning straight lines, is a mark 
that the reflected rays pass through the focus. Most chains of physical 
deduction are of this more complicated type ; and even in mathematics 
such are abundant, as in all propositions where the hypothesis includes 
numerous conditions : ^' If r circle be taken, and t/* within that circle 
a point be taken, not the centre, and ^straight lines be drawn from 
that point to the circumference, then," &c. 

§ 4. The considerations now stated remove a serious difliculty from 
the view we have taken of reasoning; vv^hich view might otherwise 
have seemed not easily reconcilable with the fact that there are De- 
'ductive or Ratiocinative Sciences. It might seem to follow, if all rea- 
soning be induction, that the diflSculties of philosophical investigation 
must lie in the inductions exclusively, and that when these were easy, 
and susceptible of no doubt or hesitation, there could be no science, or, 
at least, no difliculties in science. The existence, for example, of an 
extensive Science of Mathematics, requiring the highest scientific ge- 
nius in those who contributed to its creation, and calling for a most 
continued and vigorous exertion of intellect in order to appropriate it 
when created, may seem hard to be accounted for on the foregoing 
theory. But the considerations more recently adduced remove the 
mystery, by showing, that even when the inductions themselves are 
obvious, there may be much difficulty in finding whether the partic- 
ular case which is the subject of inquiry comes within them ; and am- 
ple room for scientific ingenuity in so combining various inductions, 
as, by means of one within which the case evidently falls, to bring it 
within others in which it cannot be directly seen to be included. 

When the more obvious of the inductions which can be made in 
any science from direct observations, have been made, and general 
formulas have been framed, detemiining the limits within which 
these inductions are applicable ; as often as a new case can be at 
once seen to come within one of the formulas, the induction is ap- 
plied to the new case, and the business is ended. But new cases 
are continually arising, which do not obviously come within any 



142 REASDNING. ^^ ' 

formula whereby the questions we want solved in respect of them 
could be answered. Let us take an instance from geometry; and 
as it is taken only for illustration, let the reader concede to us for 
the present, what we shall endeavor to prove in the next chapter, 
that the first principles of geometry are results of induction. Our 
example shall be the fifth proposition of the first book of Euclid. 
The inquiry is, Are the angles at the base of an isosceles triangle 
equal or unequal 1 The first thing to be considered is, what induc- 
tions we have, from which we can infer equality or inequality. For 
inferring equality we have the following formulse : — Things which 
being applied to each other coincide, are equals. Things which are 
equal to the same thing are equals. A whole and the sum of its 
parts are equals. The sums of equal things are equals. The dif- 
ferences of equal things are equals. There are no other formulae to 
prove equality. For inferring inequality we have the following : — 
A whole and its parts are unequals. The sums of equal things and 
unequal things are unequals. The differences of equal things and 
unequal things are unequals. In all, eight formulae. The angles at 
the base of an isosceles triangle do not obviously come within any of 
these. The formulae specify certain marks of equality and of in- 
equality, but the angles cannot be perceived intuitively to have any 
of those marks. We can, however, examine whether they have 
properties which, , in any other formulae, are set down as marks of 
those marks. On examination it appears that they have; and we 
ultimately succeed in bringing them within this formula, "The 
differences of equal things are equal." Whence comes the difficulty 
in recognizing these angles as the differences of equal things'? Be- 
cause each of them is the difference not of one pair only, but of in- 
numerable pairs of angles; and out of these we had to imagine and 
select two, which could either.be intuitively perceived to be equals, 
or possessed , some of the marks of equality set down in the various 
formulae. By an exercise of ingenuity, which, on the part of the first 
inventoT, deserves to be regarded as considerable, two .pairs of angles 
were hit upon, which united these requisites. First, it could be per- 
ceived intuitively that their differences were the angles at the base; 
iand, secondly, they possessed one of the marks of equality, namely, 
coincidence when applied to one ^another. This coincidence, how- 
ever, wag not perceived intuitively, but inferred, in conformity to 
another formula. 

To make all clear, w^e subjoin an analysis of the demonstration. 
Euclid, it will be remembered, demon- 
strates his fifth proposition by means of 
the fourth. This it is not allowable for us 
to do, because we are undertaking to trace 
deductive truths not to prior deductions, 
but to their original inductive foundation. 
We must therefore use the premisses of 
the fourth proposition instead of its con- 
clusion, and prove the fifth directly from 
first principles. To do so requires six for- 
mulas, (We must begin, as in Euclid, if 
by j)rolonging the equal sides AB, A C, ,to equal distances, and join- 
ing the extremities BE, DC.) 




TRAINS OF REASONING. 143 

First Formula. The sums of equals are equal. 

A D and A E are sums of equals by the supposition. Having that 
mark of equahty, they are concluded by this formula to be equal. 

Second Fori^ula. Equal straight lines being applied to one another 

coincide. 

AC, AB, are within this formula by supposition ; AD, AE, have 
been' brought within it by the preceding step. Both these pairs of 
sti'aight lines have the property of equality ; which, according to the 
second formula, is a mark that, if applied to each other, they will coin- 
cide. Coinciding altogether means coinciding in every part, and , of 
course at their extremities, D E and B C. 

Third Formula. Straight lines, having their extremities coincident, 

coincide. 
B E and D C have been brought within this formula by the preceding 
induction ; they will therefore coincide. 

Fourth Formula. Angles, having their sides coincident, coincide. 

The two previous inductions having shown that BE and DC coin- 
cide, and that AD, AE, coincide, the angles ABE and ACD are 
thereby brought within the fourth formula, and accordingly coincide. 

YivuvL Fonmiji. A. 'Things which coincide a.re equal. 

The angles ABE and ACD are brought within this formula by the 
induction immediately preceding. This train of reasoning being also 
applicable, mutatis mutandis, to the angles EBC, DCB, these also are 
brought within the fifth formula. And, finally, 

Sixth Formula. The differences of equals are equal. 

The angle ABC being the difference of ABE, CBE, and the angle 
AC B being the difference of ACD, DCB ; which have been proved 
to be equals ; A B C and A C B are brought within the last formula by 
the whole of the previous process. 

. The difficulty here encountered is chiefly that of figuring to ourselves 
the two angles at the base of .the triangle ABC, as remainders made 
by cutting one pair of angles out of another, while each pair shall be 
corresponding angles of ti'i angles which have two sides and the inter- 
vening angle equal. It is by this happy contrivance that so many dif- 
ferent inductions are brought to bear upon the same particular case. 
And this not being at all an obvious idea, it may be seen from an 
example so near the threshold of mathematics, how much scope there 
may well be for scientific dexterity in the higher branches of that and 
other sciences, in order -so to combine a few simple inductions, as to 
bring within each of them innumerable cases which are not obviously 
included in it ; and how long, and numerous, and complicated, maybe 
the processes necessary for bringing the inductions together, even when 
each induction may itself be very easy and simple. All the inductions 
involved in all geometry are comprised in those simple ones, the for- 
mula of which are the Axioms, and a few of the so-called Definitions. 
The remainder of the science is made up of the processes employed 
for bringing unforeseen cases within these inductions ; or (in syllogistic 



144 REASONING. 

. ^ \ ' 

language) for proving the minors necessary to complete the syllogisms; 
the majors being the definitions and axioms. In those definitions and 
axioms are laid down the whole of the marks, by an artful combina- 
tion of which men have been able to discover and prove all that is 
proved in geometry. The marks being so few, and the inductions 
which furnish them being so obvious and familiar ; the connecting of 
several of them together, which constitutes Deductions, or Trains of 
Keasoning, forms the whole difficulty of the science, and, with a ti-ifling 
exception, its whole bulk ; and hence Geometry is a Deductive Science. 

§ 5. It will be seen hereafter that there are weighty scientific 
reasons for giving to every science as much of the character of a De- 
ductive Science as possible ; for endeavoring to construct the science 
from the fewest and the simplest possible inductions, and to make 
these, by any combinations however complicated, suffice for pro^dng 
even such truths, relating to complex cases, as could be proved, if we 
chose, by inductions from specific experience. Every branch of nat- 
ural philosophy was originally experimental; each generalization 
rested upon a special induction, and was derived from its own distinct 
set of observations and experiments. From being sciences of pure 
experiment, as the phrase is, or, to speak more correctly, sciences in 
which the reasonings consist of no more than one step, and are ex- 
pressed by single syllogisms, all these sciences have become to some 
extent and some of them in nearly the whole of their extent, sciences 
of pure reasoning ; whereby multitudes of truths, already known by 
induction from as many different sets of experiments, have come to be 
exhibited as deductions or corollaries from inductive propositions of a 
simpler and more universal character. Thus mechanics, hydrostatics, 
optics, acoustics, and thermology, have successively been rendered 
mathematical; and astronomy was brought by Newton within the 
laws of general mechanics. Why it is that the substitution of this cir- 
cuitous mode of proceeding for a process apparently much easier and 
more natural, is held, and justly, to be the greatest triumph of the in- 
vestigation of nature, we are not, in this stage of our inquiry, prepared 
to examine. But it is necessary to remark, that although, by this 
progressive transformation, all sciences tend to become more and more 
Deductive, they are not therefore the less Inductive ; every step in the 
Deduction is still an Induction. The opposition is not between the 
terms Deductive and Inductive, but between Deductive and Experi- 
mental. A science is Experimental, in proportion as every new case, 
which presents any peculiar features, stands in need of a new set of 
observations and experiments, a fresh induction. It is Deductive, in 
proportion as it can draw conclusions, respecting cases of a new kind, 
by processes which bring those cases under old inductions ; by ascer- 
taining that cases which cannot be observed to have, the requisite 
marks, have, however, marks of those marks. 

We can now, therefore, perceive what is the generic distinction be- 
tween sciences which can be made Deductive, and those which must 
as yet remain Experimental. , The difference consists in our ha\dng 
been able, or not yet able, to discover marks of marks.. If by, our 
various inductions we have been able to proceed.no further than to 
such propositions as these, a a mark of b, or a and b marks of one 
another, c a mark of d, or c and d marks of one another, without any- 



TRAINS OF REASONING. 145 

tiling to connect a or b with c or d : we have a science of detached 
and mutally independent generahzations, such as these, that acids 
redden vegetable blues, and that alkalis color them green ; from 
neither of which propositions could we, directly or indirectly, infer 
the other: and a science, so far as it is composed of such propositions, 
is purely experimentah Chemistry, in the present state of our knowl- 
edge, has not yet thrown off this character. There are other sciences, 
however, of which the propositions are of this kind : a a mark of b, b a 
mark of c, c of d, d of e, &c. In these sciences we can mount the 
ladder from a to e by a process of ratiocination; we can conclude 
that « is a mark of e, and that evei-y object which has the mark a has 
the property e, although, perhaps, we never were able to observe a 
and e together, and although even d, our Only direct mark of e, may 
be not perceptible in those objects, but only inferrible. Or varying 
the first metaphor, we may be said to get from a to e underground : the 
marks b, c, d, which indicate the route, must all be possessed somewhere 
by the objects concerning which we are inquiring ; but they are below 
the surface : a is the only mark that is visible, and by it we are able 
to trace in succession all the rest. 

§ 6. We can now understand how an experimental transforms itself 
into a deductive science by the mere progress of experiment. In an 
experimental science, the inductions, as we have said, lie detached, 
as, a a mark of Z», c a mark of 6^, e a mark ofy^ and so on : now, a new 
set of instances, and a consequent new induction, may at any time 
bridge over the interval between two of these unconnected arches; b, 
for example, may be ascertained to be a mark of c, which enables us 
thenceforth to prove deductively that ^ is a mark of c. Or, as some- 
times happens, some grand comprehensive induction may raise an arch 
high in the air, which bridges over hosts of them at once : b, d,f, and 
all the rest, turning out to be marks of some one thing, or of things 
between which a connexion has already been traced. As when New- 
ton discovered that the motions, whether regular or apparently anom- 
alous, of all the bodies of the solar system, (each of which motions had 
been inferred by a separate logical operation, from separate marks,) 
were all marks of moving round a common centre, with a centripetal 
force varying directly as the mass and inversely as the square of the 
distance from that centre. This is the greatest example which has yet 
occurred of the transformation, at one stroke, of a science which was 
still to a great degi^ee merely experimental, into a deductive science. 

Transformations of the same nature, but on a smaller scale, contin- 
ually take place in the less advanced branches of physical knowledge, 
without en9,bling them to throw off the character of experimental 
sciences. Thus with regard to the two unconnected propositions be- 
fore cited, namely. Acids redden vegetable blues, Alkalis make them 
green ; it is remarked by Liebig, that all blue coloring matters which 
are reddened by acids (as well as, reciprocally, all red coloring matters 
which are rendered blue by alkalis) contain nitrogen: and it is quite 
possible to conceive that this circumstance may one day furnish a bond 
of connexion between the two propositions in question, by showing 
that the antagonist action of acids and alkalis in producing or destroy- 
ing the color blue, is the result of some one more general law. 
Although this connecting of detached generalizations is so much gain, 
T 



146 REASONING. 

it tends but little to give a deductive character to any science as a 
v\^hole ; because the new courses of observation and experiment, v^^hich 
thus enable us to connect together a few general truths, usually make 
known to us a still greater number of unconnected new ones. Hence 
chemistry, though similar extensions and simplifications of its general- 
izations are continually taking place, is still in the main an experimen- 
tal science ; and is likely so to continue, unless some comprehensive 
induction should be hereafter arrived at, which, like Newton's, shall 
connect a vast number of the smaller known inductions together, and 
change the whole method of the science at once. Chemistry has 
already one great generalization, which, though relating to one of the 
subordinate aspects of chemical phenomena, possesses within its limited 
sphere this comprehensive character ; the principle of Dalton, called 
the atomic theory, or the doctrine of chemical equivalents : which by 
enabling us to a certain extent to foresee the proportions in which two 
substances will combine, before the experiment has been tried, con- 
stitutes undoubtedly a source of new chemical truths obtainable by 
deduction, as well as a connecting principle for all truths of the same 
description previously obtained by experiment. 

§ 7. The discoveries which change the method of a science from ex- 
perimental to deductive, mostly consist in establishing, either by de- 
duction or by direct experiment, that the varieties of a particular 
phenomenon uniforaily accompany the varieties of some other- phe- 
nomenon better known. Thus the science of sound, which previously 
stood in the lowest rank of merely experimental science, became de- 
ductive when it was proved by experiment that every variety of sound 
was consequent upon, and therefore a mark of, a distinct and definable 
variety of oscillatory motion among the particles of the transmitting 
medium. When this was ascertained, it followed that every relation 
of succession or coexistence which obtained between phenomena of the 
more known class, obtained also between the phenomena which cor- 
responded to them in the other class. Every sound, being a mark of 
a particular oscillatory motion, became a mark of everything which, by 
the laws of dynamics, was known to be inferrible from that motion ; 
and everything which by those same laws was a mark of any oscilla- 
tory motion, became a mark of the coiTesponding sound. And thus 
many truths, not before suspected, concerning sound, became deduci- 
ble from the known laws of the propagation of motion through an elas- 
tic medium^ while facts already empirically known respecting sound, 
became an indication of corresponding properties of vibrating bodies, 
previously undiscovered. 

But the grand agent for transforming experimental into deductive 
sciences, is the science of number. The properties of numbers, alone 
among all known phenomena, are, in the most rigorous sense, proper- 
ties of all things whatever. All things are not colored, or ponderable, 
or even extended ; but all things are numerable. And if we consider 
this science in its whole extent, from common- arithmetic up to the 
calculus of variations, the tmths already ascertained seem all but infi- 
nite, and admit of indefinite extension. 

These truths, although afflrmable of all things whatever, of course 
apply to them only in respect of their quantity. But if it comes to be 
discovered that variations of quality in any class of phenomena, corre- 



TRAINS OF REASONING. ] 47 

spend regularly to variations o^ quantity eilhev in those same or in 
some other phenomena ; every formula of mathematics applicable to 
quantities w^hich vary in that particular manner, becomes a mark of a 
corresponding general truth respecting the variations in quality w^hich 
accompany them : and the science of quantity being (as far as any 
science can be) altogether deductive, the theory of that particular kind 
of qualities becomes, to this extent, deductive likewise. 

The most striking instance in point w^hich history affords, (though 
not an example of an experimental science rendered deductive, but of 
an unparalleled extension given to the deductive process in a science 
which was deductive already,) is the revolution in geometry which 
originated with the illustrious Descartes, and was completed by Clai- 
raut. These philosophers remarked, that to every variety of position 
in points, direction in lines, or form in curves or surfaces, (all of which 
are Qualities,) there corresponds a peculiar relation of quantity between 
either two or three rectilineal coordinates ; insomuch that if the law 
were known according to which those coordinates vary relatively to 
one another, every other geometrical property of the line or surface in 
question, whether relating to quantity or quality, would be capable of 
being inferred. Hence it followed that every geometrical question 
could be solved, if the corresponding algebraical one could; and 
.geometry received an accession (actual or potential) of new truths, cor- 
responding to every property of numbers which the progress of the' 
calculus had brought, or might in future bring, to light. In the same 
general manner, mechanics, astronomy, and in a less degree, every 
branch of natural philosophy commonly so called, have been made 
algebraical. The varieties of physical phenomena with which those 
sciences are conversant, have been found to answer to determinable 
varieties in the quantity of some circumstance or other ; or at least to 
varieties of form or position, for which corresponding equations of 
quantity had already been, or were susceptible of being, discovered 
by geometers. 

In these various transformations, the propositions of the science of 
number do but fulfil the function proper to all propositions forming a 
train of reasoning, viz., that of enabling us to arrive in an indirect 
method, by marks of marks, at such of the properties of objects as we 
cannot directly ascertain (or not so conveniently) by experiment. 
We travel from a given visible or tangible fact, through the truths 
' of numbers, to the fact sought. The given fact is a mark that a cer- 
tain relation subsists between the- quantities of some of the elements 
concerned ; while the fact sought presupposes a certain relation 
between the quantities of some other elements : now, if these last 
quantities are dependent in some known manner upon the former, or 
vice versa, we can argue from the numerical relation between the one 
set of quantities, to determine that which subsists between the other 
set ; the theorems of the calculus affording the intermediate links. 
And thus the one of the two physical facts becomes a mark of the 
other, by being a mark of a mark of a mark of it. 



148 REASONING. ' _ 

CHAPTER V, ' / 

OF DEMONSTRATION, AND NECESSARY TRUTHS, 

§ 1. If, as laid down in .the two preceding chapters, the foundation 
of all sciences, even deductive or demonstrative sciences, is Induction; 
if every step in the ratiocinations even of geometry is an act of induc- 
tion ; and if a train of reasoning is but bringing many inductions to, 
bear upon the same subject of inquiry, and dravsdng a case within one 
induction by means of another; wherein lies the peculiar certainty 
always ascribed to the sciences which are entirely, or almost entirely, 
deductive] Why are they called the Exact Sciences'? Why are 
mathematical certainty, and the evidence of demonstration, common 
phrases to express the very highest degree of assurance attainable by 
reason 1 Why are mathematics by almost all philosophers, and (by 
many) even those branches of natural philosophy which, through the 
medium of mathematics, have been converted into deductive sciences, 
considered to be independent of^ the evidence of experience and ob- 
servation, and characterized as systems of Necessary Truth 1 

The answer I conceive to be, that this character of necessity, 
ascribed to the truths of mathematics, and even (with some reserva- 
tions to be hereafter made) the peculiar certainty attributed to them, 
is an illusion; in order to sustain which, it is necessary to suppose 
that those tiiiths relate to, and express the properties of, purely 
imaginary objects. It is acknowledged that the conclusions of ge- 
ometry are deduced, partly at least, from the so-called Definitions, and 
that those definitions are assumed to be correct descriptions, as far as 
they go, of the objects with whifch geometry is conversant. Now we 
have pointed out that, from a definition as such, no proposition, unless 
it be one concerning the meaning of a word, can ever follow ; and 
that what apparently follows from a definition, follows in reality from 
an implied assumption that there exists a real thing conformable 
thereto. This assumption, in the case of the definitions of geometry, 
is false : there exist no real things exactly conformable to the defini- 
tions. There exist no points without magnitude ; no lines without 
breadth, nor perfectly straight; no circles wdth all their radii exactly 
equal, nor squares with all their angles perfectly right. It will per- 
haps be said that the assumption does not extend to the actual, but 
only to the possible, existence of such things. I answer that, accord- 
ing to any test we have of possibility, they are not even possible. 
Their existence, so far as we can form any judgment, would seem to 
be inconsistent with the physical constitution of our planet at least, if 
not of the universe. To get rid of this difficulty, and at the same 
time to save the credit of the supposed systems of necessary truth, it 
is customary to say that the points, lines, circles, and squares w^iich 
are the subject of geometry, exist in our conceptions merely, and are 
part of our minds ; which minds, by working on their own materials, 
construct an a priori science, the evidence of vv;hich is purely mental, 
and has ' nothing whatever to do with outward experience. By 
howsoever high authorities this doctrine may have been sanctioned, 
it appears to me psychologically incon-ect. The points, lines, circles, 
and squares, which any one has in his mind, are (I apprehend) simply 



DEMONSTRATION, AND NECESSARY TRUTHS. 149 

copies of the points, lines, circles, and squares which he has known in 
his experience. A line as defined by geometers is wholly inconceiva- 
ble. We can reason about a line as if it had no breadth ; because we 
have a power, which is the foundation of all the control we can exer- 
cise over the operations of our minds ; the power, when a perception 
is present to our senses, or a conception to our intellects, of attending 
to a part only of that perception or conception, instead of the whole. 
But we cannot conceive a line without breadth; we can form no 
mental picture of such a line : all the lines which we have in our 
minds are lines possessing breadth. If any one doubts this, we may 
refer him to his own experience. I much question if any one who 
fancies that he can conceive what is called a mathematical line, thinks 
so from the evidence of his consciousness : I suspect it is rather be- 
cause he supposes that unless such a conception were possible, mathe- 
matics could not exist as a science : a supposition which there will be 
no difficulty in showing to be entirely groundless. 

Since then neither in nature, nor in the human mind, do there ex- 
ist any objects exactly corresponding to the definitions of geometry, 
while yet that science cannot be supposed to be conversant about non- 
entities ; nothing remains but to consider geometry as conversant with 
such lines, angles, and figures as really exist ; and the definitions, as 
they are palled, must be regarded as some of our first and most obvi- 
ous generalizations concerning those natural objects. The correctness 
of those generalizations, as generalizations, is without a flaw : the 
equality of all the radii of a circle is true of all circles, so far as it is 
true of any one: but it is not exactly true of any, circle : it is only 
nearly true : so nearly that no error of any importance in practice will 
be incurred by feigning it to be exactly true. When we have occa- 
sion to extend these inductions, or their consequences, to cases in which 
the error would be appreciable — to lines of perceptible breadth or 
thickness,, parallels which deviate sensibly from equidistance, and the 
like — we correct our conclusions, by combining with them a fresh set 
of propositions relating to the aberration ; just as we also take in 
propositions relating to the physical or chemical properties of the ma- 
terial, if those properties happen to introduce any modification into the 
result, which they easily may, even with respect to figure and magni- 
tude, as in the case, for instance, of expansion by heat. So long, how- 
ever, as there exists no practical necessity for attending to any of the 
properties of the object except its geometrical properties, or to any of 
the natural irregularities in those, it is convenient to neglect the con- 
sideration of the other properties and of the irregularities, and to rea- 
son as if these did not exist : accordingly, we formally announce, in 
the definitions, that we intend to proceed on this plan. But it is an 
eiTor to suppose, because we resolve to confine our attention to a cer- 
tain number of the properties of an object, that we therefore conceive, 
or have an idea of, the object, denuded of its other properties. We 
are thinking, all the time, of precisely such objects as we have seen 
and touched, and with all the properties which naturally belong to 
them ; but, for scientific convenience, we feign them to be divested of 
all properties, except those in regard to which we design to consider 
them. 

The peculiar accuracy, supposed to be characteristic of the first 
principles of geometry, thus appears to be fictitious. The assertions 



150 REASONING 

on which the reasonings of the science are founded, do not, any more 
than in other sciences, exactly coiTespond with the fact ; but we sup- 
pose that they do so, for the sake of tracing the consequences which 
follow from the supposition. The opinion of Dugald Stewart respect- 
ing the foundations of geometry, is, I conceive, substantially correct ; 
that it is built upon hypotheses ; that it owes to this alone the peculiar 
certainty supposed to distinguish it ; and that in any science whatever^ 
by reasoning from a set of hypotheses, we may obtain a body of con- 
clusions as certain as those of geometry, that is, as strictly in accord- 
ance with the hypotheses, and as iri'esistibly compelling assent on 
condition that those hypotheses are true. 

When, therefore, it is affirmed that the conclusions of geometry are 
necessary truths, the necessity consists in reality only in this, that they 
necessarily follow from the suppositions from which they are deduced. 
Those suppositions are so far from being necessary, that they are not 
even true ; they purposely depart, more or less widely, from the truth. , 
The only sense in which necessity can be ascribed to the conclusions 
of any scientific investigation, is that of necessarily following from some 
assumption, which, by the conditions of the inquiry, is not to be ques- 
tioned. In this relation, of course, the derivative truths of every de- 
ductive science must stand to the inductions, or assumptions, on which . 
the science is founded, and which, whether true or untrue, certain or 
doubtful in themselves, are always supposed certain for the purposes 
of the particular science. And therefore the conclusions of all deduc- 
tive sciences were said by the ancients to be necessary propositions.' 
We have observed already that to be predicated necessarily was char- 
acteristic of the predicable Proprium, and that a proprium was any 
property of a thing which could be deduced from its essence, that is, 
from the properties included in its definition. 

§ 2. The important doctrine of Dugald Stewart, which I have en- 
deavored to enforce, has been contested by a living philosopher, Mr. 
Whewell, both in the dissertation appended to his excellent Mechani- 
cal Euclid, and in his more recent elaborate work on the Philosophy 
of the Inductive Sciences; in which last he also replies to an article 
in the Edinburgh Review (ascribed to a writer of great scientific emi- 
nence), in which Stewart's opinion was defended against his former 
strictures. Mr. Whe well's mode of refuting Stewart is to prove against 
him (as has also been done in this work), that the premisses of geom- 
etry are not definitions, but assumptions of the real existence of things 
corresponding to those definitions. This, however, is doing little for 
Mr. Whewell's purpose, for it is these very assumptions which we say 
are hypotheses, and which he, if he denies that geometry is founded on 
hypotheses, must show to be absolute truths. All he does, however, 
is to observe, that they at any rate are not arhittary hypotheses ; that 
we should not be at liberty to substitute other hypotheses for them ; 
that not only " a definition, to be admissible, must necessarily refer to 
and agree with some conception which we can distinctly frame in our 
thoughts," but that the straight lines, for instance, which we define, 
must be " those by which angles are contained, those by which trian- 
gles are bounded, those of which parallelism may be predicated, and 
the like."* And this is true ; but this has never been contradicted* 

* Whewell's MecAamca/ £uc/trf, p. 149, e< segg. 



DEMONSTRATION, AND NECESSARY TRUTHS. 151 

Those who say that the premisses of geometry are hypotheses, are not 
bound to maintain them to be hypotheses which have no relation what- 
ever to fact. Since an hypothesis framed for the purpose of scientific 
inquiry must relate to something which has real existence (for there 
can be no science respecting non-entities), it follows that any hypothe- 
sis we make respecting an object, to facilitate our study of it, must not 
involve anything which is distinctly false, and repugnant to its real 
nature : we must not ascribe to the thing any property which it has 
not ; oilr liberty extends only to suppressing some of those which it 
has, under the indispensable obligation of restoring them whenever, 
and in as far as, their presence or absence would make any material 
difference in the truth of our conclusions. Of this nature, accordingly, 
are the first principles involved in the definitions of geometry. In 
their positive part they are observed facts ; it is only in their negative 
part that they are hypothetical. That the hypotheses should be of 
this particular character, is, however, no further necessary, than inas- 
much as no others could enable us to deduce conclusions which, with 
due corrections, would be true of real objects : and in fact, when our 
aim is only to illustrate truths and not to investigate them, we are not 
under any such restriction. We might suppose an imaginary animal, 
and work out by deduction, from the known laws of physiology, its 
natural history; or an imaginary commonwealth, and from the elements 
composing it, might argue what, would be its fate. And the conclu- 
sions which we might thus draw from purely arbitrary hypotheses, 
might form a highly useful intellectual exercise : but as they could only 
teach us what would be the properties of objects which do not really 
exist, they would not constitute any addition to our knowledge : while 
on the contrary, if the hypothesis merely divests a real object of some 
portion of its properties, without clothing it in false ones, the conclu- 
sions will always express, under known liability to correction, actual 
truth. 

§ 3. But although Mr. Whewell has not shaken Stewart's doctrine 
as to the hypothetical character of that portion of the first principles of 
geometry which are involved in the so-called definitions, he has, I con- 
ceive, greatly the advantage of Stewart on another important point 
in the theory of geometrical reasoning ; the necessity of admitting, 
among those first principles, axioms as well as definitions. Some of 
the axioms of Euclid might, no doubt, be exhibited in the form of defi- 
nitions, or might be deduced, by reasoning, firom propositions similar to 
what are so called. Thus, if instead of the axiom. Magnitudes which 
can be made to coincide are equal, we introduce a definition, " Equal 
magnitudes are those which may be so applied to one another as to 
coincide ;" the three axioms which follow, (Magnitudes which are equal 
to the same are equal to one another — If equals are added to equals 
the sums are equal — If equals are taken from equals the remainders 
are equal,) may be proved by an imaginary supei-position, resembling 
that by which the fourth proposition of the first book of Euclid is de- 
monstrated. But although these and several others may be struck out 
of the list of first principled, because, though not requiring demon- 
stration, they are susceptible of it ; there will be found in the list of 
gtxioms two or three fundamental truths, not capable of being demon- 
strated : among which I agree with Mr. MHiewell in placing the prop- 



152 REASONING. . 

osition that two straight lines cannot inclose a space, (or its equivalent, 
Straight lines which coincide in two points coincide altogether,) and 
some property of parallel lines, other than that which constitutes their 
definition : the most suitable, perhaps, being that selected by Professor 
Playfair : ** Two straight lines which intersect each other cannot both 
of them be parallel to a third straight line."* 

The axioms, as well those which are indemonstrable as those which 
admit of being demonstrated, differ from that other class of funda- 
mental principles which are involved in the definitions, iii this, that 
they are true without any mixture of hypothesis. That things which 
are equal to the same thing are equal to one another, is as true of the 
lines and figures in ^ nature, as it would be of the imaginary ones 
assumed in the definitions. In this respect, however, mathematics 
is only on a par with most other sciences. In almost all sciences 
there are some general propositions which are exactly true, while the 
greater part are only more or less distant- approximations to the truth'. 
Thus in mechanics, the first law of motion, (the continuance of a move- 
ment once impressed, until stopped or slackened by some resisting force,) 
is true without a particle of qualification or error ; it is not affected by 
the frictions, rigidities, and miscellaneous disturbing causes, which 
qualify, for example, the theories of the lever and of the pulley. The 
rotation of the earth in twenty-four hours, of the same length as in our 
time, has gone on since the first accurate observations, without the 
increase or diminution of one second in all that period. These are 
inductions which require no fiction to make them be received as accu- 
rately true : but along with them there are others, as for instance the 
propositions respecting the figure of the earth, which are but approxi- 
mations to the truth ; and in order to use them for the further advance- 
ment of our knovi^ledge, we must feign that they are exactly true, 
although they really want something of being so. 

§ 4. It remains to inquire, what is the ground of our belief in axioms 
— what is the evidence on which they rest 1 I answer, they are ex- 
perimental truths ; generalizations from observation. The proposition,, 
Two straight lines cannot inclose a space — or in other words. Two 
straight lines which have once met, do not meet again, but continue to 
diverge — is an induction from the evidence of our senses. 

This opinion runs counter to a philosophic prejudice of long stand- 
ing and great strength, and there is probably no one proposition enun- 
ciated in this work for which a more unfavorable reception is to be oxt 
pected. It is, however, no new opinion ; and even if it were so, would 
be entitled to be judged, not by its novelty, but by the strength of the 
arguments by which it can be supported. I consider it very fortunate 
that so eminent a champion of the contrary opinion as Mr. Whewell, 
has recently found occasion for a most elaborate treatment of the whole 
theory of axionis, in attempting to construct the philosophy of the 

* We might, it is true, insert this property into the definition of parallel lines, framing the 
definition so as to require, both that when produced indefinitely they shall never meet, and 
afsothat any straight line which intersects one of them shall, if prolonged, meet the other. 
But by doing this we by no means get rid of the assumption ; we are still obliged to take 
for granted the geometrical truth, that all straight lines in the same plane, which have the 
former of these properties, have also the latter. For if it were possible that they should 
not, that is, if any straight lines other than those which are parallel according fo the defini- 
tion, had the property ot never meeting although indefinitely produced, the clemonstratioua, 
of the subseciuont portions of the theory of parallels could not be maintained. 



DEMONSTRATION, AND NECESSARY TRUTHS. 153 

matHematical and physical sciences on the basis of the doctrine against 
Which I now contend. Whoever is anxious that a discussion should go 
to the bottom of the subject, must rejoice to see the opposite side of 
. the question worthily represented. If what is said by such a man as 
Mr. Whewell, in support of an opinion which he has made the founda- 
tion of a systematic work, can be shown not to be conclusive, enough 
will have been done without going further to seek stronger arguments 
and a more powerful adversary. 

It is not necessary to show that the truths which we call axioms are 
originally suggested by observation, and that we should never have 
known that two straight lines cannot inclose a space if we had never 
seen a straight line : thus much being admitted by Mr. Whewell, and 
by all, in recent times, who have adopted his view of the subject. But 
they contend, that it is not experience which proves the axiom ; but that 
its truth is perceived a friori, by the constitution of the mind itself, 
from the first moment when the meaning of the proposition is appre- 
hended ; and without any necessity for verifying it by repeated trials, 
as is requisite in the case of truths really ascertained by observa- 
tion. 

They cannot, however, but allow that the truth of the axiom. Two 
straight lines cannot inclose a space, even if evident independently of 
experience, is also evident from experience. Wliether the axiom needs 
confirmation Qr Hot, it receives confirmation in almost every instant of 
our lives; since' we cannot look at any two straight lines which inter- 
sect one another, without seeing that fi-om that point they continue to 
diverge more and more. Experimental proof crowds in upon us in 
such endless profusion, and without one instance in which there can be 
even a suspicion of an exception to the rule, that we should soon have 
a stronger ground for believing the axiom, even as an experimental 
truth, than we have for almost any of the general truths which we con- 
fessedly learn from the evidence of our senses. Independently of « 
friori evidence, we should certainly believe it with an intensity of con- 
viction far gi'eater than we accord to any ordinary physical truth ; and 
this too at a time of life much earlier than that from which we date al- 
most any part of our acquired knowledge, and much too early to admit 
of our retaining any recollection of the history of our intellectual ope- 
rations at that period. Where then is the necessity for assuming that 
our recognition of these truths has a different origin from the rest of our 
knowledge, when its existence is perfectly accounted for by supposing 
its origin to be th& same % when the causes which produce belief in all 
other instances, exist in this instance, and in a degree of strength as 
much superior to what exists in other cases, as the intensity of the be- 
lief itself is superior ] The burden of proof lies upon the advocates of 
the contrary opinion : it is for them to point out some factj inconsistent 
with the supposition that this part of our knowledge of nature is derived 
from the same sources as every other part. 

This, for instance, they would be able to do, if they could prove 
chronologically that we have the conviction (at least practically) so 
early in infancy as to be anterior to those impressions on the senses, 
upon which, on the other theory, the conviction is founded. This, 
however, cannot be proved ; the point being too far back to be within 
the reach of memory, and too obscure for external observation. The 
advocates of the a priori theory are obliged to have recourse to other 
U 



154 REASONING. 

arguments. These are reducible to two, which I shall endeavor to 
state as clearly and as forcibly as possible. 

§ 5. In the first place it is said, that if our assent to the proposition 
that two straight lines cannot inclose a space, were derived from the 
senses, we could only be convinced of its truth by actual trial, that is, 
by seeing or feeling the straight lines ; whereas in fact it is seen to be 
true by merely thinking of them. That a stone thrown into water 
goes to the bottom, may be perceived by our senses, but mere think- 
ing of a stone thrown into the water will never lead us to that conclu- 
sion : not so, however, with the axioms relating to straight lines : if I 
could be made to conceive what a straight line is, without having seen 
one, I should at once recognize that two such lines cannot inclose a 
space. Intuition is " imaginary looking ;"* but experience must be 
real looking : if we see a property of straight lines to be true by merely 
fancying ourselves to be looking at them, the ground of our belief can- 
not be the senses, or experience ; it must be something mental. 

To this argument it might be added in the case of this particular 
axiom (for the assertion would not be true of all axioms), that the evi- 
dence of it from actual ocular inspection, is not only unnecessary, but 
unattainable. What says the axiom ? That two straight lines cannot 
inclose a space ; that after having once intersected, if they are pro- 
longed to infinity they do not meet, but continue to diverge from one 
another. How can this, in any single case, be proved by actual 
observation % We may follow the lines to any distance we please ; but 
we cannot follow them, to infinity : for aught our senses can testify, 
they may, immediately beyond the furthest point to which we have 
traced them, begin to approach, and at last meet. Unless, therefore, 
we had some other proof of the impossibility than observation affords 
us, we should have no ground for believing the axiom at all. 

To these arguments, which I trust I cannot be accused of under- 
stating, a satisfactory answer will, I conceive, be found, if we advert 
to one of the characteristic properties of geometrical forms — their, 
capacity of being painted in the imagination with a distinctness equal 
to reality : in other words, the exact resemblance of our ideas of form 
to the sensations which suggest them. This, in the first place, enables 
us to make (at least with a little practice) mental pictures of all possible 
combinations of lines and angles, which resemble the realities quite as 
well as any which we could make upon paper ; and in the next place, 
makes those pictures just as fit subjects of geometrical experimentation 
as the realities themselves ; inasmuch as pictures, if sufficiently accu- 
rate, exhibit of course all the properties which would be manifested 
by the realities at one given instant, and on simple inspection : and in 
geometry we are concerned only with such properties, and not with 
that which pictures could not exhibit, the mutual action of bodies one 
upon another. The foundations of geometry would therefore be laid 
in direct experience, even if the experiments (which in this case consist 
merely in attentive contemplation) were practised solely upon what we 
call our ideas, that is, upon the diagrams in our minds, and not upon 
outward objects. For in all systems of experimentation we take sorne 
objects to sei-vc as representatives of all which resemble them ; and in 

* )Vhewell's Philosophy of the Inductive Sciences, i., 130. 



DEMONSTRATION, AND NECESSARY TRUTHS. 155 

the present case the conditions which quahfy a real object to be the 
representative of its class, are completely fulfilled by an object existing 
only in our fancy. Without denying, therefore, the possibility of 
satisfying ourselves that two straight lines cannot inclose a space, by 
merely thinking of straight lines without actually looking at them ; I 
contend, that we do not believe this truth on the ground of the imagi- 
nary intuition simply, but because we know that the imaginary lines 
exactly resemble real ones, and that we may conclude from them to 
real ones with quite as much certainty as we could conclude from one 
real line to another. The conclusion, therefore, is still an induction 
from obser^-atioui And we should not be authorized to substitute 
observation of the image in our mind, for observation of the reality, if 
we had not learnt by long continued experience that all the properties 
of the, reality are faithfully represented in the image ; just as we 
should be scientifically warranted in describing the shape and color of 
an animal which we had never seen, from a photogenic picture made 
of it with a daguerreotype; but not until we had learnt by ample 
experience, that observation of such a picture is precisely equivalent 
to observation of the original. 

These considerations also remove the objection arising from the 
impossibity of ocularly following the lines in their prolongation to 
infinity. For though, in order actually -to see that two given lines 
never meet, it would be necessary to follow them to infinity : yet 
without doing so we may know that if they ever do meet, or indeed if, 
after diverging from one another, they begin again to approach, this 
must take place not at an infinite, but at a finite distance. Supposing, 
therefore, such to be the case, we can transport ourselves thither in 
imagination, and can frame a mental image of the appearance which 
one or both of the lines must present at that point, which we may rely 
upon as being precisely similar to the reality. Now, whether we fix 
our contemplation upon this imaginary picture, or call to mind the 
generalizations we have had occasion to make from former ocular 
observation, we shall either way be equally satisfied, that a line which^ 
after diverging from another straight line, begins to approach to it, 
produces the impression on our senses which we describe by the 
expression, " a bent line,'* not by the expression, ** a straight line." 

§ 6. The first of the two great arguments in support of the theoiy 
that axioms are a priori truths, having, I think, been sufficiently an- 
swered ; I proceed to the second, on which most stress is usually laid, 
and which is chiefly insisted upon by Mr. Wliewell. Axioms (it is 
asserted) are conceived by us not only as true, but as universally and 
necessarily true. Now, experience cannot possibly give to any propo- 
sition this character. I may have seen snow a hundred times, and 
may have seen that it was white, but this cannot give me entire assur- 
ance even that all snow is white ; much less that snow must be white. 
" However many instances we may have obser^^ed of the truth of a 
proposition, there is nothing to assure us that the next case shall not be 
an exception to the rule. If it be strictly true that every ruminant 
animal yet known has cloven hoofs, we still cannot be sure that some 
creature will not hereafler be discovered which has the fir&t of these 

attributes, without having the other Experience must always consist 

of a limited number of observations : and, however numerous these 



156 REASONING. •" ' "■ 

may be, they can show nothing with regard to the infinite number of 
cases in which the experiment has not been made." Moreover, axioms 
are not only universal, they are also necessary. Now " experience 
cannot offer the smallest ground for the necessity of a proposition. 
She can observe and record what has happened ; but she cannot find, 
in any case, or in any accumulation of cases, any reason for what must- 
happen. She may see objects side by side; but she cannot see a rea- 
son why they must ever be side by side. She finds certain events to 
occur in succession ; but the succession supplies, in its occurrence, no 
reason for its recurrence. She contemplates external objects ; but she 
cannot detect any internal bond, which indissolubly connects the future 
with the past, the possible with the real. To learn a proposition by ex- 
perience, and to see it to be necessarily true, are two altogether difterent 
processes of thought."* And Mr. Whewell adds, " If any one does 
not clearly compi-ehend this distinction of necessary and contingent 
truths, he v/ill not be able to go along with us in our researches into 
the foundations of human knowledge ; nor indeed, to pursue with 
success any speculation on the subject."! 

In order to learn what the distinction is, the non-recognition of which 
incurs this denunciation, let us refer again to Mr. Whewell. *' Neces- 
sary truths are those in which we not only learn that the proposition 
Z6r true, but see that it must he true; in which the negation of the 
truth is not only false, but impossible ; in which we cannot, even by 
an effort of imagination, or in a supposition, conceive the reverse of 
that which is asserted. That there are such truths cannot be doubted. 
We may take, for example, all relations of number. Three and Two, 
added together, make Five. We cannot conceive it to be otherwise. 
We cannot, by any freak of thought, imagine Three and Two to make 
Seven."* 

Although Mr. Whewell has naturally and properly ei'nployed a 
variety of phrases to bring his meaning more forcibly home, he will, I 
presume, allow that they are all equivalent ; and that what he means by 
"a necessary truth, would be sufficiently defined, a proposition the 
negation of which is not only false but inconceivable. I am unable to 
find in any of Mr. Whewell's exj^ressions, turn them what way you 
will, a meaning beyond this, and I do not believe he would contend 
that they mean anything more. 

This, therefore, is the principle asserted : that propositions, the 
negation of which is inconceivable, or in other words, which we can- 
not figure to ourselves as being false, must rest upon evidence of a 
higher and more cogent description than any which experience can 
afford. And we have next to consider whether there is any ground 
for this assertion. 

Now I cannot but wonder that so much stress should be laid upon the 
circumstance of inconceivableness, when there is such ample experience 
to show that our capacity or incapacity of conceiving a thing has very 
little to do with the possibility , of the thing in itself; but is in truth very 
much an affair of accident, and depends upon the past history and 
habits of our own minds. There is no more generally acknowledged 
fact in human nature, than the extreme difficulty at first felt in con- 
ceiving anything as possible, which is in contradiction to long estab- 

* WiiEwiiLL's Philosophy of the Inductive Sciences, i., 59—61. 
t Ibid,, 57. J Ibi^d., i., 54, 55. 



DEMONSTRATION, AND NECESSARY TRUTHS. ]57 

lished -and familiar experience ; or even to old and familiar habits of 
thought. And this difficulty is a necessary result of the fundamental 
laws of the human mind. When we have often seen and thought of 
two things together, and have never in any 'one instance either seen 
or thought of them separately, there is by the primary laws of asso- 
ciation an increasing difficulty, which in the end becomes insuperable, 
of conceiving the two things apart. This is most of all conspicuous in 
uneducated persons, who are in general utterly unable to separate any 
two ideas which have once become firmly associated in their minds; 
and if persons of cultivated intellect have any advantage on the point, 
it is only because, having seen and heard and read more, and being 
more accustomed tt3 exercise, their imagination, they have experienced 
their sensations and thoughts in more varied combinations, and have 
been prevented from forming many of these inseparable associations. 
But this advantage has necessarily its limits. The man of the most 
practised intellect is not exempt from the universal laws of our concep- 
tive faculty. If daily habit presents to him for a long period two facts in 
combination, and if he is not led during that period either by accident 
or intention to think of them apart, he will in time become incapable 
of doing so even by the strongest effi^rt ; and the supposition that the 
two facts can be separated in nature, will at last present itself to his 
mind with all the characters of an inconceivable phenomenon. There 
are remarkable instances of this in the history of science : instances, in 
which the wisest men rejected as impossible, because inconceivable, 
things which their posterity, by earlier practice and longer perseve- 
rance in the attempt, found it quite easy to conceive, and which every- 
body now knows to be true. There was a time when men of the most 
cultivated intellects, and the most emancipated from the dominion of 
early prejudice, could not credit the existence of antipodes ; were 
unable to conceive, in opposition to old association; the force of gravity 
acting upwards instead of downwards. The Cartesians long rejected 
the Newtonian doctrine of the gravitation of all bodies towards one 
another, on the faith of a general proposition, the reverse of which 
seemed to them to be inconceivable — the proposition that a body can- 
not act where it is not. All the cumbrous machinery of imaginary 
vortices, assumed without the smallest particle of evidence, appeared 
to these philosophers a more rational mode of explaining the heavenly 
motions, than one which involved what seemed to them so gi'eat an 
absurdity.* And they no doubt found it as impossible to conceive 
that a body should act upon the earth, at the distance of the sun or 
moon, as we find it to conceive an end to space or time, or two straight 
lines inclosing a space. Nevs^on himself had not been able to realize 
the conception, or we should not have had his hypothesis of a subtle 

i'* It would be difficult to name a man more remarkable at once for the greatness and the 
universality of his intellectual powers, than Leibnitz. Yet this great man gave as a reason 
for rejecting Newton's scheme of the solar system, that God could not make a body revolve 
round a distant centre, unless either by some impeUing mechanism, or by miracle : — '' Tout 
ce qui n'est pa's explicable," says he in a letter to the Abbe Conti, "par'la nature des cr^a-' 
tures, est miraculeux. II ne suffit pas de dire : Dieu a fait une telle loi de nature : done 
la chose est naturelle. II faut que la loi soit executable par les natures des creatures. Si 
Dieu doruiait cette loi, par exemple, a un corps libre, de tourner a I'entour d'un certain 
centre, ilfaudr ait oil qu'il y joigmt cVautres corps qui par leur impulsion Vobligeassent de resier 
toujours dans son orbite circulaire, ou qu'il m.U un ange a ses trousses, ou enfin ilfaudrait qu'il y 
concourut extraordinairement ; car naturellement il s'ecartera par la tangente." — Works' of 
Leibnitz, ed, Dutens, iii., 446. 



158 < REASONING. 

ether, the occult cause of gravitation; and his writings prove, that 
although he deemed the particular nature of the intermediate agency 
a matter of conjecture, the necessity oi some such agency appeared to 
him indubitable. It would seem that even now the majority of scien- 
tific men have not completely got over this very difficulty ; for though 
they have at last learnt to conceive the sun attracting the earth with- 
out any intervening fluid, they cannot yet conceive the sun illuminating 
the earth without, some such medium. 

If, then, it be so natural to the human mind, even in its highest 
state of culture, to be incapable of conceiving, and on that ground to 
believe impossible, what is afterwards not only found to be conceivable 
but proved to be true; what wonder if hi cases where the association 
is still older, more confirmed, and more familiar, and in which nothing 
ever occurs to shake our conviction, or even suggest to us any concept 
lion at variance with the association, the acquired incapacity should 
continue, and be mistaken for a natural incapacity \ It is true our ex- 
perience of the varieties in nature enables us, within certain limits, to 
conceive other varieties analogous to them. AVe can conceive the sun 
or moon falling ; for although we never saw them fall, nor ever perhaps 
imagined them falling, we have seen so many other things fall, that 
we have innumerable familiar analogies to assist the conception;' 
which, after all, we should probably have some difficulty in framing, 
were we not well accustomed to see the sun and moon move (or. 
appear to move), so that we are only called upon to conceive a slight 
change in the direction of motion, a circumstance familiar to our ex- 
perience. But when experience affords no model on which to shape 
the new conception, how is it possible for us to form it % How, for 
example, can we imagine an end to space or time ] We never saw 
any object without something beyond it, nor experienced any feeling 
without something following it. When, therefore, we attempt to 
conceive the last point of space, we have the idea irresistibly raised 
of other points beyond it. When we try to imagine the last instant 
of time, we cannot help ^conceiving another instant after it. Nor is 
there any necessity to assume, as is done by the school to which Mr. 
Whewell belongs, a peculiar fundamental law of the mind to account 
for the feeling of infinity -inherent in our conceptions of space and 
time ; that apparent infinity is sufficiently accounted for by simpler 
and universally acknowledged laws. 

Now, in the case of a geometrical axiom, such, for example, as that 
two straight lines cannot inclose a space — a truth which is testified to" 
us by our very earliest impressions of the external world — how is it 
possible (whether those external impressions be or -be not the ground 
of our belief) that the reverse of the proposition can be otherwise 
than inconceivable to us % What analogy have we, what similar order 
of facts in any other branch of our experience, to facilitate to us the 
conception of two straight lines inclosing a space % Nor is even this 
all. I have already called attention to the peculiar property of our 
impressions of form, that the ideas or mental images exactly resemble 
their prototypes, and adequately represent them for the purposes of 
scientific observation. From this, arid firom the intuitive character of 
the observation, which in this case reduces itself to simple inspection, 
we cannot so much as call up in our imagination two straight lines, in 
order to attempt to conceive them inclosing a space, without by that 



DEMONSTRATION, AND NECESSARY TRUTHS. 159 

very act repeating the philosophical experiment which establishes the 
contrary. Will it really be contended that the inconceivableness of 
the thing, under such circumstances, proves anything against the ex- 
perimental origin of the conviction 1 Is it not clear that in whichever 
mode our belief in the proposition may have originated, the impossi- 
bility of our conceiving the negative of it must, under either hypothesis, 
be the same ] As, then, Mr. Whewell exhorts those who have any 
difficulty in recognizing the distinction held by him between necessary 
and contingent truths, to study geometry — a condition which I can 
assure him I have conscientiously fulfilled — I, in return, with equal 
confidence, exhort those who agree with Mr. Whewell, to study the 
elementary laws of association ; being convinced that nothing more is 
requisite than a moderate familiarity with those laws, to dispel the 
illusion which ascribes a peculiar necessity to our earliest inductions 
from experience, and measures the possibility of things in themselves, 
by the human capacity of conceiving them. 

I hope to be pardoned for adding, that Mr. Whewell himself has 
both confirmed by his testimony the effect of habitual association in 
giving to an experimental truth the appearance of a necessary one^ and 
afforded a striking instance, of that remarkable law in his own person. 
In his Philosophy of the Inductive Sciences he continually asserts, that 
propositions which not only are not self-evident, but which we know to 
have been discovered gradually, and by great efforts of genius and pa- 
tience, have, when once established, appeared so self-evident that, but 
for historical evidence, it would have been impossible to conceive that 
they had not been recognized' from the first by all persons in a sound 
state 'of their faculties. " We now despise those who, in the Coperni- 
can controversy, could not conceive the apparent motion of the sun on 
the heliocentric hypothesis ; or those who, in opposition to Galileo, 
thought that a uniform force might be that which generated a velocity 
proportional to the space ; or those who held there was something ab- 
surd in Newton's doctrine of the different refrangibility of differently 
colored rays ; or those who imagined that when elements combine, their 
sensible qualities must be manifest in the compound; or those who were 
.reluctant to give up the distinction of vegetables into herbs, shrubs, and 
trees. We cannot help thinking that men must have been singularly 
. dull of comprehension to find a d.ifficulty in admitting what is to us so 
, plain and simple. We have a latent persuasion that we in their place 
should have been wiser and more clear-sighted ; that we should have 
taken the right side, and given our assent at once to the truth. Yet in 
reality such a persuasion is a mere delusion. The persons who, in such 
instances as the above, were on the losing side, were very far in most 
cases from being persons more prejudiced, or stupid, or naiTOw-minded, 
than the greater part of mankind now are; and the cause for which 
they fought was far from being a manifestly bad one, till it had been. so 
decided by the result of the war. ... So complete has been the victory 
of fruth in most of these instances, that at present we can hardly ima- 
gine the struggle to have been necessary. The very essence of these tri- 
umphs is, that they lead us to regard the views we reject as not only false ^ 
hut inconceivahle.'"* 

This last proposition is precisely what I contend for ; and I ask no 

^Philosophy of the Indmtive Sciences, \o\. a., "p, m. 



160 - REASONING. , . 

^ - ■ , ' 

more, in order to overthrow the whole theory of Mr. Whewell on the 
nature of the evidence of axioms. For what is that theory ] That the 
truth of axioms cannot have been learnt from experience, because their 
falsity is inconceivable. But Mr. Whewell himself says, that we are 
continually led by the natural progress of thought, to regard as incon- 
ceivable what our forefathers not only conceived but believed, nay, 
even (he might have added) were unable to conceive the contrary of. 
Mr. Whewell cannot intend to justify this mode of thought ; he cannot 
mean to say, that we can be right in regarding as inconceivable what 
others have conceived, and as self-evident what to others did not appear 
evident at all. After so complete an admission that inconceivableness 
is an accidental thing, not inherent in the phenomenon itself, but de- 
pendent oti the mental history of the person who tries to conceive it, 
how can he ever call upon us to reject a proposition as impossible on 
no other ground than its inconceivableness % Yet he not only does so, 
but has unintentionally afforded some of the most remarkable exam- 
ples which can be cited of the very illusion which he has himself so 
clearly pointed out. We select as specimens, his remarks on the evi- 
dence of the three laws of motion, and of the atomic theory. 

With respect to the laws of motion, Mr. Whewell says :" No one 
can doubt that, in historical fact, these laws were collected from expe- 
rience. That such is the case is no matter of conjecture. We know, 
the time, the persons, the circumstances, belonging to each step of each 
discovery."* After such a testimony, to adduce evidence of the fact 
would be superfluous. And not only were these laws by no means 
intuitively evident, but some of them were originally paradoxes. The 
first law was especially so. That a body, once in motion, would con- 
tinue for ever to move in the same direction with undiminished velo- 
city unless acted upon by some new force, was a proposition which 
mankind found for a long time the greatest difficulty in crediting. It 
stood opposed to apparent experience of the most familiar kind, which 
taught that it was the nature of motion to abate gradually, and at last 
terminate of itself. Yet when once the contrary doctrine was firmly 
established, mathematicians, as Mr. Whewell observes, speedily began 
to believe that laws, thus contradictory to first appearances, and which, 
even after full proof had been obtained, it had required generations to 
render familiar to the minds of the scientific world, were under " a 
demonstrable necessity, compelling them to be such as they are and 
no other ;" and Mr. Whewell, though he has " not ventured absolutely 
to pronounce" that all these laws " can be rigorously traced to an ab- 
solute necessity in the nature of things, "f does actually think in that 
manner of the law just mentioned; of which he says : " Though the 
discovery of the first law of motion was made, historically 'speaking, by 
means of experiment, we have now attained a point of view in which 
we see that it might have been certainly known to be true, independ- 
ently of experience."! Can there be a more striking exemplification 
than is here afibrded, of the effect of association which we have de- 
scribed % Philosophers, for generations, have the most extraordinary 
difficulty in putting certain ideas together ; they at last succeed in doing 
60 ; and after a sufficient repetition of the process, they first fancy a 
natural bond between the ideas, then experience a growing difficulty 

* Philosophy of the Inductive Sciences, i., 238. f Ibid., 237. % Ibid, 213. 



DEMONSTRATIOiV, AND NECESSARY TRUTHS. 161 

wliicli at last, by the continuation of the same progress, becomes an im- 
possibility, of severing them from one another. If such be the pro- 
gress of an experimental conviction of which the date is of yesterday, 
and vv^hich is in opposition to first appearances, how must it fare with 
those which are conformable to appearances familiar from the first 
dawn of intelligence, and of the conclusiveness of which, from the 
earliest records of human thought, no skeptic has suggested even a mo- 
mentary doubt 1 

'■ The other instance which we shall quote is a truly astonishing one, 
and may be called the reductio ad absurdum of the theory of inconceiv- 
ableness. Speaking of the laws of chemical composition, Mr. Whe- 
well says:* " That they could never have been clearly understood, and 
therefore never firmly established, without laborious and exact exper- 
iments, is certain ; but yet we may venture to say, that being once 
known, they possess an evidence beyond that of mere experiment. 
For how, in fact, can we conceive combinations, otherwise than as defi- 
nite in hind and quantity 1 If we were to suppose each element ready 
to combine with any other indifferently, and indifferently in any quan- 
tity, we should have a world in which all would be confusion and in- 
definiteness. There would be no fixed kinds of bodies ; salts, and 
stones, and ores, would approach to and graduate into each other by 
insensible degrees. Instead of this, we know that the world consists 
of bodies distinguishable from each other by definite differences, capa- 
ble of being classified and named, and of having general propositions 
asserted concerning them. And as^w;e cannot conceive a world in which 
this should not be the case, it would appear that we cannot conceive a 
state bf things in which the laws of the combination of elements should 
not be of that definite and measured kind which we have above asserted." 
That a philosopher of Mr. Whewell's eminence should gravely as- 
sert that we cannnot conceive a world in which the simple elements 
would combine in other than definite proportions ; that by dint of med- 
itating on a scientific truth, the original discoverer of which is still living, 
he should have rendered the association in his own mind between the 
idea of combination and that of constant proportions so familiar and in- 
timate as to be unable to conceive the one fact without the other ; is so 
signal an instance of the law of human nature for which I am contend- 
ing, that one word more in illustration must be quite superfluous. I 
shall, only, therefore, express my satisfaction that so long as the pro- 
gress of scientific instruction has not rendered this association as indis- 
soluble in the minds of most people as Mr. Whewell finds it, the 
majority of mankind will be fairly able to judge, from this example, of 
the value of the evidence which he deems sufficient to prove that a 
scientific proposition might be knovm to be true independently of 
experience.! 

* Philosophy of the Inductive Sciences, i., 384, 385. 

t The Quarterly Review for June, 1841, contains an article, of great ability, on Mr. 
Wliewell's two great works, the writer of which maintains, on the subject of axioms, the 
doctrine, advanced in the text, that they are generalizations from experience, and supports 
that opinion by a line of argument strikingly coinciding with mine. When I state that the 
whole of the present chapter was written before I had seen the article (the greater part, 
indeed, before it was published), it is not my object to occupy the reader's attention with a 
matter so unimportant as the degree of originality which may or may not belong to any 
portion of my own speculations, but to obtain for an opinion which is opposed to reigning 
doctrines, the recommendation derived from a striking concurrence of sentiment between 
two inquirers entirely independent of one another. 1 have much pleasure in citing from a 
writer of the extensive acquirements in physical and metaphysical knowledge and the ca- 



162 REASONING. 



CHAPTER VI. 

THE SAME SUBJECT CONTINUED. 

§ 1. In the examination which formed the subject of the last chapter, 
into the nature of the evidence of those deductive sciences which are 
commonly represented to be systems of necessary truth, we have been 
led to the following conclusions. The results of those sciences are 
indeed necessary, in the .sense of necessarily following from certain first 
principles, commonly called axioms and definitions; of being certainly 
true if those axioms and definitions are so. But their claim to the 

pacity of systematic thought which the article evinces, passages so remarkably in unisOB 
with my own views as the following : — ' - 

" The truths of geometry are summed up and embodied in its definitions and axioms. , . 
Let us turn to the axioms, and what do we find? • A string of propositions concerning 
magnitude in the abstract, which are equally true of space, time, force, number, and every 
other magnitude susceptible of aggregation and subdivision. Such propositions, where they 
are not mere definitions, as some of them are, carry their inductive origin on the face of 
their enunciation. . . . Those which declare that two straight lines cannot inclose a space, 
and that two straight lines which cut one another cannot both be parallel to a third, are in 
reahty the only ones which express characteristic properties of space, and these it will be 
worth while to consider more nearly. Now the only clear notion we can form of straight- 
ness is uniformity of direction, for space in its ultimate analysis is nothing but an assem- 
blage of distances and directions. And (not to dwell on the notion of continued contem- 
plation, i. e., mental experience, as included in the very idea of uniformity ; nor on that of 
transfer of the contemplating being from point to point, and of experience, during such 
transfer, of the homogeneity of the interval passed over) we cannot even propose the propo- 
sition in an intelligible form, to any one whose experience ever since he was born has not 
assured him of the fact. The unity of direction, or that we cannot march from a ^iven 
point by more than one path direct to the same object, is matter of practical experience 
long before it can by possibility become matter of abstract thought. We cannot attempt 
mentally to exemplify the conditmis of the assertion in an imaginary case opposed to it, without vi- 
olating our habitual recollection of this experience, and defacing our me7ital picture of space as 
grounded on it. What but experience, we may ask, can possibly assure us of the homo- 
geneity of the parts of distance, time, force, and measurable aggregates in general, on 
which the truth of the other axioms depends ? As regards the latter axiom, after what has 
been said it must be clear that the very same course of remarks equally applies to its case, 
and that its truth is quite as much forced on the mind as that of the former by daily and 
hourly experience, . . . including always, be it observed, in our notion of experience, that which is 
gained by contemplation of the inward picture which the mind forms to itself in any 'proposed case, 
or which it arbitrarily selects as an example — such picture, in virtue of the extreme simplicity of these 
primary relations, being called up by the imagination with as iHuch vividness and clearness as could 
be done by any external impression, which is the only meaning we can attach to the word intuition, 
as applied to such relations." 

And again, of the axioms of mechanics : — " As we admit no such propositions, other than 
as truths inductively collected from observation, even in geometry itself, it Can hardly be 
expected that, in a science of obviously contingent relations, w^e should acquiesce in a con- 
trary view. Let us take one of tbese axioms and examine its evidence : for instance, that 
equal forces perpendicularly applied at the opposite ends of equal arms of a straight lever 
will balance each other. What but experience, we may ask, in the first place, can possibly 
inform us that a force so applied will have any tendency to turn the lever on its centre at 
all? or that force can be so transmitted along a rigid line perpendicular to its direction, as 
to act elsewhere in space than along its own line of action ? Surely this is so far from be- 
ing self-evident that it has even a paradoxical appearance, which is only to be removed by 
giving our lever thickness, material composition, and molecular powers. Again we con- 
clude, that the two forces, being equal and applied under precisely similar circumstances, 
must, if they exert any effort at all to turn the lever, exert equal and opposite efforts: but 
what b, priori reasoning can possibly assure us that they rfo act under precisely similar cir- 
cumstances? that points which differ in place, are similarly circumstanced as regards the 
exertion of force ? that universal space may not have relations to universal force — or, at all 
events, that the organization of the material universe may not be such as to place that por- 
tion of space occupied by it in such relations to the forces exerted in it, as may invalidate 
the absolute similarity of circumstances assumed? Or we may argue, what have we to do 
with the notion of angular movement in the lever at all? The case is one of rest, and of 
quiescent dcstiuction of force by force. Now. how is this destruction effected ? Assuredly 



DEMONSTRATION, AND NECESSARY TRUTHS. 103 

character of necessity in any sense Leyond this, as implying an evidence 
independent of and superior to observation and experience, must depend 
upon the previous cstabHshment of such a claim in favor of the defini- 
tions and axioms themselves. With regard to axioms, we found that, 
considered as experimental truths, they rest upon superabundant and 
obvious evidence. We inquired, whether, since this is the case, it be 
necessary to suppose any other evidence of those truths than experi- 
mental evidence, any other origin for our belief of them than an expen- 
mental origin. We decided, that the burden of proof lies with those 
who maintain the affirmative, and we examined, at considerable length, 
such arguments as they have produced. The examination having led 
to the rejection of those arguments, we have thought ourselves war- 
ranted in concluding that axioms are but a class, the highest class, of 

by the counterpressure which supports the fulcrum. But would not this destruction 
equally arise, and by the same amount of counteracting force, if each force simply pressed 
its own half of the lever against the fulcrum ? And what can assure us that it is not so, 
except removal of one or other force, and consequent tilting of ihe lever? The other fun- 
damental axiom of statics, that the pressure on the point of support is the sum of the 
weights ... is merely a scientific transformation and more refined mOde of stating a coarse 
and obvious result of universal experience, viz., that the weight of a rigid body is the same, 
handle it or suspend it in what position or by what point we will, and that whatever sus- 
tains it sustains its total weight. Assuredly, as Mr. Whewell justly remarks, ' No one 
probably ever made a trial for the purpose of showing that the pressure on the support is 
equal to the sum of the weights.' , . . But it is precisely because in every action of his life 
from earliest infancy he has been continually making the trial, and seeing it made by every 
other living being about him, that he never dreams of staking its result on one additional 
attempt made with scientific accuracy. This would be as if a man should resolve to de- 
cide by experiment whether his eyes were useful for the purpose of seeing, by hermetically 
sealing himself up for half an hour in a metal case." 

On the " paradox of universal propositions obtained by experience," the same writer 
says: " If there be necessary and universal truths expressible in propositions of axiomatic 
simplicity and obviousness, and having for their subject-matter the elements of all our ex- 
perience and all our knowledge, surely these are the truths which, if experience suggests to 
us any truths at all, it ought to suggest most readily, clearly, and unceasingly. If it were 
a truth, universal and necessary, that a net is spread over the whole surface of every plan- 
etary globe, we should not travel far on our own without getting entangled in its meshes, 
and making the necessity of some means of extrication an axiom of locomotion. . . .There 
is, therefore, nothing paradoxical, but the reverse, in our being led by observation to a re- 
cognition of such truths, as general propositions, coextensive at least with all human expe- 
rience. That they pervade all the objects of experience, must ensure their continual sug- 
gestion by experience ; that they are true, must ensure that consistency of suggestion, that 
iteration of uncontradicted assertion, which commands implicit assent, and removes all oc- 
casion of exception; that they are simple, and admit of no misunderstanding, must secure 
their admission by every mind." 

" A truth, necessary and universal, relative to any object of our knowledge, must verify 
itself in every instance where that object is before our contemplation, and if at the same 
time it be simple and intelligible, its verification must be obvious. The sentiment of such a 
truth cannot, therefore, but be present to our minds whenever that object is contemplated, and must 
therefore make a part of the mental picture or idea of that object which we may on any occasion summon 
before our imagination. . . . All propositions, therefore, become not only untrue but inconceivable, if 
. , . axioms be violated in their enunciation." 

Another high authority (if indeed it be another authority) may be cited in favor of the 
doctrine that axioms rest upon the evidence of induction. " The axioms of geometry them- 
selves may be regarded as in some sort an appeal to experience, not corporeal, but mental. 
When we say, the whole is greater than its part, we announce a general fact, which rests, 
it is true, on our ideas of whole and part ; but, in abstracting these notions, we begin by- 
considering them as subsisting in space, and time, and body, and again, in hnear, and su- 
perficial, and solid space. Again, when we say, the equals of equals are equal, we men- 
tally make comparisons, in equal spaces, equal times, &c., so that these axioms, however self- 
evident, are still general propositions so far of the inductive kind, that, independently of ex, 
perience, they would not present themselves to the mind. The only difference between 
these and axioms obtained from extensive induction is this, that, in raising the axioms of 
geometry, the instances offer themselves spontaneously, and without the trouble of search, 
and are few and simple ; in raising those of nature, they are infinitely numerous, comph- 
cated, and remote, so that the most diligent research and the utmost acuteness are required 
to unravel their web and place their meaning in evidence." — Sir J. Herschel's Discourse 
on ihe Study of Natural Philosophy, pp. 95, 96. 



164 REASONING. 

inductions from experience : the simplest and easiest cases of generali- 
zation from the facts furnished to us by our senses or by our internal 
consciousness. 

While the axioms of demonstrative sciences thus appeared to be 
experimental truths, the definitions, as they are incorrectly called, of 
those sciences, were found by us to be generalizations from experience 
which are not even, accurately speaking, truths ; being propositions in 
which, while we assert of some kind of object, some property or prop- 
erties which observation shows to belong to it, we at the same time 
deny that it possesses any other properties, although in truth other 
properties do in every individual instance accompany, and in most or 
even in all instances, modify the property thus exclusively predicated. 
The denial, therefore, is a mere fiction, or supposition, made for the 
purpose of excluding the consideration of those modifying circum- 
stances, when their influence is of too trifling amount to be worth con- 
sidering, or adjourning it, when important, to a more convenient 
moment. 

\ From these considerations it would appear" that Deductiye or De-* 
monstrative Sciences are all, without exception. Inductive Sciences : 
that their evidence is that of experience, but that they are also, in virtue 
of the peculiar character of one indispensable portion of the general 
formulae according to which their inductions are made. Hypothetical 
Sciences. Their conclusions are only true upon certain suppositions, 
which are, or ought to be, approximations to the truths but are seldom, 
if ever, exactly true ; and to this hypothetical character is to be ascribed 
the peculiar certainty, which is supposed to be inherent in demon- 
stration. 

What we have now asserted, however, cannot be received as univer- 
sally true of Deductive or Demonstrative Sciences until verified by 
being applied to the most remarkable of all those sciences, that of Num- 
bers ; the theory of'the Calculus ; Arithmetic and Algebra. It is hardei: 
to believe of the doctrines of this science than of any other, either that 
they are not truths d 2yriori, but experimental truths, or that their pe- 
culijw certainty is owing tO their being not absolute but only conditional 
truths. This, therefore, is a case which merits examination apart ; and 
the more so, because on this subject we have a double set of doctrines 
to contend with; that of Mr. Whewell and the d priori philosophers on 
one side; and on the other, a philosophical theory the most opposite 
to theirs, which was at one time very generally received, and is still 
far from being altogether exploded among metaphysicians. 

§ 2. This theory"attempts to solve the difficulty apparently inherent 
in the case, by representing the propositions of the science of numbers 
'as merely verbal, and its processes as simple transformations of lan- 
guage, substitutions of one expression for another. The proposition, 
Two and one are equal to three, according to these philosophers, is not 
a truth, is not the assertion of a really existing fact, but a definition of 
the word three ; a statement that mankind have agreed to use the name 
three as a sign exactly equivalent to two and one; to call by the former 
name whatever is called by the other more clumsy phrase. According 
to this doctrine, the longest process in algebra is but a succession of 
changes in terminology, by which equivalent expressions are substi- 
tuted one for another j a series of translations of the same fact, from 



DEMONSTRATION, AND NECESSARY TRUTHS. 165 

one into another language : though how, after such a series of transla- 
tions, the fact itself comes out changed, (as when we demonstrate a new 
geometrical theorem by algebra,) they have not explained ; and it is a 
difficulty which is fatal to their theory. 

It must be acknowledged that there are peculiarities in the processes 
of arithmetic and algebra which render the above theory very plausi- 
ble, and have not unnaturally made those sciences the stronghold of 
Nominalism. The doctrine that we can discover facts, detect the 
hidden processes of nature, by an artful manipulation of language, is 
so contrary to common sense, that a person must have made some 
advances in philosophy to believe it ; men fly to so paradoxical a belief 
to avoid, as they think, some even greater difficulty, which the vulgar 
do not see. What has led many to believe that reasoning is a mere 
verbal process, is, that no other theory seemed reconcilable with the 
nature of the Science of Numbers. For we do not cany any ideas 
along with us when we use the symbols of arithmetic or of algebra. 
In a geometrical demonstration we have a mental diagram, if not one 
upon paper; AB, AC, are present to our imagination as lines, inter- 
secting other lines, forming an angle with one another, and the like ; 
but not so a and b. These may represent lines or any other magni- 
tudes, but those magnitudes are never thought of; nothing is realized 
in our imagination but a and b. The ideas which, on the particular 
occasion, they happen to represent, are banished from the mind during 
every intermediate part of the process between the beginning, when 
the premisses are translated from things into signs, and the end, when 
the conclusion is translated back from signs into things. Nothing, 
then, being in the reasoner's mind but the symbols, what can seem 
more inadmissible than to pretend that the reasoning process has to do 
with anything more ] We seem to have come to one of Bacon's Pre- 
rogative Instances ; an experimentum crucis on the nature of reasoning 
itself. 

Nevertheless it will appear on consideration, that this apparently so 
decisive instance is no instance at all ; that there is in every step of 
an arithmetical or algebraical calculation a real induction, a real infer- 
ence of facts from facts ; and that what disguises the induction 
is simply its comprehensive nature, and the consequent extreme 
generality of the language. All immbers must be numbers of some- 
thing : there are no such things as numbers in the abstract. Ten must 
mean ten bodies, or ten sounds, or ten beatings of the pulse. But 
though numbers must be numbers of som^ething, they may be numbers 
of anything. Propositions, therefore, concerning numbers, have the 
remarkable peculiarity that they are propositions concerning all things 
whatever ; all objects, all existences of every kind, known to our 
experience. All things possess quantity ; consist of parts which can 
be numbered ; and in that character possess all the properties which 
are called properties of numbers. That half of four is two must be 
ti'ue whatever the word four represents, whether four men, four miles, 
or four pounds weight. We need only conceive a thing divided into 
four equal parts, (and all things may be conceived as so divided,) to be 
able to predicate of it every property of the number foui', that is, 
every arithmetical proposition in which the number four stands on one 
side of the equation. Algebra extends the generalization still further : 
every number represents that particular number of all things without 



166 REASONING. 

distinction, but every algebraical symbol does more, it represents all 
numbers without distinction. As soon as we conceive a thing divided 
into equal parts, without knowing into what numbers of parts, we may 
call it a or x^ and apply to it, without danger of error, every alge- 
braical formula in the books. The proposition, 2(a -f- ^) = 2« -}- 2Z>, 
is a truth coextensive with the creation. Since then algebraical 
truths are true of all things whatever, and not, like those of geometry, 
true of lines only or angles onl}^, it is no wonder that the symbols 
should not excite in our minds ideas of any things in particular. 
When we demonstrate the forty-seventh proposition of Euclid, it is 
not necessary that the words should raise in us an image of all right- 
angled triangles, but only of some one right-angled triangle : so in 
algebra we need not, under the symbol a, picture to ourselves all 
things whatever, but only some one thing ; why not, then, the letter 
itself] The mere written characters, <2, Z>, x, ?/, z, serve as w^ell foi' 
representatives of Things in general, as any more complex and 
apparently more concrete conception. That we are conscious of 
them however in their character of things, and not of mere signs, is 
evident from the fact that our whole process of reasoning is carried on 
by predicating of them the properties of things. In resolving an 
algebraic equation, by what rules do we proceed % By applying at 
each step to a, h, and x, the proposition that equals added to equals 
make equals ; that equals taken from equals leave equals ; and other 
propositions founded upon these two. These are not properties of 
language, or of signs as such, but of magnitudes, which is as much as 
to say, of all things. The inferences, therefore, which are successively 
drawn, are inferences concerning Things, not symbols ; although as 
any Things whatever will serve the turn, there is no necessity for 
keeping the idea of the Thing at all distinct, and consequently the 
process of thought may, in this case, be allowed without danger to do 
what all processes of thought, when they have been performed often, 
will do if permitted, namely, to become entirely mechanical. Hence 
the general language of algebra comes to be used familiarly without 
exciting ideas, as all other general language is prone to do from mere 
habit, though in no other case than this can it be done with complete 
safety. But when we look back to see from whence the probative 
force of the process is derived, we find that at every single step, 
unless we suppose ourselves to be thinking and talking of the things, 
and not the mere symbols, the evidence fails. 

There is another circumstance, which, still more than that which we 
have now mentioned, gives plausibility to the notion that the proposi- 
tions of arithmetic and algebra are merely verbal. This is, that when 
considered as propositions respecting Things, they all have the appear- 
ance of being identical propositions. The assertion. Two and one 
are equal to three, considered as an assertion respecting objects, as 
for instance " Two pebbles and one pebble are equal to three peb- 
bles," does not affirm equality between two collections of pebbles, but 
absolute identity. It affirms that if we put one pebble to two pebbles, 
those very pebbles are three. The objects, therefore, being the very 
same, and the mere assertion that "objects are themselves" being in- 
significant, it seems but natural to consider the proposition, Two and 
one are equal to three, as asserting mere identity of signification be- 
tween the two names. 



' DEMONSTRATION, AND NECESSARY TRUTHS. 167 

This, however, though it looks so plausible, will not stand examin- 
ation. The expression, " two pebbles and one pebble," and the ex- 
pression, " three pebbles," stand indeed for the same aggregation of 
objects, but they by no means stand for the same physical fact. They 
are names of the same objects, but of those objects in two different 
states : though they denote the same things, their connoiBXion is differ- 
ent. Three pebbles in two separate parcels, and three pebbles in 
one parcel, do not make the same impression on our senses ; and the as- 
sertion that the very same pebbles may by an alteration of place and by 
arrangement be made to produce either the one set of sensations or the 
other, though it is a very familiar proposition, is not an identical one. 
It is a truth known to us by early and constant experience : an induc- 
tive truth: and such truths are the foundation of the science of Num- 
ber. The fundamental truths of that science all rest upon the evidence 
of sense ; they are proved by showing to our eyes and our fingers that 
any given number of objects, ten balls for example, may by separation 
and rearrangement exhibit to our senses all the different sets of num- 
bers the sum of which is equal to ten. All the improved methods of 
teaching arithmetic to children proceed upon a knowledge of this fact. 
All who wish to carry the child's ??iifid along with them in learning 
arithmetic; all who (as Dr. Biber in his remarkable Lectures on Edu- 
cation expresses it) wish to teach numbers, and not mere ciphers — now 
teach it through the evidence of the senses, in the manner we have 
described.* 

We may, if we please, call the proposition" Three is two and one," 
a definition of the nurnber three, and assert that arithmetic, as it has 
been asserted that geometry, is a science founded upon definitions. But 
they are definitions in the geometrical sense, not the logical ; asserting 
not the meaning of a term only, but along with it an observed matter 
of fact. The proposition, "A circle is a figure bounded by aline which 
has all its points equally distant from a point within it," is called the 
definition of a circle ; but the proposition from which so many conse- 
quences follow, and which is really a first principle of geometry, is, 
that figures answering to this description exist. And thus we may 
call, " Three is two and one," a definition of three ; but the calcula- 
tions which depend upon that proposition do not follow from the defi- 
nition itself, but from an arithmetical theorem presupposed in it, namely, 
that collections of objects exist, which while they impress the senses 
thus, °o°» niay be separated into two parts, thus, oo o. This propo- 
sition being gi'anted, we term all such parcels Threes, after which the 
enunciation of the above-mentioned physical fact will serve also for a 
definition of the word Three. 

The Science of Number is thus no exception to the conclusion we 
previously arrived at, that the processes even of deductive sciences are 
altogether inductive, and that their first principles are generalizations 

* See, for illustrations of various sorts, Professor Leslie's Philosophy of Arithmetic ; and 
see also two of the most efficient books ever written for training the infant intellect, 
Mr. Horace Grant's Arithmetic for Young Children, and his Second Stage of Arithmetic, 
both published by the Society for the Diffusion of Useful Knowledge, 

" Number," says the reviewer of Mr. Wlieweli, already cited, " we cannot help regarding 
as an abstraction, and consequently its general properties or its axioms to be of necessity 
inductively concluded from the consideration of particular cases. And surely this is the 
way in which children do acquire their knowledge of number, and in which they learn its 
axioms. The apples and the marbles are put in requisition, and through the multitude of 
gingerbread nuts their ideas acquire clearness, precision, and generality." 



1G8 REASONING. 

from experience. It remains to be examined whether this science 
resembles geometry in the further circumstance, that some of its induc- 
tions are not exactly true ; and that the peculiar certainty ascribed to 
it, on account of which its propositions are called Necessary Truths, is 
fictitious and hypothetical, being true in no other sense than that those 
propositions necessarily follow from the hypothesis of the truth of prem- 
isses which are avowedly mere approximations to truth. 

§ 3. The inductions of arithmetic are of two sorts : first, those which 
we have just expounded, such as One and one are two, Two and one 
are three, &c., which may be called the definitions of the various 
numbers, in the improj)er or geometrical sense of the word Definition; 
and secondly, the two following axioms : The sums of equals are equal, 
The difl'erences of equals are equal. These two are sufficient ; for the 
corresponding propositions respecting unequals may be proved from 
these, by the process well known to mathematicians under the name of 
rcductio ad ahsurdum. 

These axioms, and likewise the so-called definitions, are, as already 
shown, results of induction; true of all objects whatever, and, as it may 
seem, exactly true, without any hypothetical assumption of unqualified 
truth where an approximation to it is all that exists. The conclusions, 
therefore, it will naturally be inferred, are exactly true, and the science 
of number is an exception to other demonstrative sciences in this, that 
the absolute certainty which is predicable of its demonstrations is inde- 
pendent of all hypothesis. 

On more accurate investigation, however, it will be found that, even 
in this case, there is one hypothetical element in the ratiocination. In 
all propositions concerning numbers, a condition is implied, without 
which none of them would be true ; and that condition is an assump- 
tion which maybe false. The condition is, that 1 = 1; that all the 
numbers are numbers of the same or of equal units. Let this be doubt- 
■^1, and not one of the propositions of arithmetic will hold true. How 
can we know that one pound and one pound make two pounds, if one 
of the pounds may be troy, and the other avoirdupois 1 They may not 
make two pounds of either, or of any weight. How can we know that 
a forty -horse power is always equal to itself, unless we assi^me that all 
horses are of equal strength 1 It is certain that 1 is always equal in 
number to 1; and where the'mere number of objects, or of the parts 
of an object, without supposing them to be equivalent in any other 
respect, is all that is material, the conclusions df arithmetic, so far as 
they go to that alone, are true without mixture of hypothesis. There 
are a few such cases ; as, for instance, an inquiry into the amount of 
population of any country. It is indifferent to that inquiry whether 
they are grown people or children, strong or weak, tall or short ; the 
only thing we want to ascertain is their number. But whenever, from 
equality or inequality of number, equality or inequality in any other 
respect is to be inf'eri'ed, arithmetic carried into such inquiries becomes 
as hypothetical a science as geometry. All units must be assumed to 
be etpial in that other respect ; and this is never precisely tiue, for 
one pound weight is not exactly equal to another, nor one mile's length 
to another; a nicer balance, or more accurate measuring instniments, 
would always detect some difference. 

Wl\at is commonly called mathematical certainty, therefore, whicli 



DEMONSTRATION, AND NECESSARY TRUTHS. 169 

comprises the two-fold conception of unconditional truth and perfect 
accuracy, is not an attribute of all mathematical truths, but of those 
only which relate to pure Number, as distinguished from Quantity, 
in the more enlarged sense ; and only so long as we abstain from sup- 
posing that the numbers are a precise index to actual quantities. The 
certainty usually ascribed to the conclusions of geometry, and even to 
those of mechanics, is nothing whatever but certainty of inference. 
W^ can have full assurance of particular results under particular sup- 
positions, but we cannot have the same assurance that these suppositions 
are accurately true, nor that they include all the data which may exer- 
cise an influence over the result in any given instance. 

§ 4. It appears, therefore, that the method of all Deductive Sciences 
is hypothetical. They proceed by tracing the consequences of certain 
assumptions ; leaving for separate consideration whether the assump- 
tions are true or not, and if not exactly true, whether they are a suffi- 
ciently near approximation to the truth. The rea.son is obvious. Since 
it is only in questions of pure number that the assumptions are exactly 
true, and even there, only so long as no conclusions except purely nu- 
merical ones are to be founded upon them ; it must, in all other cases 
of deductive investigation, form a part of the inquiry, to determine how 
much the assumptions want of being exactly true in the case in hand. 
This is generally a matter of observation, to be repeated in every fre«h 
case ; or if it has to be settled by argument instead of observation, may re- 
quire, in every different case, different evidence, and present every de- 
gree of difficulty from the lowest to the highest. But the other part of the 
process — viz^, to determine what else may be concluded if we find, and 
in proportion as we find, the assumptions to be true — may be performed 
once for all, and the results held ready to be employed as the occasions 
turn up for use. We thus do all beforehand that can be so done, and 
leave the least possible work to be performed when cases arise and press 
for a decision. This inquiry into the inferences which can be drawn 
from assumptions, is what properly constitutes Demonstrative Science. 

It is of course quite as practicable to arrive at new conclusions from 
facts assumed, as from facts observed ; from fictitious, as from real, in- 
ductions. Deduction, as wa have seen, consists of a series of inferences 
in this form : a is a mark of h, h of c, c of d, therefore <2 is a mark of <^, 
which last may be a truth inaccessible to direct observation. In like 
manner it is allowable to say, Suppose that a were a mark of ^, h of c, 
and c of ri, a would be a mark of *^i, which last conclusion was not thought 
of by those who laid down the premisses. A system of propositions as 
complicated as geometry might be deduced from assumptions which are 
false ; as was done by Ptolemy, Descartes, and others, in their attempts 
to explain synthetically the phenomena of the solar system, on the sup- 
position that the apparent motions of the heavenly bodies were the real 
motions, or were produced in some way more or less different from the 
true one. Sometimes the same thing is knowingly done, for the pur- 
pose of showing the falsity of the assumption ; which is called a reduc- 
tio ad absurdum. In such cases, the reasoning is as follows : a is a 
mark of ^, and h of c ; now if c were also a mark o£d, a would be a mark 
of d ; but d is known to be a mark of the absence of a ; consequently a 
would be a mark of its own absence, which is a contradiction \ there- 
fore c is not a mark of d. 

Y 



170 REASONING. ': 

§ 5. It lias even been held by some philosophers, that all ratiocina- 
tion rests in the last resort upon a reductio ad ahsurdum ; since the 
way to enforce assent to it, in case of obscurity, would be to show that 
if the conclusion be denied we must deny some one at least of the 
premisses, which, as they are all supposed true, would be a contradic- 
tion. And, in accordance with this, many have thought that the pecu- 
liar nature of the evidence of ratiocination consisted in the impossibility 
of admitting the premisses and rejecting the conclusion without a con- 
tradiction in terms. This theory, however, is quite inadmissible as an 
explanation of the grounds on which ratiocination itself rests. If any 
one denies the conclusion notwithstanding his admission of the prem- 
isses, he is not involved in any direct and express contradiction until he 
is compelled to deny some premiss ; and he can only be forced to do 
this by a reductio ad ahsurdum, that is, by another ratiocination : now, 
if he denies the validity of the reasoning process itself, he can no more 
be forced to assent to the second syllogism than to the first. In truth, 
therefore, no one is ever forced to a contradiction in terms ; he can 
only be forced to a contradiction (or rather an infringement) of the 
fundamental maxim of ratiocination, namely, that whatever has a mark, 
has what it is a mark of; or (in the case of universal propositions), 
that whatever is a mark of a thing, is a mark of whatever else that 
thing is a mark of. For in the case of every correct argument, as soon 
as thrown into the syllogistic form, it is evident without the aid of any 
other syllogism, that he v/ho, admitting the premisses, fails to draw 
the conclusion, does not conform to the above axiom. 

Without attaching exaggerated importance to the distinction now 
drawn, I think it enables us to characterize in a more accurate manner 
than is usually done, the nature of demonstrative evidence and of logi- 
cal necessity. That is necessary, from which to withhold our assent 
would be to ^delate the above axiom. And since the axiom can only 
be violated by assenting to premisses and rejecting a legitimate con- 
clusion from them, nothing is necessary except the connexion between 
a conclusion and premisses ; of which doctrine, the whole of this and 
the preceding chapter are submitted as the proof. 

We have now proceeded as far in the theory of Deduction as we 
can advance in the present stage of our inquiry. Any further insight 
into the subject requires that the foundation shall have been laid of 
the philosophic' theory of Induction itself; in which theory that of 
deduction, as a mode of induction, which we have now shown it to be, 
will assume spontaneously the place which belongs to it, and will re- 
ceive its share of whatever light may be thrown upon the great intel- 
lectual operation of which it forms so important a part. 

We here, therefore, close the Second Book, The theory of Induc- 
tion-, in the most comprehensive sense of the term, willform the sub- 
ject of the Third. ^ ' 



BOOK III. 

OF INDUCTION. 



" According to the doctrine now stated, the highest, or rather the only proper object of 
physics, is to ascertain those established conjunctions of successive events, which consti- 
tute the order of the universe ; to record the phenomena which it exhibits to our observa- 
tions, or which it discloses to our experiments ; and to refer these phenomena to their gen- 
eral laws." — D. Stewart, Elements of the Philosophy of the Human Mind, vol. ii., chap. iv. 
sect. 1. 

" In such cases the inductive and deductive methods of inquiry may be said to go hand 
in hand, the one verifying the conclusions deduced by the other ; and the combination of 
experiment and theory, which may thus be brought to bear in such cases, forms an engine 
of discovery infinitely more powerful than either taken separately. This state of any de; 
partment of science is perhaps of all others the most ihteresting, and that which promises 
the most to research." — Sir J. Herschel, Discourse on the Study of Natural Philosophy, ; 



CHAPTER I. 

PRELIMINARY OBSERVATIONS ON INDUCTION IN GENERAL. 

§ 1. The portion of the present inquiry upon which we are now 
about to enter, may be considered as the principal, both from its sur- 
passing in intricacy all the other branches, and because it relates to a pro- 
cess which has been shown in the preceding Book to be that in which 
the Investigation of Nature essentially consists. We have found that 
.all Inference, consequently all Proof, and all discovery of truths not 
self-evident, consists of inductions, and the interpretation of inductions : 
that all our knowledge, not intuitive, comes to us exclusively from 
that source. What Induction is, therefore, and what conditions render 
it legitimate, cannot but be deemed the main question of the science of 
logic — the question which includes all others. It is, however, one 
which professed writers on logic have almost entirely passed over. 
The generalities of the subject have not been altogether neglected by 
metaphysicians ; but, for want of sufficient acquaintance with the pro- 
cesses by which science has actually succeeded in establishing general 
truths, their analysis of the inductive operation, even when unexcep- 
tionable as t6 correctness, has not been specific enough to be made 
the foundation of practical rules, which might be for induction itself 
what the rules of the syllogism are for the interpretation of induction: 
while those by whom physical science has been carried to its present 
high state of improvement — and who, to amve at a complete theory of 
the process, needed only to generalize, and adapt to all varieties of 
problems, the methods which they themselves employed in their ha- 
bitual pursuits— never until very lately made any serious attempt to 
philosophize on the subject, nor regarded the mode in which they ar- 
rived at their conclusions as deserving of study, independently of the 
conclusions themselves. 



172 INDUCTION. 

Althougli, for these reasons, there is not yet extant a body of Induc- 
tive Logic, scientifically constructed ; the materials for its construction 
exist, widely scattered, but abundant : and the selection and arrange- 
ment of those materials is a task with which intellects of the highest 
order, possessed of the necessary acquirements, have at length consent- 
ed to occupy themselves. Within a few years three wi'iters, profoundly 
versed in every branch of physical science, and not unaccustomed to 
carry their speculations into still higher regions of knowledge, have 
made attempts, of unequal but all of very great merit, towards the 
creation of a Philosophy of Induction : Sir John Herschel, in his Dis- 
course on the Study of Natural Philosophy ; Mr. Whewell, in his His- 
tory and Philosophy of the Inductive Sciences ; and, greatest of all, 
M. Auguste Comte, in his Cours de Philosophic Posiftive, a work which 
only requires to be better known, to place its author in the very high- 
est class of European thinkers. That the present writer does not 
consider any of these philosophers, or even all of them together, to have 
entirely accomplished this important work, is implied in his attempting 
to contribute something further towards its achievement ; but with his 
comparatively imperfect knowledge of the various physical sciences, 
the attempt would have been desperate unless the materials had 
been brought together, and had undergone a partial elaboration, by 
their more competent hands ; even if he could have dispensed with 
the many important logical ideas and principles, for the first sugges- 
tion of which he has been indebted to one or other of those writers. 

§ 2. For the purposes of the present inquiry. Induction may be de- 
fined, the operation of discovering and proving general propositions; 
It is true that (as already shown) the process of indirectly ascertaining in- 
dividual facts, is as truly inductive as that by which we establish general 
truths. But it is not a different kind of induction ; it is another form of the 
very same process : since, on the one hand, generals are but collec- 
tions of particulars, definite in kind but indefinite in number; and on the 
other hand, whenever the evidence which we derive from observation 
of known cases justifies us in drawing an inference respecting even one 
unknown case, we should on the same evidence be justified in drawing 
a similar inference with respect to a whole class of cases. The infer- 
ence either does not hold at all, or it holds in all cases of a certain de- 
scription ; in all cases which, in certain definable respects, resemble 
those we have observed. 

If these remarks are just ; if the principles and rules of inference are 
the same whether we infer general propositions or individual facts ; it 
follows that a complete logic of the sciences would be also, a complete 
logic of practical business and common life. Since there is no case of 
legitimate inference from experience, in v/hich the conclusion may not 
legitimately be a general proposition ; an analysis of the process by 
which general truths are arrived at, is virtually an analysis of all induc- 
tion whatever. Whether we are inquiring into a scientific principle or 
into an individual fact, and whether we proceed by experiment or by ra- 
tiocination, every step in the train of inferences is essentially inductive, 
and the legitimacy of the induction depends in both cases upon the same 
conditions. 

True it is that in the case of the practical inquirer, who is endeavor- 
ing to ascertain facts not for the purposes of science but for those of 



INDUCTION IN GENERAL. 173 

business, such for instance as the advocate or the judge, the chief diffi- 
culty is one in which the principles of induction will afford him no as- 
sistance. It lies not in making his inductions but in the selection of 
them ; in choosing from among all general propositions ascertained to 
be true, those which furnish him with marks by which he may trace 
whether the given subject possesses or not the predicate in question. 
In arguing a doubtful question of fact before a jury, the general prop- 
ositions or principles to which the advocate appeals are mostly, in them- 
selves, sufficiently trite, and assented to as soon as stated : his skill lies 
in bringing his case under those propositions or principles ; in calling 
to mind such of the known or recognized maxims of probability as ad- 
mit of application to the case in hand, and selecting from among them 
those best adapted to his object. Success is here dependent upon nat- 
ural or acquired sagacity, aided by knowledge of the particular subject, 
and of subjects alUed with it. Invention, though it can be cultivated, 
"cannot be reduced to rule ; there is no science which will enable a man 
to bethink himself of that which will suit his purpose. 

But when he has thought of something, science can tell him whether 
that which he has thought of will suit his purpose or not. The inquirer 
or ai'guer must be guided by his own knowledge and sagacity in his 
choice of the inductions out of which he will construct his argument. 
But the validity of the argument when constructed, depends upon 
principles and must be tried by tests which are the same for all de- 
scriptions of inquiries, whether the result be to give A an estate, or to 
enrich science with a new general truth. In the one case and in the 
other, the senses, or testimony, must decide on the individual facts ; 
the rules of the syllogism will determine whether, those facts being 
supposed coiTect, the case really falls within the formulae of the differ- 
ent inductions under which it has been successively brought ; and finally, 
the legitimacy of the inductions themselves must be decided by other 
rules, and these it is now our purpose to investigate. If this third part 
of the operation be, in many of the questions of practical life, not the 
most, but the least arduous portion of it, we have seen that this is also 
the case in some great departments of the field of science ; in all those 
which are principally deductive, and most,of all in mathematics ; where 
the inductions themselves are few in number, and so obvious and ele- 
mentary, that they seem to stand in no need of the evidence of experi- 
ence, while to combine them so as to prove a given theorem or solve a 
problem, may call for the highest powers of invention and contrivance 
with which our species is gifted. 

If the identity of the logical processes v^hich prove particular facts 
and those which establish general scientific truths, required any addi- 
tional confirmation, it would be sufficient to consider, that in many 
branches of science single facts have to be proved, as well as princi- 
ples ; facts as completely individual as any that are debated in a comt 
of justice ; but which are proved in the same manner as the other 
truths of the science, and without disturbing in any degree the homo- 
geneity of its method. A remarkable example of this is afforded by 
astronomy. The individual facts upon which that science gi-ounds 
its most important deductions, sUch facts as the magnitudes of the 
bodies of the solar system, their distances from one another, the figure 
of the earth, and its rotation, are scarcely any of them accessible to 
our means of direct observation : they are proved indirectly, by the 



174 INDUCTION. . . 

aid. of. inductions founded on otlier facts wliicli we can more easily 
reach. For example, the distance of the moon from the earth was 
determined by a very circuitous process. The share which direct 
observation had in the work consisted in ascertaining, at one and the 
same instant, the zenith distances of the moon, as seen from two 
points very remote from one another on the earth's surface. The 
ascertainment of these • angular distances ascertained their supple- 
ments ; and since the angle at the earth's centre subtended by the 
distance between the two places of observation was deducible by 
spherical trigonometry from the latitude and longitude of those places, 
the angle at the moon subtended by the same line became the fourth 
angle of a quadrilateral of which the other three angles were known. 
The four angles being thus ascertained, and two sides of the quadri- 
lateral being radii of the earth ; the two remaining sides and the diag- 
onal, or in other words, the moon's distance from the two places of 
observation and from the centre of the earth, could be ascertained, at 
least in terms of the earth's radius, from elementary theorems of geom- 
etry.. At each step in this demonsti'ation we take in a new induction, 
represented, in the aggregate of its results, by a general proposition.' 

Not only is the process by which an individual astronomical fact 
was thus ascertained, exactly similar to those by which the same 
science establishes its general truths, but moreover (as we have shown 
to be the case in all legitimate reasoning) a general proposition might 
have been concluded instead of a single fact. In strictness, indeed, 
the result of the reasoning is a general proposition ; a theorem re- 
ispecting the distance, not of the moon in particular, but of an;i/ inac- 
•cessible object ; showing in what relation that distance stands to certain 
other quantities. And although the moon is almost the only heavenly 
body the distance of which from the earth can really be thus ascer- 
tained, this is merely owing to the accidental circumstances of the 
other heavenly bodies, which render them incapable of affording such 
data as the application of the theorem requires ; for the theorem itself 
is as true of them as it is of the moon.. 

We shall fall into no error, then, if in treating of Induction, we limit 
our attention to the establishment of general propositions. The prin- 
ciples and rules of Induction, as directed to this end, are the principles 
and rules of all Induction; and the logic of Science is the universal 
Logic, applicable to all inquiries in which man can engage, and the 
test of all the conclusions at which he can arrive by inference. 



CHAPTER 11. 

OF INDUCTIONS IMPROPERLY SO CALLED. 

§ 1. Induction, then, is that operation of the mind, by which we in- 
fer that what we know to be true in a particular case or cases, will be 
true in all cases which resemble the former in certain assignable 
respects. In other words, Induction is the process by which we con- 
clude that what is true of certain individuals of a class is tme of the 



INDUCT[ONS IMPROPERLY SO CALLED. 175 

whole class, or that what is true at certain times will be true under 
similar circumstances at all times. 

This definition excludes from the meaning of the term Induction, 
various logical operations, to which it is not unusual to apply that 
name. 

Induction, as above defined, is a process of inference ; it proceeds 
from the known to the unknown ; and any operation involving no in- 
ference, any process in which what seems the conclusion is no wider 
than the premisses from which it is drawn, does not fall within the 
meaning of the term. Yet in the common books of Logic we find 
this laid down as the most perfect, indeed the only quite perfect, form 
of induction. In those books, every process which sets out from a 
less general and terminates in a more general expression — which ad- 
mits of being stated in the form, "■ This and that A are B, therefore 
every A is B" — is called an induction, whether anything be really 
concluded or not ; and the induction is asserted to be not perfect, un- 
less every single individual of the class A is included in the antecedent. 
Or premiss : that -is, unless what we affirm of the class, has already 
been ascertained to be . true of every individual in it, so that the 
nominal conclusioB - is not really a conclusion, but a mere reassertion 
of the premisses. If we were to say, All the planets shine by the 
sun's light, from observation of each separate planet, or All the 
Apostles were Jews, because this is tine of Peter, Paul, John, and 
every other apostle — these, and such as these, would, in the phrase- 
ology in question, be called perfect, and the only perfect. Inductions. 
This, however, is a totally different kind of induction from ours ; it is 
no inference from facts known to facts unknown, but a mere short- 
hand registration of facts known. The two simulated arguments, 
wliich we have quoted, are not generalizations ; the propositions pur- 
porting to be conclusions from them, are not really general proposi- 
tions. A general proposition is one in which the predicate is affirmed 
or denied of an unlimited number of individuals ; namely, all, whether 
few or many, existing or capable of existing, which possess the prop- 
erties connoted by the subject of the proposition. ''All men are mor- 
tal" does not mean all now living, but all men past, present, and to 
come. When the signification of the term is limited so as to render it 
a name not for any and every individual falling under a certain gen- 
eral description, but only for each of a number of individuals desig- 
nated as such, and as it were counted off individually, the proposition, 
though it may be general in its language, is no general proposition, 
but merely that number of singular propositions, written in an 
abridged character. The operation may be very useful, as most 
forms of abridged notation .are ; but it is no part of the investigation 
of tiTith, though often bearing an important part in the preparation of 
the materials for that investigation. 

§ 2. A second process which "requires to be distinguished from 
Induction, is one to which mathematicians sometimes give that name : 
and which so far resembles Induction properly so called, that the 
propositions it leads to are really general propositions. For example, 
when we have proved, with respect to the cnxle, that a straight line 
cannot meet it in more than two points, and when the same thing has 
been successively proved of the ellipse, the parabola, and thb hyper- 



176 INDUCTION. 

bola, it may be laid down as an universal property of the sections of 
the cone. In this example there is no induction, because there is no 
inference : the conclusion is a mere summing up of what was asserted 
in the various propositions from which it is drawn. A case somewhat, 
though not altogether, similar, is the proof of a geometrical theorem 
by means of a diagram. Whether the diagi'am be on paper or only 
in the imagination, the demonstration (as we formerly observed*) does 
not prove directly the general theorem ; it proves only that the con- 
clusion, which the theorem asserts generally, is true of the particular 
triangle or circle exhibited in the diagram : but since we perceive that 
in the same way in which we have proved it of that circle, it might 
also be proved of any other circle, we gather up into one general 
expression all the singular propositions susceptible of being thus 
proved, and embody them in an universal proposition. Having shown 
that the three angles of the triangle ABC are together equal to two 
right angles, we conclude that this is true of every other triangle, not 
because it is true of A B C, but for the same reason which proved it 
to be true of ABC. If this were to be called Induction, an appro- 
priate name for it would be. Induction by parity of reasoning. But 
'the term cannot properly belong to it ; the characteristic quality of 
Induction is wanting, since the truth obtained, though really general, 
is not believed on the evidence of particular instances. We do not 
conclude that all triangles have the property because some triangles 
have, but from the ulterior demonstrative evidence which was the 
ground of our conviction in the particular instances. 

There are nevertheless, in mathematics, some examples of so-called 
induction, in which the conclusion does bear the appearance of a 
generalization grounded upon some of the particular cases included 
in it. A mathematician, when he has calculated a sufficient number 
of the terms of an algebraical or arithmetical series to have ascer- 
tained what is called the law of the series, does not hesitate to fill up 
any number of the succeeding terms without repeating the calculations. 
But I apprehend he only does so when it is apparent from a priori 
considerations (which might be exhibited in the form of demonstration) 
that the mode of formation of the subsequent terms, each from that 
which preceded it, must be similar to the formation of the terms which 
have been already calculated. And when the attempt has been 
hazarded without the sanction of such general considerations, there 
are instances upon record in which it has led to false results. 

It is ,said that Newton discovered the binomial theorem by induc- 
tion ; by raising a binomial successively to a certain number of powers, 
and comparing those powers with one another until he detected the 
relation in which the algebraic formula of each power stands to the 
exponent of that power, and to the two terms of the binomial. The 
fact is not improbable : but a mind like Newton's, which seemed to 
arrive per saltum at principles and conclusions that ordinary mathe- 
maticians only reached by a succession of steps, certainly could not 
have performed the comparison in question without being led by it to 
the a priori ground of the law ; since any one who understands suf- 
ficiently the nature of multiplication to venture upon multiplying 
several lines of figures or symbols at one operation, cannot but perceive 

* Supra, p. 127, 128. 



mDUCTIONS IMPROPERLY SO CALLED. 177 

that in raising a binomial to a power, the coefficients must depend 
upon the laws of permutation and combination : and as soon as this is 
recognized, the theorem is demonstrated. Indeed, when once it was 
seen that the law prevailed in a few of the lower powers, its identity 
with the law of permutation would at once suggest the considerations 
which prove it to obtain universally. Evcn^ Iherefore, such cases as 
these, are but examples of what I have called induction by parity of 
reasoning, that is, not really induction, because not involving any infer- 
ence of a general proposition from particular instances.* 

§ 3. There remains a third improper use of the term Induction, 
which it is of real importance to clear up, because the theory of 
induction has been, to no ordinary degi^ee, confused by it, and because 
the confusion is exemplified in the most recent and most elaborate 
treatise on the inductive philosophy which exists in our language. 
The error in question is that of confounding a mere description of a 
set of observed phenomena, with an induction from them. 

Suppose that a phenomenon consists of parts, and that these parts 
are only capable of being observed separately, and as it were piece- 
meal. When the observations have been made, there is a convenience 
(amounting for many purposes to a necessity) in obtaining a represen- 
tation of the phenomenon as a whole, by combining, or, as we may 
say, piecing these detached fragments together. A navigator sailing 
in the midst of the ocean discovers land : he cannot at first, or by any 
one observation, determine whether it is a continent or an island ; but 
he coasts along it, and after a few days, finds himself to have sailed 
completely round it : he then pronounces it an island. Now there 
was no particular time or place of observation at which he could per- 
ceive that this land was entirely surrounded by water : he ascertained 
the fact by a succession of partial observations, and then selected a 
general expression which summed up in two or three words the whole 
of what he so observed. But is there anything of the nature of an 
induction in this process ] Did he infer anything that had not been 
observed, from something else which had ] Certainly not. That the 
land in question is an island, is not an inference from the partial facts 
which the navigator .saw in the course of his circumnavigation; it is 
the facts themselves ; it is a summary of those facts ; the description of 
a complex fact, to which those simpler ones are as the parts of a whole. 

Now there is no difference in kind between this simple operation, 
and that by which Kepler ascertained the nature of the planetary 
orbits : and Kepler's operation, all at least that was characteristic in 
it, was not more an inductive act than that of our supposed navigator. 
, The object of Kepler was to determine the real path described by 
each of the planets, or let us say the planet Mars (for it was of that 
body that he first established two of the three great astronomical 
truths which bear his name). To do this there was no other mode 
than that of direct observation : and all which observation could do 
was to ascertain a great number of the successive places of the planet ; 
or rather, -of its apparent places. That the planet occupied success- 
ively all these positions, or at all events, positions which produced the 

* I am happy to be able to refer, in confirmation of this view of what is called induction 
in mathematics, to the highest English authority on the philosophy of algebra, Mr. Pea- 
cock. See pp. 107-8 of his profound Treatise on Algebra. - 

z 



178 INDUCTION. 

same impressions on the eye, and that it passed from one of these to 
another insensibly, and without any apparent breach of continuity; 
thus much the senses, with the aid of the proper instruments, could 
ascertain. What Kepler did more than this, was to find what sort of 
a curve these different JDoints would make, supposing them to be all 
ioined together. He expressed the whole series of the observed 
places of Mars by what Mr. Whevvell calls the general conception of 
an ellipse. This operation was far fi'om being, as easy as that of the 
navio-ator who expressed the series of his observations en successive 
points of the coast by the general conception of an island. But it is 
the very same sort of operation ; and if the one is not an induction but 
a description, this must also be true of the other. 

To avoid misapprehension, we must remark that Kepler, in one 
respect, performed a real act of induction ; namely, in concluding that 
because the observed places of Mars were correctly represented by 
points in an imaginary ellipse, therefore Mars would continue to re- 
volve in tliat same ellipse ; and even in concluding that the position of 
the planet during the time which intervened between two observa- 
tions, must have coincided with the intermediate points of the curve. 
But this really inductive operation requires to be carefully distin- 
guished from" the mere act of bringing the facts actually observed 
under a general description. So distinct are these two operations, 
that the one might have been performed without the other. Men 
might and did make correct inductions concerning the heavenly mo- 
tions, before they had obtained correct general descriptions of them. 
It was known that the planets always moved in the same paths, long 
before it had been a'scertained that those paths were ellipses. Men 
early remarked that the same set of apparent positions returned pe- 
riodically. When they obtained a new description of the phenomenon, 
they did not necessarily make any further induction, nor (which is the 
true test of a new general truth) add anything to the power of predic- 
tion which they already possessed. 

§ 4. The descriptive operation which enables a number of details to 
be summed up in a single proposition, Mr. Whewell, by an aptly- 
chosen expression, has termed the Colligation of Facts.* In most of 
his observations concerning that mental process I fully agree, and 
would gladly transfer all that portion of his book into my own pages, 
I only think him mistaken in setting up this kind of operation, which 
according to the old and received meaning of the term is not induction 
at all, as the type of induction generally ; and laying down, throughout 
his work, as principles of induction, the princi^^les of mere colligation. 

Mr. Wliewell maintains that the general proposition which binds 
together the particular facts and makes them, as it were, one fact, is 
not the mere sum of those facts, but something more, since there is 
introduced a conception of the mind, which did not exist in the facts 
themselves. " The particular facts," ?ays he,t " are not merely brought 
together, but there is a new element added to the combination by the 
very act of thought by which they are combined. . . .When the Greeks, 
after long observing the motions of the planets, saw that these motions 
might be rightly considered as produced by the motion of one wheel 

* Philosophy of the Inductive Sciences, ii., 213, 214. f Ibid. 



INDUCTIONS IMrROPERLY SO CALLED. 179 

revolving in the inside of another wheel, these wheels were creations 
of their minds, added to the facts which they perceived by sense. 
And even if the wheels were no longer supposed to be material, but 
were reduced to mere geometrical spheres or circles, they were not 
the less products of the mind alone — something additional to the facts 
observed. The same is the case in all other discoveries. The facts 
are known, but they are insulated and unconnected, till the discoverer 
supplies from his own store a principle of connexion. The pearls are 
there, but they will not hang together till some one provides the string." 

That a conception of the nlind is introduced is indeed most certain, 
and Mr. Whewell has rightly stated elsewhere, that to hit upon the 
right conception is often a far more difficult, and more meritorious 
achievement, than to prove its applicability when obtained. But a 
conception implies, and corresponds to, something conceived ; and 
although the conception itself is not in the facts, but in our mind, it 
must be a conception of something w^hich really is in the facts, some 
property which they actually possess, and which they would manifest 
to our senses, if our senses were able to take cognizance of them. If, 
for instance, the planet left behind it in space a visible track, and if the 
observer were in a fixed position at such a distance above the plane of 
the orbit as would enable him to see the whole of it at once, he would 
see it to be an ellipse ; and if gifted with appropriate instruments, and 
powers of locomotion, he could prove it to be such by measuring its 
different dimensions. These things are indeed impossible to us, but 
' not impossible in themselves j if they.were so, Kepler's law could not 
be true. 

Subject to the indispensable condition which has just been stated, I 
cannot perceive that the part which conceptions have in the operation 
of studying facts, has ever been overlooked or undervalued as Mr. Whe- 
well supposes it has. No one ever disputed that in order to reason 
about anything we must have a conception of it ; or that when we 
include a multitude of things under a general expression, there is 
implied in the expression a conception of something common to those 
things. But it by no means follows that the conception is necessarily 
pre-existent, or constructed by the mind out of its own materials. If 
the facts are rightly classed under the conception,, it is because there 
is in the facts themselves something of which the conception is itself a 
copy; and which if we cannot directly perceive, it is because of the 
limited power of our organs, and not because the thing itself is not 
there." The conception itself is often obtained by abstractiqui from the 
very facts which, in Mr. Whewell's language, it is afterwards called in 
to connect. This, Mr. Whewell himself admits, when he observes, 
(which he does on several occasions,) how great a service would be ren- 
* dered to the science of physiology by the philosopher " who should 
establish a precise, tenable, and consistent conception of life."* Such 
a conception can only be abstracted from the phenomena of life itself; 
from thfe very facts which it is put in requisition t<T connect. In other 
cases (no doubt)^ instead of collecting the conception fi-om the very 
phenomena which we are attempting to colligate, we select it from 
among those w^hich have been previously collected by abstraction fi-om 
other facts. In the instance of Kepler's laws, the latter was the case. 

* Philosophy of the Inductive Sciences, vol ii., p. 173. 



180 INDUCTION. 

The facts being out of the reach of being observed, in any such man- 
ner as would have enabled the senses to identify directly the path of 
the planet, the conception requisite for framing a general description 
of that path could not be collected by abstraction from the observations 
themselves ; the mind had to supply hypothetically, from among the 
conceptions it had obtained from other portions of its experience, some 
one which would coiTectly represent the series of the observed facts. 
It had to frame a supposition respecting the general course of the phe- 
nomenon, and ask itself. If this be the general description, what will 
the details be 1 and then compare these with the details actually 
observed. If they agreed, the hypothesis would serve for a descrip- 
tion of the phenomenon : if not, it was necessarily abandoned, and 
another tried. It is such a case as this which gives color to the doc- 
trine that the mind, in framing the descriptions, adds something of its 
own which it does not find in the facts. 

Yet it is a fact, surely, that the planet does describe an ellipse ; and 
a fact which we could see, if we had adequate visual organs and a 
suitable position. Not having these advantages, but possessing the 
conception of an ellipse, or (to express the meaning in less technical 
language) knowing what an ellipse was, Kepler tried whether the ob- 
served places of the planet were consistent with such a path. He 
found they were so ; and he, consequently, asserted as a fact that the 
planet moved in an ellipse. But this fact, which Kepler did not add 
to, but found in, the motions of the planet, namely, that it occupied in 
succession the various points in the circumference of a given ellipse, 
was the very fact, the separate parts of which had been separately ob- 
served ; it was the sum of the different observations. It superadded 
nothing to the particular facts which it served to bind together: ex- 
cept, indeed, the knowledge that a resemblance existed between the 
planetary orbit and other ellipses ; an accession the nature and amount 
of which will be fully considered hereafter,* 

Having stated this fundamental difference between my views and 
those of Mr. Whewell, I must add, that his account of the manner in 
which a conception is selected, suitable to express the facts, appears 
to me perfectly just. The experience of all thinkers will, I believe, 
testify that the process is tentative ; that it consists of a succession of 
guesses ; many being rejected, until one at last occurs fit to be chosen. 
We know from Kepler himself that before hitting upon the " concep- 
tion" of an ellipse, he tried nineteen other imaginary paths, which, 
finding them inconsistent with the observations, he was obliged to re- 
ject. But as Mr. Whewell truly says, the successful hypothesis, 
although a guess, ought not to be called a lucky, but a skillful guess. 
The guesses which serve to give mental unity and wholeness to a 
chaos of scattered particulars, are accidents which occur to no minds 
but those abounding in knowledge and disciplined in scientific combi- 
nations. 

How far this tentative method, so indipensable as a means to the col- 
ligation of facts for purposes of description, admits of application to 
Induction itself, and what functions belong to it in that department, 
will be considered in the chapter of the present Book which relates to 
Hypotheses. On the present occasion we have chiefly to distinguish 

* Vide iafra, book iv., ch. 1. 



INDUCTIONS IMPROPERLY SO CALLED. 181 

this process of colligation from Induction properly so called : and that 
the distinction may be made clearer, it is well to advert to a curious 
and interesting remark of Mr. Whewell, which is as strikingly true of 
the former operation, as it is unequivocally false of the latter. 

In different stages of the progress of knowledge, philosophers have 
employed, for the colligation of the same order of facts, different con- 
ceptions. The early and rude observations of the heavenly bodies, in 
which minute precision was neither attained nor sought, presented no- 
thing inconsistent with the representationof the path of a planet as an 
exact circle, having the earth for its centre. As observations increased 
in accuracy, and facts were, disclosed which were not reconcilable 
with this simple supposition, for the colligation of those additional 
facts, the supposition was varied ; and varied again and again as facts 
became more numerous and precise. The earth was removed fi'om 
the centre to some, other point within the circle ; the planet was sup- 
posed to revolve in a smaller circle called an epicycle, round an im- 
aginary point which revolved in a circle round the earth : in proportion 
as observation elicited fresh facts contradictory to these representations, 
other epicycles and other eccentrics were added, producing additional 
.complication ; until at last Kepler swept all these circles away, and 
substituted the conception of an exact ellipse. Even this is found not 
to represent with complete correctness the accurate observations of 
the present day, which disclose many slight deviations from an orbit 
exactly elliptical. Now Mr. Whewell has remarked that these suc- 
cessive general expressions, though apparently so conflicting, were all 
correct : they all answered the purpose of colligation : they all enabled 
the mind to represent to itself with facility, and by a simultaneous 
glance, the whole body of facts at that time ascertained; each in its 
turn served as a correct description of the phenomena, so far as the 
senses had up to that time taken cognizance of them. If a necessity 
afterwards arose for discarding one of these general descriptions of 
the planet's orbit, and framing a different imaginary line, by which to 
express, the series of observed positions, it was because a number of 
new facts had now been added, which it was necessary to combine 
with, the old facts into one general description..^ But this did not affect 
the correctness of the former expression, considered as a general state- 
ment of the only facts which it was intended to represent. And so 
tiTie is this, that, as is well remarked by M. Comte, these ancient gen- 
eralizations, even the rudest and most imperfect of them, that of uni- 
form movement in a circle, are so far from being entirely false, that 
they are even now habitually employed by astronomers when only a 
rough approximation to correctness is required. " L'astronomie mo- 
derne, en detruisant sans retour les hypotheses primitives, envisagees 
comme lois reelles du monde, a soigneusement maintenu leur valeur 
positive et permanente, la propriete de representor commodement les 
phenom^.nes quand il s'agit d'une premiere ebauche. Nos ressources 
a cet egard sont mem.e bien plus etendues, precisement a cause que 
nous ne nous faisons aucune illusion sur la realite des hypotheses ; ce 
qui nous permet d'employer sans scrupule, en chaque cas, celle que 
nous jugeons la plus avantageuse."* 

Mr. Wheweli's remark, therefore, is as just as it is interesting. Suc- 

* COMTB, Cours de Philosophie Positive, vol, il, p, 202. 



182 INDUCTION. 

cessive expressions for tlie colligation of observed facts, or, in other 
words, successive descriptions of a phenomenon as a whole, which has 
been ob.^erved only in parts, may, though conflicting, be all correct as 
far as they go. But it would surely be absurd to assert this of con- 
flicting inductions. 

The philosophic study of facts may be undertaken for three dif- 
ferent purposes : the simple description of the facts ; their explana- 
tion ; or their prediction : meaning by prediction, the determination 
of the conditions under which similar facts may be expected again to 
occur. To the first of these three operations the name of Induction 
does not properly belong : to the other two it does. Now, Mr. 
Whewell's observation is true of the first alone. Considered as a 
mere description, the circular theory of the heavenly motions repre- 
sents perfectly well their general features ; and by adding epicycles 
without limit, those motions, even as now known to us, might be 
expressed with any degree of accuracy that might be required. The 
only real advantage of the elliptical theory, as a meie description, 
would be its simplicity, and the consequent facility of conceiving it 
and reasoning about it : for it would not really be more true than the 
other. Different descriptions, therefore, may be all true : but not, 
•surely, different explanations. The doctrine that the heavenly bodies 
moved by a virtue inherent in their celestial nature ; the doctrine that 
they were moved by impact, (which led to the hypothesis of vortices 
as the only impelling force capable of whirling bodies in circles,) and 
the Newtonian doctrine, that they are moved by the composition of a 
centripetal with an original projectile force ; all these are explana- 
tions, collected by real induction from supposed parallel cases ; and 
they Were all successively received by philosophers, as scientific 
truths on the subject of the heavenly bodies. Can it be said of 
these, as we said of the different descriptions, that they are all true 
as far as they go 1 Is it not clear that one only can be true in any 
degree, and the other two must be altogether false 1 So much for 
explanations,: let. us now compare different predictions: the first, 
that eclipses will occur whenever one planet or satellite is so situated 
as to cast its shadow upon another ; the second, that they will occur 
whenever some great calamity is impending over mankind. Do 
these two doctrines only differ in the degree of their truth, as ex- 
pressing real facts with unequal degrees of accuracy ? Assuredly 
the one is true, and the other absolutely false. 

In every way, therefore, it is evident that when Mr. Whewell 
explains induction as the colligation of facts by means of appro- 
priate conceptions, that is, conceptions which will really express 
them, he confounds mere description of the observed facts with in- 
ference from those facts, and ascribes to the latter what is a char- 
acteristic property of the former. 

There is, however, between Colligation and Induction, a rea,! 
correlation, which it is important to conceive cori'ectly. Colligation 
is not always induction ; but induction is always colligation. The 
assertion that the plg,nets move in ellipses, was but a mode of rep- 
resenting observed facts ; it was but a colligation ; while the assertion 
that they are drawn, or tend, towards the sun, was the statement 
of a new fact, inferred by induction. But the induction, once made„ 
accomplishes the purposes of colligation likewise. It brings the sam@ 



GROUND OF INDUCTION. 183 

facts, wliicli Kepler had connected by his conception of an elHpse, 
under the additional conception of bodies acted upon by a central 
force, afid serves therefore as a new bond of connexion for those 
facts ; a new principle foi' their classification. 

Moreover, that general description, which is improperly confounded 
with induction, is nevertheless a necessary preparation for induction ; 
no less necessary than correct observation of the facts themselves. 
Without the previous colligation of detached observations by means 
'of one. general conception, we could never have obtained any basis for 
an induction, except in the case of phenomena of very limited compass. 
We should not be able to affirm any predicates at all, of a subject in- 
capable of being observed otherwise than piecemeal : much less could 
we extend those predicates by induction to other similar subjects. 
Induction, therefore, always presupposes, not only that the necessary 
observations are made with the necessary accuracy, but also that the 
results of these observations are, so far as practicable, connected 
'together by general descriptions, enabling the mind to represent to 
itself as wholes whatever "phenomena are capable of being so rep- 
resented. 

To suppose, however, that nothing more is required from the concep- 
tion than that it shall serve to connect the observations, would be to 
substitute hypothesis for theory and imagination for proof. The 
connecting link must be some character which really exists in the facts 
themselves, and which would manifest itself therein if the conditions 
could be realized which our organs of sense require. 

AVhat more may be usefully said on the subject of Colligation, or of 
the correlative expression invented by Mr. Whewell, the Explication 
of Conceptions, and generally on the subject of ideas and mental 
representations as connected with the study of facts, will find a more 
appropriate place in the Fourth Book, on the Operations Subsidiary 
to Induction : to which the reader must refer for the removal of any 
difficulty which the present discussion may have left. 



CHAPTER III. 

OP THE GROUND OF INDUCTION. 



§ 1. Induction properly so called, as distinguished from those mental 
operations, sometimes though improperly designated by the name, 
which I have attempted in the preceding chapter to characterize, may, 
then, be summarily defined as Generalization from Experience. It 
consists in infemng from some individual instances in which a phe- 
nomenon is observed to occur, that it occurs in all instances of a. 
certain class ; namely, in all which resemble the former, in what are 
regarded as the material circumstances. 

In what way the material circumstances are to be distinguished from 
those which are immaterial, or why some of the circumstances are, 
material and others not so, we are not yet ready to point out. We 
must first obsei've, that there is a principle implied in the very state- 
ment of w^hat Induction is ; an assumption wdth regard to the course 



184 INDUCTION. 

of nature and the order of the universe : namely, that there are such , 
things in nature as parallel cases ; that what happens once, will, under 
a sufhcient degi'ee of similarity of circumstances, happen again, and 
not only again, but always. This,, I say,, is an assumption, involved in 
every case of induction. And, if we consult the actual course of 
nature, we find that the assumption is warranted ; the fact is so. The 
.universe, we find, is so constituted, that whatever is tiTie in any one 
case, is true in all cases of a certain description ; the only difficulty is, 
to find wA(2^^ description. 

This universal fact, which is our warrant for all inference from expe- 
rience, has been described by different philosophers in different forms 
of language : that the" course of nature is uniform ; th,at the utiiverse is 
governed by general laws ; and the like. One of the most usual of 
these modes of expression, but also one of the most inadequate, is that 
which has been brought into familiar use by the inetaphysicians of the 
school of Reid and Stewart.- The disposition of the human mind to 
generalize from experience- — a^ propensity considered by these philo- 
sophers as an instinct of oiu: nature — they usually describe under the ' 
narbe of "our intuitive conviction that the future will resemble the 
past." Now it has been well pointed out by Mr. Bailey,* that (whether 
the tendency be or not an original and ultimate element of our nature),, 
Time, in its modifications of past, present, and future, has no concern 
either with the belief itself, or with the grounds of it. We believe' 
that fire will burn to-morrOw, because it. burned to-day and yesterday; 
but we believe, on precisely the same grounds, that it burned before 
we were born, and that it burns this very day in Cochin-China. .It is 
not from the past to the future, as past and fiiture, that we infer, but 
from the known to the unknown ; from facts observed to facts unob- 
served; from what we have perceived, or been directly conscious of, 
to what has not come within our experience. In this last predicament 
is the whole region of the fiiture; but also the vastly greater portion 
of the present and of the past. 

Whatever be the most proper mode of expressing it, the proposition 
that the course of nature is unifbrm, is the fiindamental principle, or 
general axiom, of Induction. It would yet be a great error to offer 
this large generalization as any explanation of the inductive process. 
On the contrary, I hold it to be itself an instance of induction, a<nd 
induction by no means of the most obvious kind. Far from being the 
first induction we make, it is one of the last, or at all events one of 
those which are latest in attaining strict philosophical accuracy. As 
a general maxim, indeed, it has scarcely entered into the minds of any 
but philosophers ; nor even by them, as we shall have many opportu- ' 
nities of remarking, have its extent and limits been always very justly 
conceived. Yet this principle, though so far from being our earliest 
induction, must be considered as our wan-ant for all the others, in this 
sense, that unless it were true, all other inductions would be fallacious.. 
And this, as we have already seen, is the sole mode in which the gene- 
ral propositions which we place at the head of our reasonings when 
we throw them into syllogisms, ever really contribute to their validity. 
Archbishop Whatcly has well remarked, that every induction is a 
syllogi*m with the major premiss suppressed ; or (as I prefer express" 

* Essays oti the Pursuit of Tnith. 



GROUND OF INDUCTION. 185 

mg it), that every induction may be thrown into the form of a syllo- 
gism, by supplying a major premiss. If this be actually done, the 
principle which we are now considering, that of the uniformity of the 
course of nature, will appear as the ultimate major premiss of all in- 
ductions ; and will, therefore, stand to all inductions in the relation in 
which, as has been shown at so much length, the major .proposition of 
a syllogism always stands tO the conclusion; not contributing at all to 
prove it, but being a necessary condition of its being proved ; since no 
conclusion is proved -for which there cannot be found a true major 
premiss.* '■ 

It was not to be expected that in the case of this axiom, aily more 
than of other axioms, there should be unanimity among philosophers 
with respect to the grounds upon which it is to be received as tru^. 
I have already stated that I regard it as itself a generalization from 
experience. Others hold it to be a principle .which, antecedently to 
any verification by experience, we are compelled by the constitution 
of our thinking faculty to assume as true. Having so recently, and. at 
so much length, combated a similar doctrine as applied to the axioms 
of mathematics, by arguments which are in a great measure applicable 
to the present case, I shall defer the more particular discussion of this 

* From the fact, that every induction may be expressed in the form of a syllogism, 
Archbishop Whatply concludes that Induction itself is but a peculiar case of ratiocination, 
and that the universal type of all Inference, or Reasoning, is the Syllogism. Our own 
inquiries have led us to a directly opposite result. Instead of resolving Induction into 
Ratiocination, it has appeared to us that Ratiocination is itself resolvable into Induction. 
The Archbishop's theory may, I think, be shown to be fallacious by following out his own 
train of thought. The induction, " John, Peter, Thomas, &c., are mortal, therefore all 
mankind are mortal," may, as he justly says, be thrown into a syllogism by prefixing as a 
major premiss (what is at any rate a necessary condition of the validity of the argument) 
namely, that whatever is true of John, Peter, Thomas, &c., is true of all mankind. So 
far the case is made out ; and Archbishop Whately (who, endowed with a penetrating and 
active rather than a patient and persevering intellect, seldom fails to cast his sounding line 
to a greater depth than his predecessors, and when he has done this, scarcely seems to 
care whether he reaches the bottom or not) omitted to ask himself the further question, 
How vye come by the major premiss? It is not self-evident ; nay, in all cases of unwarranted 
generalization, it is not true. How, then, is it arrived at ? Necessarily either by induction 
or ratiocination ; and if by induction, then, on the Archbishop's principles, it is by ratiocina- 
tion still, that is, by a previous syllogism. This previous syllogism it is, therefore, necessary 
to construct. There is, in the long run, only one possible construction : the real proof that 
whatever is true of John, Peter, &c., is true of all mankind, can only be, that a different 
supposition would be inconsistent with the uniformity which_ we know to exist in the 
course of nature. Whether there would be this inconsistency or not, may be a matter of 
long and delicate inquiry; but unless there would, we have no sufficient ground for the 
major of the inductive syllogism. It hence appears, that if we throw the whole course of 
any inductive argument into a series of syllogisms, we shall arrive by more or fewer steps 
at- an ultimate syllogism, which will have for its major premiss the principle, or axiom, of 
the uniformity of the course of nature. Having reached this point, we have the whole 
field of induction laid out in syllogisms, and every instance of inference from experience 
exhibited as the conclusion of ratiocination, except one ;.but that one, unhappily, includes 
all the rest. Whence came the universal major? What proves to us that nature is 
governed by general laws ? Where are the premisses of the syllogisna of vvdiich that is the 
conclusion? Here, at least, is a case of induction which cannot be resolved into syllogism. 

And undoubtedly it would be the ideal perfection of Inductive Philosophy if all other 
general truths could be exhibited as conclusions deduced from that widest generalization 
of all. But such a mode of presenting them, however useful in giving coherence and 
systematic unity to our thoughts, would be an inversion of the real order of proof This great 
generalization must itself have been founded on prior generahzations : the obscurer laws 
of nature were discovered by means of it, but the more obvious ones must have been 
understood and assented to as general truths before it was ever heard of. We should 
never have dared to affirm that all phenomena take place according to general laws, if we had 
not first arrived, in the case of a great mulcitude of phenomena, at some knowledge of the 
laws themselves ; which could be done no otherwise than by induction. Archbishop 
Whately's theory, therefore, implying, as it does, the consequence that we never could 
have had a single well-grounded induction unless we had already reached that highest 
generalization, must, I conceive, be regarded as untenable. 
A A 



186 INDUCTION. 

controverted pdint in regard to the fundamental axiom of induction, 
until a more advanced period of our inquiry.* , At present it is of 
more importance to understand thoroughly the import of the axiom 
itself For the proposition, that the course of nature is uniform, pos- 
sesses rather the brevity suitable to popular, than the precision requi- 
site in philosophical, language : its terms require to be explained, and 
a stricter than their ordinary signification given to them, before the 
truth of the assertion can be admitted. . 

§ 2. Every person's consciousness assures him that he does not al- 
ways expect uniformity in the course of events ; he does not always 
believe that the unknown will be similar to the known, that the fu- 
ture will resemble the past. Nobody believes that the succession of 
rain and fine weather will be the same in every future year as in the 
present. Nobody expects to have the same dreams repeated every 
night. On the contrary, everybody mentions it as something extraor- 
dinary, if the course of nature is constant, and resembles itself, in these 
particulars. To look for constancy where constancy is not to be ex- 
pected, as, for instance, that a day which has once brought good for- 
tune will always be a fortunate day, is justly accounted superstition. 

The course of nature, in truth, is not only uniform, it is also infi- 
nitely various. Some phenomena are always seen to recur in the very 
same combinations in which we met- with them at first; others seem 
altogether capricious ; while some, which we had been accustomed to 
regard as bound down exclusively to a particular set of combinations, 
we unexpectedly find detached from some of the elements with which 
we had hitherto found them conjoined, and united to others of quite 
a contrary description. To an inhabitant of Central Africa, fifty years 
ago, no fact probably appeared to rest upon more uniform experience 
than this, that all human beings are black. To Europeans, not many 
years ago, the proposition, All swans are white, appeared an equally 
unequivocal instance of uniformity in the course of nature. Further 
experience has proved to both that they were mistaken ; but they had 
to wait fifty centuries for this experience. During that long , time, 
mankind believed in an uniformity of the course of nature where no 
such uniformity really existed. 

According to the notion which the ancients entertained of induction, 
the foregoing were cases of as legitimate inference as any inductions 
whatever. In these two instances, in which, the conclusion being 
false, the ground of inference must have been insufficient, there was, 
nevertheless, as much ground for it as this conception of induction ad- 
mitted of. The induction of the ancients has been well described by 
Bacon, under the name of '' Inductio per enumerationem simplicem, 
ubi non reperitur instantia contradictoria." It consists in ascribing 
the character of general truths to all propositions which are true in 
every instance that we happen to know of This is the kind of induc- 
tion, if it deserves the name, which is natural to the mind when unac- 
customed to scientific methods. The tendency, which some call an 
instinct, and which others account for by association, to infqr the fu- 
ture from the past, the known from the unknown, is simply a habit of 
expecting that what has been found true once or several times, 

* Infra, chap, xxu 



GROUND OF INDUCTION. 187 

and never yet found false, will be found true again. Whether the 
instances are few or many, conclusive or inconclusive, does not much 
affect the matter : these are considerations which occur only on re- 
flection : the unprompted tendency of the mind is to generalize its ex- 
perience, provided this points all in one direction ; provided no other 
experience of a conflicting character comes unsought. The notion of 
seeking it, of experimenting for it, of interrogating nature (to use 
Bacon's expression), is of much later growth. The observation of nature, 
by uncultivated intellects is purely passive : they take the facts which 
present themselves, without taking the trouble of searching for more : 
it is a superior mind only which asks itself what facts are needed to 
enable it to come tO a sute conclusion, and then looks out for these. 

But although we have always a propensity to generalize from un- 
varying experience, we are not always warranted in doing so. Be-, 
fore we can be at liberty to conclude that something is universally true 
because we have never known an instance to the contrary, it must be 
proved to us that if there were in nature any instances to the contrary, 
we should have known of them. This assurance, in the great majority 
of cases, we cannot have, or can have only in a very moderate degree. 
The possibility of having it, is the foundation on which we shall see 
hereafter that induction by simple enumeration may in some remark- 
able cases amount to full proof* No such assurance, however, can 
be had, on any of the ordinary subjects of scientific inquiry. Popular 
notions are usually founded upon induction by simple enumeration ; 
in science it carries us but a little way. We are forced to begin with 
it ; we' must often rely upOn it provisionally, in the absence of means 
of more searching investigation. But, for the accurate study of nature^ 
we require a surer and a more potent instrument. 

It was, above all, by pointing out the insufficiency of this rude and 
loose conception of Induction, that Bacon merited the title so generally 
awarded to him, of Founder of the Inductive Philosophy. The value 
of his own contributions to a more philosophical theory of the subject 
has certainly been exaggerated. Although (along with some funda- 
mental errors) his writings contain, more or less fully developed, 
several of the most important principles of the Inductive Method^ 
physical investigation has now far outgrown the Baconian conception 
of Induction, Moral and political inquiry, indeed, are as yet far 
behind that conception. The current and approved modes of reason- 
ing on these subjects are still of the same vicious description against 
which Bacon protested : the method almost exclusively employed by 
those professing to treat such matters inductively, is the very inductio 
per enumerationem simplicem which he condemns ; and the experience, 
which we hear so confidently appealed to by all sects, parties, and in- 
terests, is still, in his own emphatic words, mera palpatio. 

§ 3. In order to a better understanding of the problem which the 
logician must solve if lie would establish a scientific theory of Induc- 
tion, let us compare a few cases of incorrect inductions with others 
which are acknowledged to be legitimate. Some, we know, which 
were believed for centuries to be correct, were nevertheless incorrect. 
That all swa,ns are white, cannot have been a good induction, since 

* Infra, chap, xxi= xsii. 



188 INDUCTION. 

the conclusion has turned out erroneous. The experience, however, 
on which the conclusion rested was genuine. From the earliest 
records, the testimony of all the inhabitants of the known world was 
unanimous on the point. The uniform experience, therefore, of the in- 
habitants of the known world, agreeing in a common result, without 
one known instance of deviation from that result, is not always suffi- 
cient to establish a general conclusion. 

But let us now turn to an instance apparently not very dissimilar to 
this. Mankind were wrong, it seems, in concluding that all swans 
were whife : are we also wrong, when we conclude that all men's 
heads grow above their shoulders, and never below, in spite of the 
conflicting testimony of the naturalist Pliny ] As there w^ere black 
swans, although civilized men had existed for three thousand years on 
the earth without meeting with them, may there not also be " men 
whose heads do grow beneath their shoulders," notwithstanding a 
rather less perfect unanimity of negative testimony from all observers 1 
Most persons would answer No ; it was more credible that a bird 
should vary in its color, than that man should vary in the relative posi- 
tion of his principal organs. And there is no doubt that in so saying 
they would be right : but to say why they are right, would be impos- 
sible, without entering, more deeply than is usually done, into the true 
theory of Induction. 

Again, there are cases in which we reckon with the most unfailing 
confidence upon uniformity, and other cases in which we do not count 
upon it at all. In some, we feel complete assurance that the future will 
resemble the past, the unknown be precisely similar to the known. In 
others, however invariable may be the result obtained from the in- 
stances which we have observed, we draw from them no more than a 
very feeble presumption that the like result will hold in all other cases. 
That a straight line is the shortest distance between two points, we do 
not doubt to be true even in the region of the fixed stars. When a chem- 
ist announces the existence and properties of a newly-discovered sub- 
stance, if we 'confide in his accuracy, we feel assured that the conclusions 
he has arrived at will hold universally, although the induction be founded 
but on a single instance. We do not withhold our assent, waiting for 
a repetition of the experiment ; or if we do, it is from a doubt whether 
the one experiment was properly made, not whether if properly made 
it would be conclusive. Here then, is a general law of nature, in- 
ferred without hesitation from a single instance ; an universal propo- 
sition from a singular one. Now mark another case, and contrast it 
with this. Not all the instances which have been observed since the 
beginning of the world, in support of the general proposition that all 
crows are black, would be deemed a sufficient presumption of the 
truth of the proposition, to outweigh the testimony of one unexcep- 
tionable witness who should affirm that in some region of the earth 
not fully explored, he had caught and examined a crow, and had found 
it to be gray. 

Why is a single instance, in some cases, sufficient for a complete in- 
duction, while in others, myriads of concurring instances, without a 
single exception known or presumed, go such a very little way towards 
establishing an universal proposition '? Whoever can answer this ques- 
tion knows more of the philosophy of logic than the wisest of the an- 
cients, and has solved the great problem of induction. 



LAW OF CAUSATION. 195 

exception to them ; and philosophers have been led, although (as I 
have endeavored to show^) erroneously, to consider their evidence as 
lying not in experience, but in the original constitution of the human 
intellect. If, therefore, from the laws of space and number, we were 
able to deduce uniformities of any other description, this would be 
conclusive evidence to us that those other uniformities possessed the 
same degi'ee of rigorous certainty. But this we cannot do. From 
laws of space and number alone, nothing can be deduced but laws of 
space and number. 

Of all truths relating -to phenomena, the most valuable to us are 
those which relate to the order of their succession. On a knowledge 
of these is founded every reasonable anticipation of future facts, and 
whatever power we possess of influencing those facts to our advantage. 
Even the laws of geometry are chiefly of j^ractical importance to us as 
being a portion of the premisses from which the order of the succession 
of phenomena may be inferred, 

•Inasmuch as the motion of bodies, the action of forces, and the 
propagation of influences of all sorts, take place in certain lines and 
over definite spaces, the properties of those lines and spaces are an 
important part of the laws to which those phenomena are themselves 
subject. Moreover, motions, forces, or other influences, and times, are 
numerable quantities ; and the properties of number are applicable to 
them as to all other things. But although the laws of number and 
space are important elements in the ascertainment of uniformities of 
succession, they ca^n do nothing towards it when taken by themselves. 
They can only be made instrumental to that purpose when we combine 
with them additional premisses, expressive of uniformities of succession 
already known. By taking, for instance, as premisses, these proposi- 
tions : that bodies acted upon by an instantaneous force move with 
uniform velocity in straight lines ; that bodies acted upon by a con- 
tinuous force move -ti^ith accelerated velocity in straight lines ; and 
that bodies acted upon by two forces in different directions move in 
the diagonal of a parallelogram, whose sides represent the direction 
and quantity of those forces ; we may by combining these truths with 
propositions relating to the properties of straight lines and of parallelo- 
gi'ams, (as that a triangle is half of a parallelogram of the same base 
and altitude,) deduce another important uniformity of succession, viz., 
that a body moving round a centre of force describes areas propor- 
tional to the times. But unless there had been laws of succession in 
our premisses, there could have been no truths of succession in our 
conclusions. A similar remark might be extended to every other class 
of phenomena really peculiar ; and, had it been attended to, would 
have prevented many chimerical attempts at demonstrations of the 
indemonstrable, and explanations of what cannot be explained. 

It is not, therefore, enough for us that the laws of space, which are 
only laws of simultaneous phenomena, and the laws of number, which 
though true of successive phenomena do not relate to their succession, 
possess that rigorous certainty and universality of which we are in 
search. We must endeavor to find some law of succession which has 
those same attributes, and is therefore fit to be made the foundation of 
processes for discovering, and of a test for verifying, all other uniformi- 
ties of succession. This fundamental law must resemble the truths of 
geometry in their most remarkable peculiarity, that of never being, in 



196 INDUCTION. 

any instance whatever, defeated or suspended by any change of cir- 
cumstances. 

Now among all those uniformities in the succession of phenomena, 
which common observation is sufficient to bring to light, there are very 
few which have any, even apparent, pretension to this rigorous inde- 
feasibility : and of those few, one only has been found capable of com- 
pletely sustaining it. In that one, however, we recognize a law which 
is universal also in another sense ; it is coextensive with the entire 
field of successive phenomena, all instances whatever of succession 
being examples of it. This law is the Law of Causation. It is an 
universal truth that every fact which has a beginning has a cause. 

This generalization may appear to some minds not to amount to 
much, since after all it asserts only this : " it is a law, that every event 
depends upon some law." We must not, however, conclude that the 
generality of the principle is merely verbal ; it will be found upon 
inspection to be no vague or unmeaning assertion, but a "most import- 
ant and really fundamental truth. 

§ 2. The notion of Cause being the root of the whole theory of Induc- 
tion, it is indispensable that this idea should, at the very outset of Our 
inquiry, be, with the utmost practicable degree of precision, fixed and 
determined. If, indeed, it were necessary for the purposes of induc- 
tive logic that the strife should be quelled, which has so long raged 
among the different schools of metaphysicians, respecting the origin 
and analysis of our idea of causation ; the promulgation, or at least 
the general reception, of a true theory of induction, might be con- 
sidered desperate, for a long time to come. But in this as in most 
other respects, the science of the Investigation of Truth by means of 
Evidence, has no need to borrow any premisses from the science of 
the ultimate constitution of the human mind, except such as have at 
last, though often after long controversy, been incorporated into all the 
existing systems of mental philosophy, or all but such as may be re- 
garded as essentially effete. 

I premise, then, that when in the course of this inquiry I speak of 
the cause of any phenomenon, I do not mean a cause which is not 
itself a phenomenon ; I make no research into the ultimate, or ontolo- 
gical cause of anything. To adopt a distinction familiar in the wri- 
tings of the Scotch metaphysicians, and especially of Reid, the causes 
with which I concern myself are not efficient, but physical causes. 
They are causes in that sense alone, in which one physical fact may be 
said to be the cause of another. Of the efficient causes of phenomena, 
or whether any such causes exist at all, I am not called upon to give 
an opinion. The notion of causation is deemed, by the schools of 
metaphysics most in vogue at the present moment, to imply a myste- 
rious and most powerful tie, such as cannot, or at least does not, exist 
between any physical fact and that other physical fact upon which it is 
invariably consequent, and which is popularly termed its cause : and 
thence is deduced the supposed necessity of ascending higher, into the 
essences and inherent constitution of things, to find the true cause, the 
cause which is not only followed by, but actually produces, the effect. 
No such necessity exists for the purposes of the present inquiry, nor 
will any such doctrine be found in the following pages. But neither 
will there be found anything incompatible with it. We are in no way 



LAW OF CAUSATION. 197 

concerned in tlie question. The only notion of a cause, which the 
theory of induction requires, is such a notion as can be gained from 
experience. The Law of Causation, the recognition of which is the 
main pillar of inductive philosophy, is but the familiar truth, that inva- 
riability of succession is found by observation to obtain between every 
fs^ct in nature and some other fact which has preceded it ; independ- 
ently of all consideration respecting tl^e ultimate mode of production 
of phenomena, and of every other question regarding the nature of 
*' Things in themselves." 

Between the phenoipena, then, which exist at any instant, and the 
phenomena which exist at the succeeding instant, there is an invariable 
order of succession ; and, as we said in speaking of the general uni- 
formity of the course of nature, this web is composed of separate fibres^ 
this collective order is made up of particular sequences, obtaining inva- 
riably among the separate parts. To certain facts, certain facts always 
do, and, as we believe, always will, succeed. The invariable antece- 
dent is termed the cause ; the invariable consequent, the effect. And 
the universality of the law of causation consists in this, that every con- 
sequent is connected in this manner with some particular antecedent, 
or set of antecedents. Let the fact be what it may, if it has begun to 
exist, it was preceded by some fact or facts, with which it is invaria- 
bly connected. For every event, there exists some combination of 
objects or events, some given concurrence of circumstances, positive 
and negative, the occurrence of which wuU always be followed by that 
phenomenon. We -may not have found out what this concurrence of 
circumstances may be ; but we never doubt that there is such a one, 
and that it never occurs without having the phenomenon in question 
as its effect or consequence. Upon the universality of this truth de- 
pends the possibility of reducing the inductive process to rules. The 
undoubted assurance we have that there is a law to be found if we only 
knew how to find it, will be seen presently to be the source from which 
the canons of the Inductive Logic derive their validity. 

§ 3. It is seldom, if ever, between a consequent and one single an- 
tecedent, that this invariable sequence subsists. It is usually between 
a consequent and the sum of several antecedents ; the concurrence of 
them all being requisite to produce, that is, to be certain of being fol- 
lowed by, the consequent. In such cases it is very common to single 
out one only of the antecedents under the denomination of Cause, call- 
ing the others merely Conditions. Thus if a man eats of a particular 
dish, and dies in consequence, that is, would not have died if he had 
not eaten of it, people would be apt to say that eating of that dish 
was the cause of his death. There needs not, however, be any inva- 
riable connexion between eating of the dish and death ; but there 
certainly is, among the circumstances 'which took place, some combi- 
nation or other upon which death is invariably consequent : as, for 
instancOj the act of eating of the dish, combined with a particular bodily 
constitution, a particular state of present health, and perhaps even a 
certain state of the atmosphere ; the whole of which circumstances 
perhaps constituted in this particular case the conditions of the phenora= 
enon, or in other words the set of antecedents which determined it, 
and but for wbich it would not have happened. The real Cause, is 
the whole of these antecedents; and we have, philosophically speak- 



198 INDUCTION. 

ing, no right to give tlie name of cause to one of them, exclusively of 
the others. AVhat, in the case we have supposed, disguises the incor- 
rectness of the expression, is this : that the various conditions, except 
the single one of eating the food, v^ere not events (that is, instantaneous 
chanfyes, or successions of instantaneous changes) but *to?'e5, possessing 
more or less of permanency ; and might therefore have preceded the 
effect by an indefinite length of duration, for v^ant of the event which 
was requisite to complete the required concurrence of conditions : 
while as soon as that event, eating the food, occurs, no other cause is 
waited for, but the effect begins immediately to take place: and, hence „ 
the 'appearance is presented of a more immediate and closer connexion 
between the effect and that one antecedent, than between the effect 
and the remaining conditions. But although we may think proper to 
give the name of cause to that one condition, the fulfilment of which 
completes the tale, and brings about the effect without further delay ; 
this condition has realfy no closer relation to the effect than any of the 
other conditions has. The production of the consequent required 
that they should all ea:^^ immediately previous, though not that they 
should all begin to exist immediately previous. The statement of the 
cause is incomplete, unless in some shape or other we introduce all 
the conditions. A man takes mercury, goes out of doors, and catches- 
cold. We say, perhaps, that the cause of his taking cold was ex- 
posure to the air. It is clear, however, that his having taken mercury 
may have been a necessary condition of his catching cold; and though 
it might consist with usage to say that the cause of his attack was ex- 
posure to the air, to be accurate we ought to say that the cause w^as 
exposure to the air while under the effect of mercury. 

If we do not, when aiming at accuracy, enumerate all the condi- 
tions, it is only because some of them will in most cases be under- 
stood wdthout being expressed, or because for the purpose in view 
they may without detriment be overlooked. For example, when we 
say, the cause of a man's death was that hie foot slipped in climbing a 
ladder, we omit as a thing unnecessary to be stated the circumstance 
of his weight, though quite as indispensable a condition of the effect 
which took place. When we say that the assent of the crown to a 
bill makes it law, we mean that the assent, being never given until all 
the other conditions are fulfilled, makes up the sum of the conditions, 
although no one now regards it as the principal one. When the deci- 
sion of a legislative assembly has been determined by the casting vote 
of the chairman, we often say that this one person was the cause of all 
the effects which resulted from the enactment. Yet we do not really 
suppose that his single vote contributed more to the result than that 
of any other person who voted in the affirmative ; but, for the purpose 
we have in view, which is that of fixing him with the responsibility, the 
share which any other j)erson took in the transaction is not material. 

In all these instances the fact which was dignified by the name of 
cause, was the one condition which came last into existence. But it 
must not be supposed that in the employment of the term this or any 
other rule is always adhered to. Nothing can better show the absence 
of any scientific ground for the distinction between the cause of a jihe- 
nomenon and its conditions, than the capricious manner in which we 
select from among the conditions that which we choose to denominate 
the cause. However numerous the conditions may be, there is hardly 



LAW OF CAUSATION. 199 

any of them which may not, according to the purpose of our immediate 
discourse, obtain that nomhial preeminence. This will be seen by 
analyzing the conditions of some one familiar phenomenon. For 
example, a stone thrown into water falls to the bottom. What are the 
conditions of this event 1, In the first place there ^ust be a stone, and 
water, and the stone must be thrown into the water ; but, these suppo- 
sitions forming part of the enunciation of the phenomenon itself, to 
include them also among the conditions would be a vicious tautology, 
and this class of conditions, therefore, have never received the name of 
cause from any j^i^t the schoolmen; by whom they were called the ma- 
terial cause, causa mater lalis. The next condition is, there must be 
an earth : and accordingly it is . often said, that the' fall of a stone is 
caused by the earth; or by a po,wer or property of the earth, or a- force 
exerted by the earth, all of which are merely roundabout ways of say- 
ing that it is caused by the earth ; or, lastly, the earth's attraction; which 
also is only a technical rhode of saying that the earth causes the motion, 
with the additional particularity that the motion is toivards the earth, 
which is not a character of the cause, but of the effect. Let us now 
pass to another condition. It is not enough that the earth should exist; 
the body must be within that distance from it, in which the earth's 
attraction preponderates over that of any other body. Accordingly we 
may say, and the expression would be confessedly correct, that the 
cause of the stone's falling is its being within the siihe^'e of the earth's 
attraction. We proceed to a further condition. The stone is immersed 
in water : it is therefore a condition of its reaching the ground, that its 
specific gravity exceed that, of the surrounding fluid, or in other words 
that it surpass in weight an equal volume of water. Accordingly, any 
one would be acknowledged to speak correctly who said, that the cause 
of the stone's going to the bottom is its exceeding in sjDecific gravity 
the fluid in which it is immersed. 

Thus we. see that each and every condition of the- phenomenon may 
be taken in its turn, and with equal propriety in common parlance, but 
with equal impropriety in. scientific discourse may be spoken of as if 
it were the entire cause. And in practice that particular condition is 
usually styled the Cause, whose share in the matter is superficially the 
most conspicuous, or whose requisiteness to the production of the effect 
we happea to be insisting upon at the moment. So great is the force 
of this last consideration, that it often induces us to give the name of 
cause- even to one of the negative conditions. We say, for example, 
The cause of the army's being surprised was the sentinel's being off 
his post. But since the sentinel's absence was not what created the 
enemy, or made the soldiers to be asleep, how did it cause them to be 
surprised ? All that is really meant is, that the event would not have 
happened if he had been at his duty. His being off his post was no 
producing cause, but the mere absence of a preventing cause : it was 
simply equivalent to his non-existence. From nothing, from a mere 
negation, no consequences can proceed. All effects are connected, by 
the law of causation, with some set ^i positive conditions ; negative ones, 
it is true, being almost always required in addition. In other words" 
every fact or phenomenon which has a beginning, invariably arises' 
when some certain combination of positive facts exists, provided cer- 
tain other positive facts do not exist. 

Since, then, mankind are accustomed, with acknowledged propriety 



200 INDUCTION. 

SO far as the ordinances of language are concerned, to give the name 
of cause to almost any one of the conditions of a phenomenon, or any 
portion of the whole number, arbitrarily selected, without excepting 
even those conditions which are purely negative, and in themselves 
incapable of causing anything ; it will probably be admitted without 
longer .discussion, that no one of the conditions has more claim to that 
title than another, and that the real cause of the phenomenon is the as- 
semblage of all its conditions. There is, no doubt, a tendency (which 
our first example, that of death from taking a particular food, suffi- 
ciently illustrates) to associate the idea of causation with the proximate 
antecedent evenly rather than with any of the antecedent states, ox 
permanent facts, which may happen also to be conditions of the phe- 
nomenon ; the reason being that the event not only exists, but begins' 
to exist immediately previous : while the other conditions may have 
preexisted for an indefinite time. And this tendency shows itself very 
visibly in the different logical fictions which are resorted to even by' 
philosophers, to avoid the necessity of giving the name of cause to 
anything which had existed for an indeterminate length of time before 
the effect. Thus, rather than say that the earth causes the fail of 
bodies, they ascribe it to 2. force exerted by the earth, or an attraction 
by the earth, abstractions which they can represent to themselves a^ 
exhausted by each effort, and therefore constituting at each successive . 
instant a fi'esh act, simultaneous with, or only immediately preceding, 
the effect. Inasmuch as the coming of the circumstance which com- 
pletes the assemblage of conditions, is a change or event, it thence 
happens that an event is always the antecedent in closest apparent 
proximity to the consequent : and this may account for the illusion 
which disposes lis to look upon the proximate event as standing more 
peculiaily in the position of a cause than any of the antecedent states. 
But even this peculiarity of being in closer proximity to the effect 
than any other of its conditions, is, as we have already seen, far 
from being necessary to the common notion of a cause ; with which 
notion, on the contrary, any one of the conditions, either positive or 
negative, is found, upon occasion, completely to accord. 

The cause, then, philosophically speaking, is the sum total of the con- 
ditions, positive and negative, taken together; the whole of the contin- 
gencies of every description, which being realized, the consequent 
invariably follows. The negative conditions, however, of any phenom- 
enon, a special enumeration of which would generally be very prolix, 
may l)e all summed up under one head, namely, the absence of pre- 
venting or counteracting causes. The convenience of this mode of 
expressioti is grounded mainly upon the fact, that the effects of any 
cause in counteracting another cause may in most cases be, with strict 
scientific exactness, regarded as a mere extension of its own proper and 
separate effects. If gravity retards the upward motion of a projectile, 
and deflects it into a parabolic trajectory, it produces, in so doing, the, 
very same kind of effect, and even (as mathematicians know) the same 
quantity of effect, as it does in its ordinary operation of causing the 
fall of bodies when simply deprived of their support. If an alkaline 
solution mixed with an acid destroys its sourness, and prevents it from 
reddening vegetable blues, it is because the specific effect of the alkali 
is to combine with the acid, and form a compound with totally different 
qualities. This property, which causes of aU descriptions possess, of 



LAW OF CAUSATION.^ 201 

preventing the effects of other causes by virtue (for the most part) of 
the same laws, according to which they produce their own,* enables 
us, by establishing the general axiom that all causes are liable to be 
counteracted in their effects by one another', to dispense with the con- 
sideration of negative conditions entirely, and limit the notion of cause 
to the assemblage of the positive conditions of tho phenomenon : one 
negative condition invariably understood, and the same in all instances 
(namely, the absence of all counteracting causes) being sufficient, along 
\^ith the sum of the positive conditions, to make up the whole set of 
circumstances upon which the phenomenon is dependent. 

§ 4. Among the positive conditions, as we have seen that there are 
some to which, in common parlance, the terai cause is more readily 
and frequently awarded, so there are others to which it is, in ordinary 
circumstances, refused. In most cases of causation a distinction is 
commonly drawn between something which acts, and some other thing 
which is acted upon, between an agent and a patient. Both of these, 
it would be universally allowed, are conditions of the phenomenon ; 
but it would be thought absurd to call the latter the cause, that title 
being reserved for the former. The distinction, however, vanishes on 
examination, or rather is found to be only verbal ; arising from an in- 
cident of mere expression, namely, that the object said to be acted upon, 
and which is considered as the scene in whiclr the effect takes place, is 
commonly included in the phrase by which the effect is spoken of, so 
that if it were also reckoned as part of the cause, the seeming incon- 
gruity would arise of its being supposed to cause itself. In the in- 
stance which we have already had, of falling bodies, the question was 
thus put :— What is the cause which makes a stone fall 1 and if the 
answer had been "the stone itself," the expression vs^ould have been 
in apparent contradiction to the meaning of the word cause. The 
stone, therefore, is conceived as the patient, and the earth (or, accord- 
ing to the common and most unphilosophical practice, some occult 
quality, of the earth) is represented as the agent, or cause. . But that 
there is nothing fundamental in the distinction may be seen from this, 
^at if we do but alter the mere wording of the question, and express 
it thus, What is the cause which produces vertical motion towards the 
earth ] we might now, without any incongi'uity, speak of the stone or 
other heavy body as the agent, which, by virtue of its own laws or 
properties, commences moving towards the earth; although to save the 
established doctrine of the inactivity of matter, men usually prefer here 
also to ascribe the effect to an occult quality, and say that the cause is 
not the stone itself, but the weight or gravitation of the stone. 

* There are a few exceptions ; for there are some properties of objects which seem to be 
purely preventive ; as the property of opaque bodies, by which they intercept the passage 
of hght. Ttiis, so far as we are able to understand it, appears an instance not of one cause 
^counteracting another by the same law whereby it produces its own effects, but of an 
agency which manifests itself in no other way than m defeating the effects of another 
agency. If we knew upon vvnat other relations to light, or upon what peculiarities of 
structure opacity depends, we might find that this is only an apparent, not a real, excep- 
tion to the general proposition in the text. In any case it needs not affect the practical 
application. The formula which includes all the negative conditions of an effect in the 
single one of the absence of counteracting causes, is not violated by such cases as this ; 
although, if all counteracting agencies were of this description, there would be no pur- 
pose served by employing the formula, since we should still have to enumerate specially 
the negative conditions of each phenomenon, instead of regarding them as implicitly con- 
tained in the positive laws of the various other agencies in nature. 

Cc 



202 ■ . INDUCTION. 

Those who have contended for a radical -distinGtion between agent 
and patient, have generally conceived the agent as that which causes 
some state of, or some change in the state of, another object which is 
called the patient. But a little reflection will show that the license 
we assume of speaking of phenomena as states of the various objects 
which take part in them, (an artifice of which so much use has been 
made by some philosophers. Brown in particular, for the apparent 
explanation of phenomena,) is simply a sort of logical fiction, useful 
sometimes as one among several modes of expression, but which 
should never be supposed to be the. statement of a philosophical truth. 
Even those of the attributes of an object which might seem with 
greatest propriety to be called states of the object itself, its sensible 
qualities, its color, hardness, shape, and the like, are, in reality, (as no 
one has pointed out more clearly than Brown himself,) phenomena of 
causation, in which the substance is distinctly the agent, or producing 
cause, the patient being pur own organs, and those of other sentient 
beings. What we call the states of objects, are always sequences into 
which those objects enter, generally as antecedents or causes; and 
things are neVer more active than in the production of those phenomena 
in which they are said to be acted upon. Thus, in the last example, 
that of a sensation produced in our organs, are not the laws of our 
organization, and even those of our minds, as directly operative in 
determining the effect produced, as the laws of the outward object ? 
Though we call prussic acid the agent of a man's death, are not the 
whole of the vital and organic properties of the patient as actively 
instrumental as the poison, in the chain of effects which so rapidly 
terminates his sentient existence? In the process of education, we 
may call the teacher the agent, and the scholar only the material acted 
upon; yet in truth all the facts which preexisted in the scholar's mind 
exert either cooperating or counteracting agencies in relation to the 
teacher's efforts. It is not light alone which is the agent in vision, but 
light coupled with the active properties of the eye and brain, and with 
those of the visible object. The distinction between agent and patient 
is merely verbal : patients are always agents ; in a great proportion, 
indeed, of all natural phenomena, they are so to such a degree as 
to react most forcibly ^up on the causes which acted upon them: and 
even when this is not the case, they contribute, in the same manner as 
any of the other conditions, to the production of the effect of which 
they are vulgarly treated as the mere theatre. All the positive con- 
ditions of a phenomenon are alike agents, alike active ; and in any 
expression of the cause which professes to be a complete one, none of 
them can with reason be excluded, except such as have already been 
implied in the words used for describing the effect; nor by including 
even these would there be incurred any but a merely verbal incon- 
sistency. 

§ 5. It now remains to advert to a distinction which is of first-rate 
importance both for clearing up the notion of cause, and for obviating 
a very specious objection often made against the view which we have 
taken of the subject. 

When we define the cause of anything (in the only sense in which 
the present inquiry has any concern with causes) ,to be " the antecedent 
which it invariably follows," we do not use thit phrase as exactly 



LAW OF CAUSATION. 203 

synonymous with " the antecedent which it invariably lias followed in 
our past experience." Such a mode of viewing causation would be 
liable to the objection very plausibly urged by Dr. Reid, namely, that 
according to this doctrine night must be the- cause, of day, and day the 
cause of night; since these phenomena have invariably succeeded one 
another from the beginning of the world. But it is necessary to our 
using the word cause, that we should believe not only that the ante- 
cedent always has been followed by the consequent, but that, as long 
as the present constitution of things endures, it always vnll be so. And 
this would not be true of day and night. We do not believe tliat night' 
will be followed by day under any imaginable circumstances, but only 
that it will-be ^o,prov.ided the sun rises above the horizon. If the sun 
ceased to rise, which, for aught we know, may be perfectly compatible 
with the general laws of matter, night would be, or might be, eternal. 
On the other hand, if the sun is above the horizon, his light not extinct, 
and no opaque body between us and him, we believe firmly that unless 
a change takes place in the properties of matter, this combination of 
antecedents will be followed by the consequent, day ; that if the com- 
bination of antecedents could be indefinitely prolonged, it would be 
always day ; and that if the same combination had always existed, it 
would always have been day, quite independently of night as a previous 
condition. Therefore is it that we do not call night the cause, nor even 
a condition of day. The existence of the sun (or some such luminous 
body), and there being no opaque medium in a straight line*" between 
that body and the part of the earth where we are situated, are the sole 
conditions ; and the union of these, without the additioli of any super- 
fluous circumstance, constitutes the cause. This is what writers mean 
when they say that the notion of cause involves the idea of necessity, 
If there be any meaning which confessedly belongs to the term neces- 
sity, it is unconditionalness. That which is necessary, that v/hicli must 
be, means that which will be, whatever supposition we may make in 
regard to all other things. The succession of day and night evidently 
is not necessary in this sense. It is conditional upon the occurrence of 
other antecedents. That which will be followed by a given consequent 
when, and only when, some third circumstance also exists, is not the 
cause, even although no case should have ever occurred in which the 
phenomenon took place without it. 

Invariable sequence, therefore, is not synonymous with causation, 
unless the sequence, besides being invariable, is unconditional. There 
are sequences as uniform in past experience as any others whatever, 
which yet we do not regard as cases of causation, but as conjunctions, 
in some sort accidental. Such, to a philosopher, is that of day and 
night. The one might have existed for any length of time, and the 
other not have followed the sooner for its existence ; it follows only if 
certain other antecedents exist; and where those antecedents existed, 
it would follow in any case. No one, probably, ever called night the 
cause of day ; mankind must so soon have arrived at the very obvious 
generalization, that the state of general illumination which we call day 

* I use the words " straight line" for brevity and simplicity. In reality the'line in ques- 
tion is not exactly straight, for, from the effects of refraction, we actually see the sun for a 
short interval during which the opaque mass of the earth is interposed in a direct line be- 
tween the sun and our eyes ; thus realizing, though but to a limited extent, the coveted 
desideratum of seeing round a corner. 



204 - INDUCTION. 

would follow the presence of a sufficiently luminous body, whether 
darkness had preceded or not. 

' We may define, therefore, the cause of a phenomenon to be the an- 
' decedent, or the concurrence of antecedents, upon which it is invariably 
and unconditionally consequent. Or if we adopt the convenient modi- 
fication of the meaning of the word cause, which confines it to the as- 
semblage of positive conditions, without the negative, then instead of 
"unconditionally," we must say, "subject to no other than negative 
conditions." 

It is evident, that from a limited number of unconditional. sequences, 
there will result a much greater number of conditional ones. Certain 
causes being given, that is, certain antecedents which are uncondition- 
ally followed by certain consequents ; the mere coexistence of these 
causes will give rise to an unlimited number of additional uniformities. 
If two causes exist together, the effects of both will exist together ; 
and if many causes coexist, these causes (by what we shall term here^ 
after, the intermixture of their laws) will give rise to new effects, 
accompanying or succeeding one another in some particular order, 
which order will be invariable while the causes continue to coexist, but 
no longer. The motion of the earth in a given orbit round the sun is 
a series of changes which follow one another as antecedents and con- 
sequents, and will continue to dp so while the sun's attraction, and the 
force with which the earth tends to advance in a direct line through 
space, continue to coexist in the same quantities as at present. But 
vary either of these causes, and the unvarying succession of motions 
would cease to take place. The series of the earth's motions, there- 
fore, though a case of sequence invariable within the limits of human 
experience, is not a case of causation. It is not unconditional. 

To distinguish these conditionally uniform sequences from those 
which are uniform unconditionally ; to ascertain whether an apparently 
invariable antecedent of some consequent is really one of its conditions, 
or whether, in the absence of that antecedent, the effect would equally, 
have followed from some other portion of the circumstances which are 
present whenever it occurs ; is a principal part of the great problem 
of Induction ; and is one of those questions, the principles of the solu- 
tion of which will, it is to be hoped, result from the inquiry we have 
undertaken. 

§ 6. Does a cause always stand with its effect in the relation of an- 
tecedent and consequent] Do we not often say of two simultaneous 
facts that they are cause and effect — as when we say that fire is the 
cause of warmth, the sun and moisture the cause of vegetation, and the 
like % It is certain that a cause does not necessarily perish because 
its effect has been produced ; the two, therefore, do very generally 
coexist ; and there are some appearances, and some common expres- 
sions, seeming to imply not only that causes may, but that they must, 
be Contemporaneous with their effects. Cessante causd, cessat et effec- 
tus^ has been a dogma of the schools : the necessity for the continued 
existence of the cause in order to the continuance of the effect, seems 
to have been once a general doctrine among philosophers. Mr. Whe- 
wcU observes that Kepler's numerous attempts to account for the 
motion of the heavenly bodies on mechanical principles, were rendered 
abortive by his always supposing that the force which set those bodies 



LAW OF CAUSATION. 205 

in motion must continue to operate in order to keep up the motion 
which it at first produced. Yet there were at all times many familiar 
instances in open contradiction to this supposed axiom. A coup de 
soleil gives a man a brain fever : will the fever go off as soon as he is 
moved out of the sunshine 1 A sword is run through his body : must 
the sword remain in his body in order that he may continue dead 1 
A ploughshare once made, remains a ploughshare, without any contin- 
uance of heating and hammering, and even after the man who heated 
and hammered it has been gathered to his fathers. On the other hand, 
the pressure which forces up the mercury in an exhausted tube must 
be continued in order to sustain it in the tube. This (it may be 
replied,) is because another force is acting without intermission, the 
force of gravity, which would restore it to its level, unless counter- 
poised by a force equally constant. _ But again ; a tight bandage 
causes pain, which pain will sometimes go, off as soon as the bandage 
is removed. The illumination which the sun diffuses over the earth 
ceases when the sun goes down. 

The solution of these difficulties will be found in a very simple dis- 
tinction. The conditions which are necessary for the first production 
of a phenomenon, are occasionally also necessary for its continuance ; 
but more commonly its continuance requires no condition except neg- 
ative ones. Most things, once produced, continue as they are, until 
something changes or destroys them ; but some require the permanent 
presence of the agencies which produced them at first. These may, 
if we please^ be considered as instantaneous phenomena, requiring to 
be renewed at each instant by the cause by which they were at first 
generated. Accordingly, the illumination of any given point of space 
has always been looked upon as an instantaneous fact, which perishes 
and is perpetually renewed as long as the necessary conditions subsist. 
If we adopt this language we are enabled to avoid admitting that the 
continuance of the cause is ever required to maintain the effect. We 
may say, it is not required to maintain but to reproduce the effect, or 
else to counteract some force tending to destroy it. And this may be 
a convenient phraseology. But it is only a phraseology. The fact 
remains, that in some cases (though these are a minority), the continu- 
ance of the conditions which produced an effect is necessary to the 
continuance of the effect. 

As to the ulterior question, whether it is strictly necessary that the 
cause, or assemblage of conditions, should precede, by ever so short an 
instant, the production of the effect, (a question raised and argued with 
much ingenuity by a writer from whom we have quoted,*) we think 
the inquiry an unimportant one. There certainly are cases in which 
the effect follows without any interval perceptible to our faculties ; and 
when there is an interval we cannot tell by how many intemiediate 
Jinks imperceptible to us that interval may really be filled up. But 
even granting that an effect may commence simultaneously with its 
cause, the view I have taken of causation is in no way practically af- 
fected. Whether the cause and its effect be necessarily successive or 
not, causation is still the law of the succession of phenomena. Every- 
thing which begins to exist must have a cause ; what does not begin to 
exist does not need a cause ; what causation has to account for is the 

* The reviewer of Mr. Whewell in the Quarterly Review. 



206 • INDUCTION. 

origin of phenomena, and all the successions of phenomena must be 
resolvable into causation. These are the axioms of our doctrinOo If 
these be granted, we can afford, though I see no necessity for doing 
so, to drop the words antecedent and consequent as applied to cause 
and effect. I have no objection to define a cause, the assemblage of 
phenomena, which occurring, some other phenomenon invariably com- 
mences, or has its origin. Whether the effect coincides in point of 
time . with, or immediately follows, the hindmost of its conditions, 
is immaterial. At all events it does not precede it ; and when we are 
in doubt, between two coexistent phenomena, which is cause and which 
•effect, we rightly deem the question solved if we can ascertain which 
■of them preceded the other. - - ' ' 

§ 7. It continually happens that several different phenomena, vdiifch 
are not in the slightest degree dependent or conditional upon one 
another, are found all to depend, as the phrase is, upon one and the 
same agent ; in other words, one and the game phenomenon is seen to 
be followed by several sorts of effects quite heterogeneous, but which 
go on simultaneously one with another ; provided, of course, that all 
other conditions requisite for each of them also exist. Thus, the sun 
produces the celestial motions, it produces daylight, and it produces 
heat. The earth causes the fall of heavy bodies, and it also, in its 
capacity of an immense magnet, causes the phenomena of the magnetic 
needle. A crystal of galena causes the sensations of hardness, of 
weight, of cubical fornj, of gi ay color, and many others between which 
we can trace no interdependence. The purpose to which the phraseol- 
ogy of Properties and Powers is specially adapted, is the expression of 
this sort of cases. When the same phenomenon is followed (either 
subject or not to the presence of other conditions) by effects of differ-' 
ent and dissimilar orders, it -is usual to say that each different sort of 
effect is produced by a different property of the cause. Thus we disr 
tinguish the attractive, or gravitative, property of the earth, and its 
magnetic property ; the gravitative, luminiferous, and calorific proper^ 
ties of the sun ; the color, shape, weight, and hardness of the crys- 
tal. These are mere phrases, which explain nothing, and add nothing 
to our knowledge of the subject; but considered as abstract names 
denoting the connexion between the different effects produced and the 
object which produces them, they are a very powerful instrument of 
abridgment, and of that acceleration of the process of thought which 
abridgment accomplishes. " ■ 

This class of considerations leads us to a conception which we shall 
find of great importance in the interpretation of nature ; that of a Per- 
manent Cause, or original natural agent. There exist in nature a num^- 
ber of permanent causes, which have subsisted ever since the human 
race has been in existence, and for an indefinite and probably enormous 
length of time previous. The sun, the earth and planets, with their 
various constituents, air, water, and the other distinguishable substances, 
whether simple or compound, of which nature is made up, are such 
Permanent Causes. These have existed, and the effects or consequen- 
ces which they were fitted to produce have taken place, (as often as the 
other conditions of the production met,) from the very beginning of our 
experience. But we can give, scientifically speaking, no account of the 
origin of the Permanent Causes themselves. Why these particular nat- 



LAW OF CAUSATION. 207 

ural agents existed originally and no others, or why they are commin- 
gled in such and such proportions, and distributed in such and such a 
manner throughout space, is a question we cannot answer. More than 
this : we can discover nothing regular in the distribution itself; we can 
reduce it to no uniformity, to no law. There are no means by which, 
from the distribution of these causes or agents in one part of space, we 
could conjecture whether a similar distribution prevails in another. 
The coexistence, therefore, of Primeval Causes, ranks, to us, among 
merely casual concurrences : and all those sequences or coexistences 
among the effects of several such causes, which, though invariable while 
those causes coexist, v/ould, if the coexistence terminated, terminate 
along with it, we do not class as cases of causation, or laws of nature : 
we can only calculate upon finding these sequences or coexistences 
where we know, by direct evidence, that the natural agents on the 
properties of which they ultimately depend, are distributed in the re- 
quisite manner. These Permanent Causes -are not always objects; 
they are sometimes events, that is to say, periodical cycles of events, 
that being the only mode in which events can possess the property of 
permanence. Not only^ for instance, is the earth itself a permanent 
cause, or primitive natural agent, but the earth's rotation is so too r it 
is a cause which has produced, from the earliest period (by the aid of 
other necessary conditions), the succession of day and night, the ebb 
and flow of the sea, and many other effects, while, as we can assign no 
cause (except conjecturally) for the rotation itself, it is entitled to be 
ranked as a primeval cause. It is, however, only the origin of the ro- 
tation which is mysterious to us : once begun, its continuance is account- 
ed for by the first law of motion (that of the permanence of rectilineal 
motion once impressed) .combined with the gravitation of the parts of 
the earth towards one another. 

All phenomena without exception which begin to exist, that is, all 
except the primeval causeS:, are effects either immediate or remote of 
those primitive facts, or of some combination of them. There is no 
Thing produced, no event happening, in the universe, which is not con- 
nected by an uniformity, or invariable sequence, with some one or more 
of the phenomena which preceded it ; insomuch that it will happen again 
as often as those phenomena occur again, and as nO other phenomenon 
having the character of a counteracting cause shall coexist. These an- 
tecedent phenomena, again, were connected in a similar manner with 
some that preceded them; and so on, until we reach, as the ultimate 
step, either the properties of some one primeval cause, or the conjunc- 
tion of several. The whole of the phenomena of nature were therefore 
the necessary, or in other words, the unconditional, consequences of 
the original collocation of, the Permanent Causes. 

The state of the whole universe at any instant, we believe to be the 
consequence of its state at the previous instant: insomuch that if we 
knew all the agents which exist at the present moment, their colloca- 
tion in space, and their properties, in other words the laws of their 
agency, we could predict the whole subsequent history of the universe, 
at least unless some new volition of a power capable of controlling the 
universe should supervene.* And if any particular state of the entire 

* To the universality which mankind are agreed in ascribing to the Law of Causation, 
there is one claim of exception, one disputed case, that of the Human Will; the determina- 
tions of which a large class of metaphysicians are not willing to regard as following the 



208 INDUCTION. 

universe sliould ever recur a second time, (w^hicli, however, all experi- 
ence combines to assure us will never happen,) all subsequent states 
would return too, and history would, like a circulating decimal of many 
figures, periodically repeat itself: — 

Jam redit et \'irgo, redewit Saturma regna 

Alter erit turn Tiphys, et altera quse vehat Argo 
Delectos heroes ; eruntquoque altera bella, 
Atque iterum ad Troiam magnus mittetur Achilles. 

And though things do not really revolve in this eternal round, the whole 
series of events in the history of the universe, past and future, is not the 
less capable, in its own nature, of being constructed a priori by any 
one whom we can suppose acquainted with the original distribution of 
all natural agents, and with the whole of their properties, that is, the 
laws of succession existing between them and their effects : saving the 
infinitely more than human powers of combination and calculation 
which would be required, even in one possessing the data, for the actual 
performance of the task. 

§ 8. Since everything which occurs in the universe is determined by 
laws of causation and collocations of the original causes, it follows that 
the coexistences which are observable among effects cannot be them- 
selves the subject of any similar set of laws, distinct from laws of causa- 
tion. Uniformities there are, as well of coexistence as of succession, 
among the effects ; but these must in all cases be a mere result either 
of the identity or of the coexistence of their causes : if the causes did 
not coexist, neither could the effects. And these causes being also 
effects of prior causes, and these of others, until we reach the primeval 
causes, it follows that (except in the case of effects' which can be traced 
immediately or remotely to one and the same cause), the coexistences 
of phenomena can in no case be universal, unless the coexistences of 
the primeval causes to which the effects are ultimately traceable, can 
be reduced to an universal law: but we have seen that they. cannot. 
There are, accordingly, no original and independent, in other wgrds, 
no unconditional, uniformities of coexistence between effects of different 
causes ; if they coexist, it is only because the causes have casually coex- 
isted. The only independent and unconditional coexistences which are 
sufficiently invariable to have any claim to the character of laws, are 
between different and mutually independent effects of the same cause; 
in other words, between different properties of the same natural agent. 
This portion of the Laws of Nature will be treated of in the latter part 

causes called motives, according to as strict laws as those which they suppose to exist in 
the world of mere matter. This controverted point will undergo a special examination 
when we come to treat particularly of the Logic of the Moral Sciences (Book vi., ch. 3). 
In the mean time I may remark that these metaphysicians, who, it must be observed, ground 
the main part of their objection upon the supposed repugnance of the doctrine in question 
to our consciousness, seem to me to mistake the fact which consciousness testifies against. 
"What is really in contradiction to consciousness, they would, I think, on strict self-exam- 
ination, find to be, the application to human actions and volitions of the ideas involved in 
the common use of the term N,ecessity ; which I agree with them in thinking. highly objec- 
tionable. But if they would consider that by saying that a man's actions necessarily follow 
from his character, all that is really meant (for no more is meant in any case whatever of 
causation) is that he invariably does act in conformity to his character, and that any one who 
thoroughly knew his character could certainly predict how he would act in any supposable 
case ; they probably would not find this doctrine either contrary to their experience or 
revolting to their feelings. And no mofe than this is contended for by any one but an 
Asiatic fatalist. 



LAW OF CAU3ATI0N. 209 

of tlie present Book, under tlie name of the Specific Properties of 
Kinds. 

§ 9. Before concluding this chapter, it seems desirable to take 
notice of an apparent, but not a real opposition between the doctrines 
which I have laid down respecting causation, and those maintained in 
a work which I hold to be far the greatest yet produced on the Phi- 
losophy of the Sciences, M. Comte's Cours de Philosophie Positive. 
M. Comte asserts as his first principle, that the causes of phenomena 
are beyond the reach of the human faculties, and that all which is ac- 
cessible to us is their laws, or, as he explains the term, their constant 
relations of succession or of similarity. Accordingly M, Comte sedu- 
lously abstains, in the subsequent part of his work, fi-om the use of the 
word Cause : an example which I have not followed, for reasons which 
I will proceed to state. I most fully agree with M. Comte that ulti- 
mate, or, in the phraseology of metaphysicians, ejicient causes, which 
are conceived as not being phenomena, nor perceptible by the senses 
at all, are radically inaccessible to the human faculties : and that the 
*' constant relations of succession or of similarity" which exist among 
phenomena themselves, (not forgetting, so far as any constancy can be 
traced, their relations of coexistence,) are the only subjects of rational 
investigation. When I speak of causation, I have nothing in view, 
other than those constant relations : but I think the terms causation, 
and cause and effect, important to be preserved, for the purpose of 
distinctively designating one class of those relations, namely, the rela- 
tions of succession which so far as we know are unconditional ; as 
contrasted with those which, like the succession of day and night, de- 
pend upon the existence or upon the coexistence of other antecedent 
facts. This distinction corresponds to the great division which Mr. 
Whewell and other writers have made of the field of science, into the 
investigation of what they term the Laws of Phenomena, and the 
investigation of causes ; a phraseology, as I conceive, altogether 
vicious, inasmuch as the ascertainment of causes, such causes as the 
human faculties can ascertain, namely, causes which are themselves 
phenomena, is, therefore, merely the ascertainment of other and more 
universal Laws of Phenomena. And I cannot but look upon the 
revival, on English soil, of the doctrine (not only refuted by the school 
of Locke and Hume, but given up by their great rivals Reid and 
Stewart) that efficietit causes are within the reach of human knowl- 
edge, as a remarkable instance of what has been aptly called " the 
peculiar zest which the spirit of reaction against modern tendencies 
gives to ancient absurdities." 

Yet the distinction between those constant relations of succession or 
coexistence which Mr. Whewell terms Laws of Phenomena, and 
those which he terms, as I do, Laws of Causation, is grounded (how- 
ever incorrectly expressed) upon a real difference. It is no doubt 
with great injustice that Mr. Whewell (who has evidently given only 
a most partial and cursory inspection to M. Comte's work,) assumes 
that M. Comte has overlooked this fundamental distinction, and that 
by excluding the investigation of causes, he excludes that of all the 
most general truths. No one really acquainted with M. Comte's 
admirable speculations could have so completely misapprehended their 
whole spirit and pui-port. But it does appear to me that his disinclina- 
D D 



210 INDUCTION. 

tion to employ the word Cause has occasionally led him to attach less 
importance than it deserves to this great distinction, upon which alone, 
I am convinced, the possibility rests of framing a rigorous Canon of 
Induction. Nor do I see what is gained by avoiding this particular 
word, when M. Comte is forced, like other people, to speak continually 
of the properties of things, of agents and their action, oi forces, and 
the like ; terms equally liable to perversion, and which are partial and 
inadequate expressions for what no word that we possess, except 
Cause, expresses in its full generality. I believe, too, that when the 
ideas which a word is commonly used to convey are overclouded with 
mysticism, the obscurity is not likely to be so effectually dispelled by 
abstaining from its employment, as by bringing out into full clearness 
the portion of real meaning which exists in the various cases where 
the term is most familiarly employed, and thereby giving a legitimate 
satisfaction to that demand of the intellect which has caused the term 
to remain in use. 



CHAPTER VI. 

OF THE COMPOSITION OF CAUSES. 



§ 1. To complete the general notion of causation on which the rules 
of. experimental inquiry into the laws of nature must be founded, 
one distinction still remains to be pointed out : a distinction so funda- 
mental, and of so much importance, as to require a chapter to itself 

The preceding discussions have rendered us familiar with the case 
in which several agents, or causes, concur as conditions to the pro- 
duction of an effect ; a case, in truth, almost universal, there being 
very few effects to the production of which no m.ore than one agent 
contributes. Suppose, then, that two different agents, operating 
jointly, are followed, under a certain set of collateral conditions, by a 
given effect. If either of these agents, instead of being joined with 
the other, had operated alone, under the same set of conditions in all 
other respects, some effect would probably have followed ; which 
would have been different from the joint effect of the two, and more 
or less dissimilar to it. Now, if we happen to know what would be 
the effects of each cause when acting separately from the other, we 
are often able to arrive deductively, or a priori, at a correct prediction 
of what wdll arise from their conjunct agency. To enable us to do 
this, it is only necessary that the same law which expresses the effect 
of each cause acting by itself, shall also correctly express the part due 
to that cause, of the effect which follows, from the two together. This 
condition is realized in the extensive- and important class of phenomena 
commonly called mechanical, namely, the phenomena of the communi- 
cation of motion (or of pressure, which is tendency to, motion) from 
one body to another. In this important class of cases of causation, 
one cause never, properly speaking, defeats or frustrates another ; both 
hove their full effect. If a body is propelled in two directions by two 
forces, one tending to drive it to the norths and the other to the east, 
it is caused to move in a given time exactly as far in both directions as 



COMPOSITION OF CAUSES. 211 

the two forces would separately have carried it ; and is left precisely 
where it would have arrived if it had been acted upon first by one of 
the two forces, and afterwards by the other. This law of nature is 
called, in mechanical philosophy, the jjrinciple of the Composition of 
Forces : and in imitation of that well-chosen expression, I shall give 
the name of the Composition of Causes to the principle which is 
exemplified in all cases in which the joint effect of several causes is 
identical with the sum of their separate effects. 

This principle, however, by no means prevails in all departments of 
the field of nature. The chemical combination of two substances 
produces, as is well known, a third substance with properties entirely 
different from those of either of the two substances separately, or of 
both of them taken together. Not a trace of the properties of hydro- 
gei) or of oxygen is observable in those of their compound, water. 
The taste of sugar of lead is not the sum of the tastes of its component 
elements, acetic acid and lead or its oxide; nor is the color of green 
vitriol a mixture of the colors of sulphuric acid and copper. This 
e;x;plains why mechanics is a deductive or demonstrative science, and 
chemistry not. In the one, we can compute the effects of all combina- 
tions of causes, whether real or hypothetical, from the laws which we 
know to, govern those causes when acting separately; because they 
continue to observe the same laws when in combination, which they 
observed when separate : vvhatever would have happened in conse- 
quence of each cause taken by itself, happens when they are together, 
and we have only to cast up the results. Not so in the phenomena 
which are the peculiar subject of the science of chemistry. There, 
most of the uniformities to which the causes conformed when separate, 
cease altogether when they are conjoined ; and we are not, at least in 
the present state of our knowledge, able to foresee what result will 
follow from any new combination, until we have tried it by specific 
experiment. 

If this be true of chemical combinations, it is still more true of those 
far more complex combinations of elements which constitute organized 
bodies ; and in which those extraordinary new uniformities arise, which 
are called the lavvs of life. All organized bodies are composed of 
parts, similar to those composing inorganic nature, and which have 
even themselves existed in an inorganic state ; but the phenomena of 
life, which result from the juxtaposition of those parts in a certain 
manner, bear no analogy to any of the effects which would be produced 
by the action of, the component substances considered as mere physical 
agents. To whatever degree we might imagine our knowledge of the 
properties of the several ingredients of a living body to be extended 
and perfected, it is certain that no mere summing up of the separate 
actions of those elements will ever amount to the action of the living 
body itself The tongue, for instance, is, like all other parts of the 
animal frame, composed of gelatine, ffbrin, and other products of the 
chemistry of digestion, but from no knowledge of the properties of 
those substances could we ever predict that it could taste, unless gel- 
atine or fibrin could themselves taste ; for no elementary fact can be in 
the conclusion, which was not first in the premisses. 

There are thus two different modes of the conjunct action of causes ; 
from which arise two modes of conflict, or mutual interference, between 
laws' of nature. Suppose, at a given point of time and space, two or 



212 INDUCTION. 

more causes, wliicli, if they acted separately, would produce effects 
contrary, or at least conflicting with each other; one of them tending 
to undo, wholly or partially, what the other tends to do. Thus, the 
expansive force of the gases generated by the ignition of gunpow- 
der tends to project a bullet towards the sky, while its gravity tends to 
make it fall to the ground. A stream running into a reservoir at one 
end tends to fill it higher and higher, while a drain at the other extremity 
tends to empty it. Now, in such cases as these, even if the two causes 
which are in joint action exactly annul one another, still the laws of 
both are fulfilled; the effect is the same as if the drain had been open 
for half an hour first,* and the stream had flowed in for as long after- 
wards. Each agent produced the sarne amount of effect as if it had 
acted separately, though the contrary effect which was taking place 
during the same time .obliterated it as fast as it was produced. Here, 
then, we have two causes, producing by their joint operation an effect 
which at first seems quite dissimilar to those which they produce sep- 
arately, but which on examination proves to be really the sum of those 
separate effects. It will be noticed that we here enlarge the idea of the 
sum of two effects, so as to include what is commonly called their dif- 
ference, but which is in reality the result of the addition of opposites ; 
a conception to which, as is well known, mankind are indebted for that 
admirable extension of the algebraical calculus, which has so vastly in- 
creased its powers as an instrument of discovery, by iijtroducing into 
its reasonings (with the sign of subtraction prefixed, and under the 
name of Negative Quantities) every description whatever of positive 
phenomena, provided they are of such a quality in reference to those 
previously introduced, that to add the one is equivalent to subtracting 
an equal quantity of the other. 

There is, then, one mode of the mutual interference of laws of na- 
ture in which, even when the concurrent causes annihilate each other's 
effects, each exerts its full efficacy according to its own law, its law as 
a separate agent. But in the other description of cases, the two agen- 
cies which are brought together cease entirely, and a totally different 
set of phenomena arise : as in the experiment of two liquids which, 
when mixed in certain proportions, instantly become a solid mass, in- 
stead of merely a larger amount of liquid. 

§ 2. This difference between the case in which the joint effect of - 
causes is the sum of their separate effects, and the case in which it is 
heterogeneous to them ; between laws which work together without 
alteration, and laws which, when called upon to v/ork together, cease 
and give place to others ; is one of the fundamental distinctions in 
nature. The former case, that of the Composition of Causes, is the 
general one; the other is always special and exceptional. There are 
no objects which do not, as to sorne of their phenomena, obey the prin- 
ciple of the Composition of Causes ; none that have not some laws 
which are rigidly fulfilled in every" combination into which the objects 
enter. The weight of a body, for instance, is a property which it 
retains in all the combinations in which it is placed. The weight of a 
chemical compound, or of an organized body, is equal to the sum of 

* I omit, for simplicity, to take into account the effect, in this latter case, of the diminu- 
tion of pressure, in diminishing the flow of the water through the drain ; which evidently 
iu no way affects the truth or applicability of the principle. 



COMPOSITION OF CAUSES. 213 

the weights of the elements which compose it. The weight either 
of the elements or of the compound will vary, if they be earned fur- 
ther from their centre of attraction, or brought nearer to it ; but what- 
ever affects the one affects the other. They always remain precisely 
equal. So again, the component parts of a vegetable or animal sub- 
stance do not lose their mechanical and chemical properties as sepa- 
rate agents, when, by a peculiar mode of juxtaposition, they, as an 
aggregate whole, acquire physiological or vital properties in addition. 
Those bodies continue, as before, to obey mechanical and chemical 
laws, in so far as the operation of those laws is not counteracted by the 
new laws which govern them as organized beings. When, in short, a 
concurrence of causes takes place which calls into action new laws, 
•bearing no analogy to any that we can trace in the separate operation 
of the causes, ,the new laws may supersede one portion of the previous 
laws but coexist with another portion, and may even compound the 
effect of those previous laws with their own. 

Again, laws which were themselves generated in the second mode, 
may generate others in the first. Though there be laws which, like 
those of chemistry and physiology, owe their existence to a breach of 
the principle of Composition of Causes, it does not follow that these 
peculiar, or as they might be termed, heteropatliic laws, are not capa- 
ble of composition with one another. The causes which by one com- 
bination have had their laws altered, may carry their new laws with 
them unaltered into their ulterior combinations. And hence there is 
no reason to despair of ultimately raising chemistry and physiology to 
the condition of deductive sciences ; for though it is impossible to de- 
duce all chemical and physiological truths from the laws or properties 
of simple substances or elementary agents, they may probably be de- 
ducible from laws which commence when these elementary agents are 
brought together into some moderate number of not very complex 
combinations. The Laws of Life will never be deducible from the 
mere laws of the ingredients, but the prodigiously complex Facts of 
Life may all be deducible from comparatively simple laws of life ; 
which laws (depending indeed upon combinations, but upon compara- 
tively simple combinations, of antecedents), may in more complex 
circumstances be strictly compounded with one another, and with the 
physical and chemical laws of the ingredients. The details of the 
vital phenomena even now afford innumerable exemplifications of the 
Composition of Causes; and in proportion as these phenomena are 
more accurately studied, there appears more and more reason to 
believe that the same laws which operate in the simpler combinations 
of circumstances do, in fact, continue to be observed in the more com- 
plex. * This will be found equally true in the phenomena of mind; 
and even in social and political phenomena, the result of the laws of 
mind. It is in the case of chemical phenomena that the least progress 

* For abundant illustrations of this remark, I may refer to the writings of Dr. W. B, 
Carpenter, of Bristol, and especially his treatise on General Physiology, in which the high- 
est generalizations which the science of life has yet reached, and the best modern concep- 
tion of that science as a whole, are exhibited in a manner equally perspicuous and philo- 
sophical. On the details of such a treatise the present writer would be an incompetent wit- 
ness : these however have been sufheiently vouched for by some of the highest living 
authorities ; while of the genuinely scientific spirit which pervades it, those may be per- 
mitted to express an opinion, who would not be entitled to offer to a work on such a sub» 
ject, any other praise. 



214 INDUCTION. 

has yet been made in bringing tlie special laws under general ones 
from which tliey may be deduced ; but there are even in chemistry 
many circumstances to encourage the hope that such general laws 
will hereafter be discovered. The different actions of alchemical 
compound will never, undoubtedly, be found to be the sum of the 
actions of its sejDarate elements ; but there may exist, between the 
properties of the compound and those of its elements, some constant 
relation, which if discoverable by a sufficient induction, would enable 
us to foresee the sort of compound which will result from a new com- 
bination before we have actually tried it, and to judge of what sort of 
elements some new substance is compounded before we have analyzed 
it : a problem, the solution of which has been propounded by M. 
Comte as the ideal aim and purpose of chemical speculation. The 
great law of definite proportions, first discovered in its full generality 
by Dalton, is a complete solution of this problem in one single aspect 
(of secondary importance it is true), that of quantity : and in respect 
to quality, we have already some partial generalizations sufficient to 
indicate the possibility of ultimately proceeding further. We can 
predicate many common properties of the kind of compounds which 
result from the combination, in each of the small number of possible 
proportions, of any acid whatever with any base. We have also the 
very curious law, discovered by Berthollet, that two soluble salts 
mutually decompose one another whenever the new combinations 
which result produce an insoluble compound : or one less soluble 
than the two former. Another uniformity has been observed, com- 
monly called the law of isomorphism ; the identity of the crystalline 
forms of substances which possess in common certain peculiarities of 
chemical composition. Thus it appears that even heteropathic laws, 
such laws of combined agency as are not compounded of the laws of 
the separate agencies, are yet, at least in some cases, derived from 
them according to a fixed principle. There may, therefore, be laws 
of the generation of laws from others dissimilar to them; and in chem- 
istry, these undiscovered laws of the dependence of the properties of 
the compound on the properties of its elements, may, together with' 
the laws of the elements thernselves, furnish the premisses by which 
the science is destined one day to be rendered deduGtive, 

It would seem, therefol^e, that there is no class of phenomena in 
which the Composition of Causes does not obtain : that as a general 
rule, causes in combination produce exactly the same effects as when 
acting singly : but that this rule, though general, is not universal ; that 
in some instances, at some particular points in the transition from sep- 
arate to united action, the laws change, and an entirely new set of 
effects are either added to, or take the place of, those which arise from 
the separate agency of the same causes ; the laws of these new effects 
being again susceptible of composition, to an indefinite extent, like the 
laws which they superseded. 

§ 3. That effects are proportional to their causes is laid down, by 
some writers, as an axiom in the theory of causation ; and great use is 
sometimes made of this principle in reasonings respecting the laws of 
nature, although it is encumbered with many difficulties and apparent 
exceptions, which much ingenuity has been expended in showing Aot 
to be real ones. This proposition, in so far as it is true, enters as a 



COMPOSITION OF CAUSES. 215 

particular case into the general principle of the Composition of Causes : 
the causes compounded being, in this instance, homogeneous ; in which 
case, if in any, their joint effect might be expected to be identical with 
the sum of their separate effects. If a force equal to one hundred 
weight, will raise a certain body along an inclined plane, a force equal 
to two hundred weight will, we know, raise two bodies exactly similar, 
and thus the effect is proportional to the cause. But does not a force 
equal to two hundred weight, actually contain in itself two forces each 
equal to one hundred weight, which, if employed apart, would sepa- 
rately raise the two bodies in question 1 The fact, therefore, that 
when exerted jointly they raise both bodies at once, results from the 
Composition of Causes, and is a mere instance of the general fact that 
mechanical forces are subject to the law of Composition. And so in 
every other case which can be supposed. For the doctrine of the 
proportionality of effects to their causes cannot of course be applicable 
to cases in which the augmentation of the cause alters the kind of effect; 
that is, in which the surplus quantity superadded to the cause does not 
become compounded with it, but the two together generate an alto- 
gether new phenomenon. Suppose that the application of a certain 
quantity of heat to a body merely increases its bulk, that a double 
quantity melts it, and a triple quantity decomposes it ; these three 
effects being heterogeneous, no ratio, whether corresponding or not to 
that of the quantities of heat applied, can be established between them. 
Thus we see that the supposed axiom of the proportionality of effects 
to their causes fails at the precise point where the principle of the 
Composition of Causes also fails ; viz., where the concuiTence of 
causes is such as to determine a change in the properties of the body 
generally, and render it subject to new laws, more or less dissimilar 
to those to which it conformed in its previous state of existence. . The 
recognition, therefore, of any such law of proportionality, is superseded 
by the more comprehensive principle, in which as much of it as is true 
is implicitly asserted. 

The general remarks on causation, which seemed necessary as an 
introduction to the theory of the inductive process, may here termi- 
nate. That process is essentially an inquiry into cases of causation. 
All the uniformities which exist in the succession of phenomena, and 
most of those which prevail in their coexistence, are either, as we have 
seen, themselves laws of causation, or consequences resulting from, 
aiid corollaries capable of being deduced from, such laws. If we could 
determine what causes are correctly^ assigned to what effects, and what 
effects to what causes, we should be virtually acquainted with the 
whole course of nature. All those uniformities which are mere results 
of causation, might then be explained and accounted for ; and every 
individual fact or event might be predicted, provided we had the 
requisite data, that is, the requisite knowledge of the circumstances 
which, in the particular instance, preceded it. 

To ascertain, therefore, what are the laws of causation which exist 
in nature ; to determine the effects of eveiy cause, and the causes of 
all effects, is the main business of Induction ; and to point out how this 
is done is the chief object of Inductive Logic. 



216 INDUCTION. 

^ CHAPTER VII. 

OF OBSERVATION AND EXPERIMENT. 

§ 1. It results from the preceding exposition, that the process of 
ascertaining what consequents, in nature, are invariably connected 
with what antecedents, or in other words what phenomena are related 
to each other as causes and effects, is in some sort a process of analysis. 
That every fact which begins to exist has a cause, and that this cause 
must be found somewhere among the facts which immediately pro- 
ceded its occurrence, may be taken for certain. The whole of the 
present facts are the infallible result of all past facts, and more imme- 
diately of all the facts which existed at the moment previous. HerCj 
then, is a great sequence, which we know to be uniform. If the whole 
prior state of the entire universe could again recur, it would again be 
followed by the whole present state. The question is, how to resolve 
this complex uniformity into the simpler uniformities , which compose 
it, and assign to each portion of the vast antecedent that portion of the 
consequent which is attendant upon it. 

This operation, which we have called analytical, inasmuch as it is 
the resolution of a complex whole into the component elements, is 
more than a merely mental analysis. No mere contemplation of the 
phenomena, and partition of them by the intellect alone, will of itself 
accomplish the end we have now in view. Nevertheless, such a men- 
tal partition is an indispensable first step. The order of nature, as per- 
ceived at a first glance, presents at every instant a chaos followed by 
another chaos. We must decompose each chaos into single facts. 
We must learn to see in the chaotic antece«dent a multitude of dis- 
tinct antecedents, iji the chaotic consequent a multitude of distinct 
consequents. This, supposing . it done, will not of itself tell us on 
which of the antecedents each consequent is invariably, attend ant. To 
determine that point, we must endeavor to effect a separation of the 
facts from one another, not in our minds only, but in nature. The 
mental analysis, however, must take place first. And every one 
knows that in the mode of performing it, one intellect diflers im- 
mensely from another. It is the essence of the act of observing ; for the 
observer is not he who merely sees the thing which is before his eyes, 
but he who sees what parts that thing is composed of To do this 
well is a rare talent. One person, from inattention, or attending only 
in the wroi;ig place, overlooks half of what he sees ; another sets down 
much more than he sees, confounding it with what he imagines, or 
with what he infers ; another takes note of the kind of all the circum- 
stances, but being inexpert in estimating their degree, leaves the 
quantity of each vague and uncertain; another sees indeed the whole, 
but makes such an awkward division of it into parts, throwing things 
into one mass which require to be separated, and separating others 
which might more conveniently be considered as one, that the result 
is much the same, sometimes even worse, than if no analysis had been 
attempted at all. It would be possible to point out what qualities of 
mind, and modes of mental culture, fit a person for being a good 
observer ; that, however, is a question not of Logic, but of the theoiy 



OBSERVATION AND EXPERIMENT. 217 

of Education, in the most enlarged sense of the term. There is not 
properly an Art of Observing. There may be rules for observing. 
But these, like rules for inventing, are properly instructions for the 
preparation of one's own mind ; for putting it into the state in which 
it will be most fitted to observe, or most likely to invent. They are, 
therefore, essentially rules of self-education, which is a different thing 
from Logic. They do not teach how to do the thing, but how to make 
ourselves capable of doing it. They are an art of strengthening the 
limbs, not an art of using them. 

The extent and minuteness of observation which may be requisite, 
and the' degree of decomposition to which it may be necessary to carry 
the mental analysis, depend upon the particular purpose in view. To 
ascertain the state of the whole universe at any particular moment is 
impossible, but would ^also be useless. In making chemical experi- 
ments, we should not think it necessary to note the position of the 
planets ; because experience has shown, as a very superficial experi- 
ence is sufficient to show, that in such cases that circumstance is not 
material to the result : and, accordingly, in the age when men believed 
in the occult influences of the heavenly bodies, it might have been un- 
philosophical to omit ascertaining the precise condition of those bodies 
at the moment of the experiment. As to the degree of minuteness of 
the mental subdivision; if we were obliged to break down what we 
observe into its very simplest elements, that is, literally into single facts, 
it would be difficult to say where we should find them : we can hardly 
ever affirm that our divisions of any kind have reached the ultimate 
ilnit. But this, too, is fortunately unnecessary. The only object of the 
mental separation is to suggest the requisite physical separation, so 
that we may either accomplish it ourselves, or seek for it in nature; 
and we have done enough when we have carried the subdivision as far 
as the point at which We are able to see what observations or experi- 
ments we require. It is only essential,, at whatever point our mental 
decomposition of facts may for the present have stopped, that we should 
hold ourselves ready and able to carry it further as occasion requires, 
and should not allow the freedom of our discriminating faculty to be 
imprisoned by the swathes and bands of ordinary classification ; as was 
the case with all early speculative inquirers, not excepting the Greeks, 
to whom it hardly ever occurred that what was called by one abstract 
name might, in rOality, be several phenomena, or thatthere was a pos- 
sibility of decomposing the facts of the universe into any elements but 
those which ordinary language already recognized. 

§ 2. The different antecedents and consequents being, then, supposed 
to be, so far as the case requires, ascertained and discrhninated from 
one another ; we are to inquire which is connected with which. In 
every instance which comes under our observation, there are many 
antecedents and many consequents. If those antecedents could not be 
severed from one another except in thought, or if those consequents 
never were found apart, it would be impossible for us to distinguish 
{a posterio7-i at least) the real laws, or to assign to any cause its effect, 
or to any effect its cause. To do so, we must be able to meet with 
some of the antecedents apart from the rest, and observe what follows 
from them; or some of the consequents, and observe by what they are 
preceded. We must, in short, follow the Baconian rule of varying 
E E 



218 . INDUCTION. 

the circumstances. This is, indeed, only the first rule of physical inqui- 
ry, and not, as some have thought, the sole rule ; but it is the founda? 
tion of all the rest. 

For the purpose of varying the circumstances, we may have recourse 
(according to a distinction commonly made) either to observation or to 
experiment ; we may either find an instance in nature, suited to our 
purposes, or, by an artificial arrangement of circumstances, make one. 
The value of the instance depends upon what it is in itself, not upon 
the mode in which it is obtained : its employment for the purposes of 
induction depends upon the same principles in the one case and in the 
other ; as the uses of money are the same whether it is inherited or 
acquired. There is, in short, no difference in kind, no real logical 
distinction, between the two processes of investigation. There are, 
however, practical distinctions to which it is of considerable importance 
to advert. 

§ 3. The first and most obvious distinction between Observation and 
Experiment is, that the latter is an immense extension of the foiTner. 
It not only enables us to produce a much greater number of variations 
in the circumstances than nature spontaneously offers, but, moreover, 
in thousands of cases, to produce the precise sort of variation which 
we are in want of for discovering the law of the phenomenon ; a ser- 
vice which nature, being constructed on a quite different scheme from 
that of facilitating our studies, is seldom so friendly as to bestow upon 
us. For example,. in order to ascertain what principle in the atmos- 
phere enables it to sustain life, the variation we require is that a living 
animal should be immersed in each component element of the atmos- 
phere separately. But nature does not supply either oxygen or azote 
in a separate state. We are indebted to artificial experiment for our 
knowledge that it is the former, and not the latter, which supports 
respiration ; and even for our knowledge of the very existence of the 
two ingredients. 

Thus far the advantage of experimqntation over simple observation 
is universally recognized : all are aware that it enables us to obtain 
innumerable combinations of circumstances which are not to be found 
in nature, and so add to nature's experiments a multitude of experi- 
ments of our own. But there is another superiority (or, as Bacon 
would have expressed it, another prerogative), of instances artificially 
obtained over spontaneous instances — of our own experiments over 
even the same experiments when made by nature — which is not of less 
importance, and which is far from being felt and acknowledged in the 
same degree. 

When we can produce a phenomenon artificially, we can take it, as 
it were, home with us, and observe it in the midst of circumstances 
with which in all other respects we are accurately acquainted. If we 
desire to know what are the effects of the cause A, and are able to 
produce A by any means at our disposal, we can generally determine 
at our own discretion, so far as is compatible with the nature of the 
phenomenon A, the whole of the circumstances which shall be present 
along with it : and thus, knowing exactly the simultaneous state of every- 
thing else whickis within the reach of A's influence, we have only to 
observe what alteration is made in that state by the presence of A. 

For example, by the electrical machine we can produce in the midst 



OBSERVATION AND EXPERIMENT. 219 

of known circumstances, the plienomena which nature exhibits oh a 
grander scale underthe form of lightning and thunder. Now let any 
one consider what amount of kiiowiedge of the effects and laws of elec- 
tric agency mankind could ever have obtained from the mere observation 
of thunder-storms, and compare it with that which they have gained, 
and may expect to gain, from electrical and galvanic experiments. 
This example is the more striking, now that we have reason to believe 
that electric action is of all natural phenomena (except heat) the most 
pervading and universal, which, therefore, it might antecedently have 
been supposed could stand least in need of artificial means of produc- 
tion to enable it to be studied ; w^hile the fact is so much the contrary, 
that without the electric machine, the voltaic battery, and the Leyden 
jar, we should never have suspected the existence of electricity as one 
of the great agents in nature ; the few electric phenomena we should 
have known of would have continued to be regarded either as super- 
natural, or as a sort of anomalies and eccentricities in the order of the 
universe. 

When we have succeeded in insulating the phenomenon which is the 
subject of inquiry, by placing it among known circumstances, we may 
produce further variations of circumstances to any extent, and of such 
kinds as we think best calculated to bring the laws of the phenomenon 
into a clear light. By introducing one well defined circumstance after 
another into the experiment, we obtain assurance of the m'anner in 
which the phenomenon behaves under an indefinite variety of possible 
circumstances. Thus, chemists, after having obtained some newly-dis- 
covered substance in a pure state, (that is, having made sure that there 
is nothing present whicn can interfere with and modify its agency,) 
introduce various other substances, one by one, to ascertain whether it 
will combine with them, or decompose them, and with what result; 
and also apply heat, or electricity, or pressure, to discover what will 
happen to the substance under each of these circumstances. 

But if, on the other hand, it is out of our powder to produce the phe- 
nomenon, and we have to seek for instances in which nature produces 
it, the task before us is one of quite another kind. Instead of being 
able to choose what the concomitant circumstances shall be, we now 
have to discover what they are ; which, when we go beyond the sim- 
plest and most accessible cases, it is next to impossible to do, with any 
precision and completeness. Let us take, a^ an exemplification of a phe- 
nomenon which we have no means of fabricating artificially, a human 
mind. Nature produces many ; but the consequence of our not being 
able to produce it by art is, that in every instance in which we see a 
human mind developing itself, or acting upon other things, we see it 
surrounded and obscured by an indefinite multitude of unascertainable 
circumstances, rendering the use of the common experimental methods 
almost delusive. We may conceive to what extent this is true, if we 
consider, among other things, that whenever nature produces a human 
mind, she produces, in close connexion with it, also a body : that is, a 
vast complication of physical facts, in no two cases perhaps exactly 
similar, and most of which (except tho mere structure, which we can 
examine in a sort of coarse way after it has ceased to act) are radically 
out of the reach of our means of exploration. If, instead of a human 
mind, we suppose the subject of investigation to be a human society 
or State all the same difficulties recur in a greatly augmented degree. 



220 INDUCTION. 

We have thus akeady come within sight of a conclusion, which the^ 
progress of the inquiry will, I think, bring before us with the clearest 
evidence : namely, that in the sciences which deal with phenomena in 
which artificial experiments are impossible (as in the case of astron- 
omy), or in which they have a very limited range (as in physiology, 
mental philosophy, and the social science), induction from direct 
experience is practised at a disadvantage generally equivalent to 
impracticability : from which it follows that the methods of those 
sciences, in order to accomplish anything worthy of attainment, must 
be to a great extent, if not principally, deductive. ^This is already 
known to be the case with the first of the sciences we have men- 
tioned, astronomy ; that it is not generally recognized as true of the 
others, is probably one of the reasons why they are still in their 
infancy. But any further notice of this topic would at present be 
premature. 

§ 4. If what is called pure Observation is at so great a disadvantage 
compared with artificial experimentation, in one department of the 
direct exploration of phenomena, there is another branch in which the 
advantage is all on the side of the former. 

Inductive inquiry having for its object to ascertain what causes are 
connected with what effects, w^e may begin this search at either end of 
the road which leads from the one point to the other : we may either 
inquire into the effects of a given cause, or into the causes of a given 
effect. The fact that light blackens chloride of silver might have been 
discovered, either by experiments upon light, trying what effect it' 
would produce on various substances, or by observing that portions of 
the chloride had repeatedly become black, and inquiring into the 
circumstances. The effect of the urali poison might have become 
known either by administering it to animals, or by examining how it 
happened that the wounds which the Indians of Guiana inflict with 
their arrows prove so uniformly mortal. Now it is manifest from the 
mere statement of the exarnples, without any theoretical discussion, 
that artificial experimentation is applicable only to the former of these 
modes of investigation. We can take a cause, and try what it will 
produce : but we cannot take an effect, and try what it will be pro- 
duced by. We can only watch till we see it produced, or are enabled 
to produce it by accident. 

This would be of little importance, if it always depended upon our 
choice from which of the two ends of the sequence we would under- 
take our inquiries. But we have seldom any option. As we can only 
travel from the known to the unknown, we are obliged to commence 
at whichever end we are best acquainted with. If the agent is more 
familiar to us than its effects, we watch for, or contrive, instances of 
the agent, under such varieties of circumstances as dre open to us, and 
observe the result. If, on the contrary, the conditions on which a 
phenomenon depends are obscure, but the phenomenon itself familiar, 
we must commence our inquiry from the effect. If we are struck with 
the fact that chloride of silver has been blackened, and have" no 
suspicion of the cause, we have no resource but to compare instances 
in which the fact has chanced to occur^ until by that comparison we 
discover that in. all those instances the substance had been exposed to 
the light. If we knew nothing of the Indian ari'ows but their fatal 



OBSERVATION AND EXPERIMENT 221 

effect, accident alone could turn our attention to experiments on the 
urali : in the regular course of investigation, we could only inquire, or 
try to observe, w^hat had been done to the arrow^s in particular instances. 

Wherever, having nothing to guide us to the cause, w^e are obliged 
to set out from the effect, and to apply the rule of varying the circum- 
stances to the consequents, not. the antecedents, we are necessarily 
destitute of the resource of artificial experimentation. We cannot, at 
our choice, obtain consequents, as we can antecedents, under any set 
of circumstances compatible with their nature. There are no means of 
producing effects bat through their causes, and by the supposition the 
causes of the effect in question are not known to us. We have there- 
fore no expedient but to study it where it offers itself spontaneously. 
If nature happens to present us with instances sufficiently varied in 
their circumstances, and if we are able to discover either among the 
proximate antecedents, or among some other order of antecedents, 
something which is always found when the effect is found, however 
various the circumstances, and never found when it is not ; we may 
discover, by mere observation without experiment, a real uniformity in 
nature. 

But although this is certainly the most favorable case for sciences of 
pure observation, as contrasted with those in which artificial experi- 
ments are possible, there is in reality no case which more strikingly 
illustrates the inherent imperfection of direct induction when not 
founded upon experimentation. Suppose that, by a comparison of 
cases of the effect, we have found an antecedent which appears to be, 
and perhaps is, invariably connected with it: we have not yet proved 
that antecedent to be the cause, until we have reversed the process, 
and produced the effect by means of that antecedent. If we can pro- 
duce the antecedent artificially, and if, when we do so, the effect fol- 
lows, the induction is complete; that antecedent is the cause of that 
consequent.* But we then have added the evidence of experiment to 
that of simple observation. Until we had done so, we had only proved 
invariaole antecedence, but not unconditional antecedence, or causa- 
tion. Until it had been shown by the actual production of the, antece- 
dent under known circumstances, and the occurrence thereupon of the 
consequent, that the antecedent was really the condition on which it 
depended ; the uniformity of succession which was proved to exist 
between them might, for aught we knew, be (like the succession of 
day and night) no case of causation at all ; both antecedent and con- 
sequent might be successive stages of the effect of an ulterior cause. 
Observation, in short, without experiment (and without any aid from 
deduction) can ascertain uniformities, but cannot prove causation. 

In order to see these remarks verified by the actual state of the 
sciences, we have only to think of the condition of natural history. In 
zoology, for example, there is an immense number of uniformities 
ascertained, some of coexistence, others of succession, to rnany of 
which, notwithstanding considerable variations of the attendant circum- 
stances, we know not any exception: but the antecedents, for the 
most part, are such as we cannot artificially produce ; or, if we Can, it 

* Unless, indeed, the consequent was generated not by the antecedent, but by the means 
we employed to produce the antecedent. As, however, these means are under our power, 
there is so far a probability that they are also sufficiently within our knowledge, to enable 
us to judge whether that could be the case or not. 



222 r INDUCTION. 

is only by setting in motion the exact process by which nature pro- 
duces them ; and this being to us a mysterious process, of which the 
main circumstances are not only unknown but unobservable, the name 
of experimentation would here b& completely misapplied. Such are 
the facts : and what is the result 1 That on this vast subject, which 
affords so much and such varied scope for observation, we have not, 
properly -speaking, ascertained a single cause, a single unconditional 
uniformity. We know not, in the case of almost any of the phenom- 
ena that we find conjoined, which is the conditioi;i of the other; which 
is cause, and which effect, or whether either of them is so, or they are 
not rather all of them conjunct effects of causes yet to be discovered, 
complex results of laws hitherto unknown. 

Although some of the foregoing observations may be, in technical 
strictness of arrangement, premature in this place, it seemed that a 
few general remarks upon the difference between Sciences of mere 
Observation and Sciences of Experimentation, and the extreme disad- 
Y-antage under which directly inductive inquiry is necessarily carried 
on in the former, were the best preparation for discussing the methods 
of direct induction; a preparation rendering superfluous much that 
must otherwise have been introduced, with some inconyenience, into 
the heart of that discussion. To the consideration of these Methods 
we now proceed. 



•CHAPTER VIII. 

OF THE FOUR METHODS OF EXPERIMENTAL INaUIRY. 

§ 1. The simplest and most obvious' modes of singling out from 
^niong the, circumstances which precede or follow a phenomenon, 
those with which it is really connected by an invariable law, are two 
in number. One is, by comparing together different instances in which 
the phenomenon occurs. The other is by comparing instances in 
which the phenomenon does occur, with instances in other respects 
similar in which it does not. These two methods may be respectively 
denominated, the Method of Agreement, and the Method of Difference. 

In illustrating these methods it will be necessary to bear in mind 
the two-fold character of inquiries into the laws of phenomena ; which 
may be either inquiries into the cause of a given effect, or into the 
effects or properties of a given cause. We shall consider the methods 
in their application to either order of investigation, and shall draw our 
examples equally from both. 

We shall denote antecedents by the large letters of the alphabet, 
and the consequents -coiTesponding to them_ by the small. Let A, 
then, be an agent or cause,, and let the object of our inquiry be to 
ascertain what are the effects of this cause. If we cail either find, or 
produce, the agent A in such varieties of circumstances, that the 
different cases have no circumstance in common except A ; then, 
whatever effect we find to be produced in all our trials must, it would 
seem, be the effect of A. Suppose, for example, that A is tried alotig 
vl^ith B and C, and that the effect is ahc; and suppose that A is next 



THE FOUR EXPERIMENTAL METHODS. 223 

tried with D and E, but without B and C, and that the effect is ade. 
Then we may reason thus : b and c are not effects of A, for they were 
not produced by it in the second experiment; nor are d and e, for they 
were not produced in the first. Whatever is, really the effect of A 
must have been produced in both instances ; now this condition is 
fulfilled by no circumstance except a. The phenomenon a cannot 
have been the effect of B or C, since it waa produced where they 
were not; lior of 1) or E, since it was produced where they were not. 
Therefore it is the effect of A. 

For example, let the antecedent A be the . contact of an alkaline 
substance and an oil. This combination being tried under several 
varieties of circumstance resembling each other in nothing else, the 
results agree in the production of a greasy and detersive or saponaceous 
substance : it is therefore concluded that the combination of an oil 
and an alkali causes the production .of a soap. It is thus we inquire, 
by the Method of Agreement, into the effect of a given cause. 

In a similar manner we may inquire into the cause of a given effect. 
Let a he the effect. Here, as shown in the last chapter, we have only 
the resource of observation without experiment : we cannot take a 
phenomenon of which we know not the origin, and try to find its mode 
of production by producing it ; if we succeeded in such a random trial 
-it could only be by accident. , But if we can observe a in two difterent 
combinations, abc and ade; and if we know, or can discover, that the 
antecedent circumstances in these cases respectively were ABC and 
ADE; we may conclude by a reasoning similar to that in the pre- 
cedin-g example, that A is the antecedent connected with the consequent 
a by a law of causation. B and C, we may say, cannot be causes of «, 
since on its second occurrence they were not present ; nor are D and E, 
for they were not present on its first occurrence. A, alone of the 
five circumstances, was found among the antecedents of a in both 
instances. 

For example, let the effect a be crystalization. We compare in- 
stances in which bodies are known to assume crystaline structure, but 
which have no other point of agreement ; and we find them to have 
one, and as far as we can observe, only one, antecedent in common : 
the deposition of a solid matter from a liquid state, either a state of 
fusion or of solution. We conclude., therefore, that the solidification 
of a substance from a liquid state is an invariable antecedent of itS' 
crystalization. 

in this example we may go further,.. and say, it is not only the 
invariable antecedent but the cause. For in this case we, are able, 
after detecting the antecedent A, to produce it artificially, and by 
finding that a follows it, verify the result of our induction. The 
importance of thus reversing the proof was never more strikingly 
manifested than when, by keeping a phial of water charged with 
siliceous particles undisturbed for years, a chemist (I believe Dr. 
Wollaston)^ succeeded in obtaining crystals of quartz; and in the 
equally interesting experiment in which Sir James Hall produced 
artificial marble, by the cooling of its materials from fusion under 
immense pressure : two admirable examples of the light which may 
be thrown upon the most secret processes of nature by v/ell-contiived 
interrogation of her. 

But if we cannot artificially produce the phenomenon A, the con- 



224 INDUCTION. 

elusion that it is the cause of a remains subject to very considerable 
doubt. Though an invariable, it may not be the unconditional ante- 
cedent of a, but may precede it as day precedes night or night day. 
This uncertainty arises from the impossibility of assuring ourselves that 
A is the onli/ immediate antecedent common to both the instances. If 
we could be certain of having ascertained all the invariable antece- 
dents, we might be sure that the unconditional invariable antecedent, 
or cause, must be found somewhere among them. ■ Unfortunately it is 
hardly ever possible to ascertain all the antecedents, unless the phe- 
nomenon is one which we can produce artificially. Even then the 
difficulty is merely lightened, not removed : men knew how to raise 
water in pumps long before they adverted to what was really the 
operating circumstance in the means they employed, namely, the 
pressure of tjie atmosphere on the open surface of the water. It is, 
however, much easier to analyze completely a set of arrangements 
made by ourselves, than the whole complex mass of the agencies 
which nature happens to be exerting at the moment when she produ- 
ces any given phenomenon. We may overlook some of the material 
circumstances in an experiment with an electrical machine ; but we 
shall, at the worst, be better acquainted with them than with those of 
a thunder-storm. 

The mode of discovering and proving laws of nature, which we 
have now examined, proceeds upon the following axiom : Whatever 
circumstance can be excluded, without prejudice to the phenomenon, 
or can be absent notwithstanding it presence, is not connected with it 
in the way of causation. The casual circumstances being thus elimi- 
nated, if only one remains, that one is the cause which we are in 
search of: if more than one, they either are, or contain among them, 
the cause : and so, mutatis mutandis, of the effect. As this method 
proceeds by comparing different instances to ascertain in what they 
agree, I have termed it the Method of Agreement : and we may 
adopt as its regulating principle the - following canon: — 

First Canon. 

If two -or more instances of the phenomenon under investigation have 
only one circumstance in common^ the circumstance in which alone all 
the instances agree, is the cause (or effect) of the given phenomenon. 

Quitting for the present the Method pf Agreement, to which we 
shall almost immediately return, we proceed to a still more potent 
insti'ument of the investigation of nature, the Method of Difference. 

§ 2. In the Method of Agreement, we endeavored to obtain in- 
stances which agreed in the given circumstance but differed in every 
other : in the present method we require, on the contrary, two in- 
stances resembling one another in every other respect, but differing in 
the presence or absence of the phenomenon we wish to study. If our 
object be to discover the effects of an agent A, we must procure A in 
some set of ascertained circumstances, as ABC, and having noted the 
effects produced, compare them with the effect of the remaining 
circumstances BC, when A is absent. If the effect of ABC is abc, 
and the effect of BC, he, it is evident that the effect of A is a. So 



THE FOUR EXPERIMENTAL METHODS. 225 

again, if we begin at the other end, and desire to investigate the cause 
of an effect «, we must select an instance, as ahc, in which the effect 
occurs, and in which the antecedents were ABC, and we must look 
out for another instance in which the remaining circumstances, Z>c, 
occur without a. If the antecedents, in that instance, are BC, we 
know that the cause of a must be A : either A alone, or A in conjunc- 
tion with some of the other circumstances present. 

It is scarcely necessary to give examples of a logical process to 
which we owe almost all the inductive conclusions we draw in daily 
life. When a man is shot through the heart, it is by this method we 
know that it was the gun-shot which killed him:, for he was in the 
fullness of life immediately before, all circumstances being the same, 
except the wound. 

The axioms which are taken for granted in this method are evidently 
the following : Whatever antecedent cannot be excluded without pre- 
venting the phenomenon, is the cause, or a condition, of that phenom- 
enon ; Whatever consequent can be excluded, with no other differ- 
ence in the antecedents than the absence of a particular one, is the 
effect of that one. Instead of comparing different instances of a phe- 
nomenon, to discover in what they agree, this method compares an 
instance of its occurrence with an instance of its non-occurrence, to 
discover in what they differ. The canon which is the regulating prin- 
ciple of the Method of Difference may be expressed as follows : — 

Second Canon. 

If an instancy 'iTt which the phenomenon under investigation occurs, 
and an instance in which, it does not occur, have every circumstance save 
one in common, that one occurring only in the former ; the circumstance 
in which alone the two instances differ, is the effect, or cause., or a neces- 
sary part of the cause, of the phenomenon. 

§ 3. The two methods which we have now stated have many features 
of resemblance, but there are also many distinctions between them. 
.Both are methods of elimination. This tei'm (which is employed in 
the theory of equations to denote the process by which one after 
another of the elements of a question is excluded, and the solution 
made to depend upon the relation between the remaining elements 
only,) is well suited to express the operation, analagous to this, which 
has been understood since the time of Bacon to be the foundation of 
experimental inquiry : namely, the successive exclusion of the various 
circumstances which are found to accompany a phenomenon in a given 
instance, in order to ascertain what are those among them which can 
be absent consistently with the existence of the phenomenon. The 
Method of Agreement stands on the ground that whatever can be 
eliminated, is not connected with the phenomenon by any law. The 
Method of Difference has for its foundation, that whatever cau not be 
eliminated, is connected with the phenomenon by a law. 

Of these methods, that of Difference is more particularly a method 
of artificial experiment ; while that of Agreement is more especially 
the resource we employ where experimentation is impossible. A few 
reflections will prove the fact, and point out the reason of it. 

It is inherent in the peculiar character' of the Method of Difference, 
Fp 



226 INDUCTION. 

that the nature of the combinations which it requires is much more 
sti'ictly defined than in the Method of Agreement. The two instances 
which are to be compared with one another must be exactly similar, 
in all circumstances except the one which we are attempting to inves- 
tigate : they must be in the relation of ABC and BC, or of abc and 
be. It is true that this similarity of circumstances needs not extend 
to such as are already known to be immaterial to the result. And in 
the case of most phenomena we leani at once, from the most ordinary 
experience, that most of the coexistent phenomena of the universe 
may be either present or absent without affecting the given phenome- 
non ; or, if present, are present indifferently when the phenomenon 
does not happen, and when it does. Still, even -limiting the identity 
which is required between the two instances, ABC and BG, to such 
circumstances a;s are not already known to be indifferent; it is very 
seldom that nature affords two instances, of which we can be assured 
that they stand in this precise relation to one another. ~ In the spon- 
taneous operations of nature there is generally such complication and 
such obscurity, they are mostly either on so overwhelmingly large or 
on so inaccessibly minute a scale, we are so ignorant of a great part 
of the facts which really take place, and even- those of which we are 
not ignorant are so multitudinous, and therefore so seldom exactly 
alike in any two cases, that a spontaneous experiment, of the kind 
required by the Method of Difference, is commonly not to be found. 
When, on the contrary, we obtain a phenomenon by an artificial 
experiment, a pair of instances such as the method requires is obtained 
almost as a matter of course, provided the process does not last a long 
time. . A certain state of surrounding circumstances existed before we 
commenced the experiment : this is BC. We then introduce A ; say, 
for instance, by merely bringing an object from another part of the 
room, before there has been time for any change in the other ele- 
ments. It is, in short (as M. Cojnte observes), the very nature of an 
experiment, to introduce into the preexisting state of circurnstances a 
change perfectly definite. We choose a previous state of things with 
which we are well acquainted, so that no unforeseen alteration in that 
state is likely to pass unobserved ; and into this we introduce, as 
rapidly as possible, the phenomenon which we wish to study ;, so that 
we in general are entitled to feel complete assurance, that the pre- 
existing state, and the state which we have produced, differ in nothing 
except in the presence or absence of that phenomenon. If a bird is 
taken from a cage, and instantly plunged into carbonic, acid gas, the 
experimentalist maybe fully -assured (at all ev.ents after one or two 
repetitions) that no cii'curastance capable of causing suffocation had 
supervened in the interim, except the change from immersion in the 
atmosphere to immersion in carbonic acid gas. There is one doubt, 
indeed, which may remain in some cases of this description ; the 
effect may have been produced not by the. change, but by the means 
we employed to produce the change. The possibility, however, of this 
last supposition generally admits of being conclusively tested by other 
experiments. It thus appears that in the study of the various kinds 
of phenomena which we can, by our voluntary agency, modify or 
control, we can in general satisfy the requisitions of the Method of 
Difference; but that by the spontaneous operations of nature those 
requisitions are seldom fulfilled. 



THE FOUR EXPERIAJENTAL METHODS. 227 

The reverse of this is the case with the Method of Agreement. 
We do not here require instances of so special and determinate a kind. 
Any instances whatever, in which nature presents us with a phenom- 
enon, may be examined for the purposes of this method ; and if all 
such instances agree in anything, a conclusion of considerable value is 
already attained. We can seldom, indeed, be sure that this one point 
of agreement is the only one ; but our ignorance does not, as in the 
Method of Difference, vitiate the conclusion-; the certainty of the 
result, as far as it goes, is not affected. We have ascertained one 
invariable antecedent or consequent, however many other invariable 
antecedents or consequents may still remain unascertained. If ABC, 
ABE, A FG, are all equally followed by a, then a is an invariable 
consequent of A. li ahc, ade, afg, all number A among their ante- 
cedents, then A is connected as an antecedent, by some invariable 
law, with a. But to determine whether this invariable antecedent is 
a cause, or this invariable consequent an effect, we must be able, in 
addition, to produce the one by means of the other ; or, at least, to obtain 
that which alone constitutes our assurance of having produced, any- 
thing, namely, an instance in which the effect, a, has come into exist- 
ence, wdtli no other change in the preexisting circumstances than the 
addition of A. And this, if. we can do it, is an application of the 
Method of Difference, not of the Method of Agreement. 

It thus appears to be by the Method of Difference alone that we can 
ever, in the way of direct experience, arrive with certainty at causes. 
The Method of Agixement leads only to laws of phenomena, as Mr. 
Whewell calls them, but which (since laws of causation are also laws 
of phenomena) I prefer to designate as uniformities in which the ques- 
tion of causation must for the present remain undecided. The Method 
of Agreement is chiefly to be resorted to, as a means of suggesting 
applications of the Method of Difference (as in the last example the com- 
parison of ABC, ADE, AFG-, suggested that A was the antecedent 
on which to try the experiment whether it could produce «) ; or, as an 
inferior resource, in case the Method of Difference is impracticable ; 
which, as we before showed generally arises from the impossibility of 
artificially producing the phenomena. And' hence it is that the Method 
of Agreement, although applicable in principle to either case, is more 
, emphatically the method of investigation on those subjects where arti- 
ficial experimentation is impossible ; because on those it is, generally, 
our only resource of a directly inductive nature ; while, in the phenome- 
na which we can produce at pleasure, the Method of Difference gene- 
rally affords a more efficacious process, which will ascertain causes as 
well as mere laws. 

§ 4. Our next remark shall be, that there are inany cases in which, 
although our power of producing the phenomenon is complete, the 
Method of Difference either cannot be made available at all, or not 
without a previous employment of the Method of Agreement. This 
occurs when the agency by which we can produce the phenomenon is 
not that of one single antecedent, but a combination of antecedents, 
which we have noj)ower of separating fi.-om each other and exhibiting 
apart. For instance, suppose the subject of inquiry to be the cause of 
the double refi'action of light. We can produce this phenomenon at 
pleasure, by employing any one of the many substances which are 



228 INDUCTION. 

known to refract light in that peculiar manner. But if, taking one of 
those substances, as Iceland spar for example, we wish to determine 
on which of the properties of Iceland spar this remarkable phenomena 
depends, we can make no use, for that purpose, of the Method of Dif- 
ference ; for we cannot find another substance precisely resembling 
Iceland spar except in some one property. The only mode, therefore, 
of prosecuting this inquiry is that afforded by the Method of Agree- 
ment ; by which, in fact, through a comparison of all the known sub- 
stances which had the property of doubly refracting light, it was ascer- 
tained that they agreed in the single circumstance of being crystaline 
substances ; and although the converse does not hold, although all crys- 
taline substances have not the property of double refraction, it was 
concluded, with reason, that there is a real connexion between these 
two properties; that either crystaline structure, .or the cause which 
gives rise to that structure, is one of the conditions of double refraction. 

Out of this employment of the Method of Agreement arises a pecu- 
liar modification of that method, which is sometimes of great avail in 
the investigation of nature. In cases similar to the above, in which it 
is not possible to obtain the precise pair of instances which our second 
canon requires — instances agreeing in every antecedent except A, or in 
every consequent except a ; we may yet be able, by a double employ- 
ment of the Method of Agreement, to discover in what the instances 
which contain A or a, differ from those which do not. 

If we compare various instances in which a occurs, and find that 
they all have in common the circumstance A, and (as far as can be 
observed) no other circumstance, the Method of Agi-eement, so far bears 
testimony to a connexion between A and a. In order to convert this 
proof of connexion into proof of causation by the direct Method of 
Difference, we ought to be able in some one of these instances, as for 
example ABC, to leave out A, and observe whether by doing so, a is 
prevented. Now supposing (what is often the case) that we are not 
able to try this decisive experiment; yet, provided we can by any 
means discover what would be its result if we could try it, the advan- 
tage will be the same. Suppose, then, that a§ we previously examined 
a variety of instances in which a occuiTed, and found them to agree in 
containing A, so we now observe a variety of instances in which a does 
not occur, and find them agree in 7iot containing A ; which establishes, 
by the Method of Agreement, the same connexion between the absence 
of A and the absence of a, which was before established between their 
presence. As, then, it had been shown that whenever A is present a 
is present, so it being now shown that when A is taken away a is re- 
moved along with it, we have by the one proposition ABC, ahc, by 
the other BC, be, the positive and negative instances which the Method 
of Difference requires. Thus, if it be true that all animals which have 
a well-developed respiratory system, and therefore aerate the blood 
perfectly, agree in being warm-blooded, while those whose respiratory 
system is imperfect do not maintain a temperature much exceeding 
that of the surrounding medium, we may argue from this two-fold expe- 
rience, that the change which takes place in the blood by respiration 
is the cause of animal heat. 

This method may be called the Indirect Method of Difference, or 
the Joint Method of Agreement and Difference ; and consists in a double 
employment of the Method of Agreement, each proof being indepen- 



THE FOUR EXPERIMENTAL METHODS. 229 

dent of the other, and corroborating it. But it is not equivalent to a 
proof by the direct Method of Difference. For the requisitions of the 
Method of Difference are not satisfied, unless we can be quite sure 
either that the instances affirmative of a agree in no antecedent what- 
ever but A, or that the instances negative of a agree in nothing but the 
negation of A. Now if it were possible, which it never is, to have this 
assurance, we should not need the joint method; for either of the two 
sets of instances separately would then be sufficient to prove causation. 
This indirect method, therefore, can only be viewed as a gi'eat exten- 
sion and improvement of the Method of Agreement, but not as partici- 
pating in the more cogent nature of the Method of Difference. The 
following may be stated as its canon : — 

' Third Canon. 

If two or more instances in which the phenomenon occurs have only 
one circumstance in common^ while two or more instances in which it does 
not occur have nothing in common, save the absence of that circumstaiice ; 
the circumstance in which alone the two sets of instances differ^ is the 
effect, or cause, or a necessary part of the cause, of the phenomenon. 

We shall presently show that the Joint Method of Agreement and 
Difference constitutes, in another respect not yet adverted to, an im- 
provement upon the common Method of Agreement, namely, in being 
unaffected by a characteristic imperfection of that method, the nature 
of which still remains to be pointed out. But as we cannot enter into 
this exposition without introducing a new element of complexity into 
this long and intricate discussion, I shall postpone it to the next chapter, 
and shall at once proceed to the statement of two other methods, 
which will complete the enumeration of the means which mankind 
possess for exploring tHe laws of nature by specific observation and 
experience. 

§ 5. The first of these has been aptly denominated the Method of 
Residues. Its principle is very simple. Subducting from any given 
phenomenon all the portions which by virtue of preceding inductions, 
can be assigned to known causes, the remainder will be the effect of 
the antecedents which had been overlooked, or of which the effect was 
as yet an unknown quantity. 

Suppose, as before, that we have the antecedents ABC, followed 
by the consequents ahc, and that by previous inductions, (founded, we 
will suppose, upon the Method of Difference,) we have ascertained the 
causes of some of these effects, or the effects of some of these causes ; 
and are by this means apprised that the effect of A is a, and that the 
effect of B is h. Subtracting the sum of these effects from the total 
phenomenon, there remains c, which now, without any fresh experi- 
ment, we may know to be the effect of C. This Method of Residues 
is in ti-uth a peculiar modification of the Method of Difference. If the 
instance ABC, abc, could have been compared with a single instance 
AB, ab, we should have proved C to be the cause of c, by the com- 
mon process of the Method of Difference. In the present case, how» 
ever, instead of a single instance A B, we have had to study separately 
the causes A and B, and to infer from the effects which they produce 



230 INDUCTION. 

separately, what effect tliey must produce in the case ABC where 
they act together. Of the two instances, therefore, which the Method 
of Difference requires — the one positive, the other negative — -the nega- 
tive one, or that in which the given phenomenon is absent, is not the 
direct result of observation and experiment, but has been arrived at 
by deduction. As one of the forms of the Method of Difference, the 
Method of Residues partakes of its rigorous certainty, provided the 
previous inductions, those which gave the effects of A and B, were ob- 
tained by the same infallible method, and provided we are certain that 
C is the only antecedent to which the residual phenomenon c can be 
referred ; the only agent of which we had not already calculated and 
subducted the effect. But as we can never be quite certain of this, 
the evidence derived from the Method of Residues is not complete, 
unless we can obtain C artificially and try it separately, or unless its 
agency, when once suggested, can be accounted for, and proved de- 
ductively, from known laws. 

Even with these reservations, the Method of Residues is one of the 
most important among our instruments of discovery. Of all the methods 
of investigating laws of nature, this is the most fertile in unexpected 
results ; often informing us of sequences in which neither the cause nor 
the effect were sufficiently conspicuous to attract of themselves the 
attention of observers. The agent C may be an obscure circumstance, 
not likely to have been perceived unless sought for, nor likely to have 
been sought for until attention had been awakened by the insufficiency 
of the obvious causes to account for the whole of the effect. And c 
may be so disguised by its intermixture with a and h, that it would 
scarcely have presented itself spontaneously as a subject of separate 
study. Of these uses of the method, we shall presently cite some 
remarkable examples. The canon of the Method of Residues is as 
follows : — 

Fourth Canon. 

Suhduct from any phenomenon such part as is known by previous 
inductions to be the effect of certain antecedents, and the residue of the 
phenomenon is the effect of the remaining antecedents. 

§ 6. .There remains a class of laws which it is impracticable to 
ascertain by any of the three /methods which I have attempted to 
characterize ; namely, the laws of those Permanent Causes, or inde- 
structible natural agents, which it is impossible either to exclude or to 
isolate : which we can neither hinder from being present, nor contrive 
that they should be present alone. It would appear at first sight that 
we could by no means separate the effects of these agents from the 
effects of those other phenomena with which they cannot be prevented 
from coexisting. In respect, indeed, to most of the permanent causes, 
no such difficulty exists ; since, though wo cannot eliminate them as 
coexisting facts, we caji eliminate them as influencing agents, by 
simply trying our experiment in a local situation beyond the limits of 
their influence. The pendulum, for example, has its oscillations 
disturbed by the vicinity of a mountain ; we remove the pendulum to 
a sufficient distance from the mountain, and the disturbance ceases: 
from these data we can determine by the Method of Difference, the 
amount of effect really due to the mountain ; and beyond a certain 



THE FOUR EXPERIMENTAL METHODS. 231 

distance everything goes on precisely as it would do if the mountain 
exercised no influence whatever, which, accordingly, we, with sufficient 
reason, conclude to be the fact. 

The difficulty, therefore, in applying the methods already treated of 
to determine the effects of Permaneni Causes, is confined to the cases 
in which it is impossible for us to get out of the local limits of their 
influence. The pendulum can be removed from the influence of the 
mountain, but it cannot be removed from the influence of the earth : 
we cannot take away the earth from the pendulum, nor the pendulum 
from the earth, to ascertain whether it would continue to vibrate if the 
action which the earth exerts upon it were withdrawn. On what 
evidence, then, do we ascribe its vibrations to the .earth's influence ^ 
Not on any sanctioned by the Method of Difference ; for one of 
the two instances, the negative instance, is wanting. Nor by the 
Method of Agreement ; for although all pendulums agree in this, that 
during their oscillations the earth is always present, why may we, not 
as well ascribe the phenomenon to the sun, which is equally a co- 
existent fact in all the experiments ? It is evident that to establish 
even so simple a fact of causation as this, there was required some 
method over and above those which we have yet examined. 

As another example, let us take the phenomenon Heat. Independ- 
ently of all hypothesis as to the real nature of the agency so called, 
this fact is certain, that we are unable to exhaust any body of the whole 
of its heat. It is equally certain that no one ever perceived heat not 
emanating from a body. Being unable, then, to separate Body and Heat, 
we cannot effect such a variation of circumstances as the foregoing three 
methods require ; we cannot ascertain, by those methods, what por- 
tions of the phenomena exhibited by any body are due to the heat con- 
tained in it. If we could observe a body with its heat, and the same 
body entirely divested of heat, the Method of Difterence would show 
the effect due to the heat, apart from that due to the body. If we 
could observe heat under circumstances agreeing in nothing but heat, 
and therefore not characterized also by the presence of a body, we 
could ascertain the effects of heat, from an instance of heat with a body 
and an instance of heat without a body, by the Method of Agi'eement ; 
or, if we pleased, we could determine by the Method of Difference 
what effect was due to the body, when the remainder which was due to 
the heat would be given by the Method of Residues. But we can .do 
none of these things ; and without them the application of any of the 
three methods to the solution of this problem would be illusory. It 
would be idle, for instance, to attempt to ascertain the effect of heat by 
subtracting from the phenomena exhibited by a body, all that is due to 
its other properties ; for as we have never been able to observe any 
bodies without a portion of heat in them, the effects due to that heat 
may form a part of the very results, which we affect to subtract in order 
that the effect of heat may be shown by the residue. 

If, therefore, there were no other methods of experimental investi- 
gation than these three, we should be for ever unable to determine 
the effects due to heat as a cause. But we have still a resource. 
Though we cannot exclude an antecedent altogether, we may be able 
to produce, or nature may produce for us, some modification in it. By 
a. modification is here meant, a change in it, not amounting to its total 
removal. If some modiiication in the antecedent A is always followed 



232 INDUCTION. 

by a change in the consequent a, the other consequents h and c re- 
maining the same ; or, vice versd, if every change in a is found to have 
been preceded by some modification in A, none being observable in 
any of the other antecedents ; we may safely conclude that a is, wholly 
or in part, an effect traceable to A, or at least in some way connected 
with it through causation. For example, in the case of heat, though 
we cannot expel it altogether from any body, we can modify it in quan- 
tity, we can increase or diminish it ; and doing so, we find by ihe va- 
rious methods of experimentation or observation already treated of, 
that such increase or diminution of heat is followed by expansion or 
contraction of the body. In this manner we arrive at the conclusion, 
otherwise unattainable by us, that one of the effects of heat is to enlarge 
the dimensions of bodies ; or what is the same thing in other words, to 
widen the distances between their particles. 

A change in a thing, not amounting to its total removal, that is, a 
change which leaves it still the same thing it was, must be a change 
either in its quantity, or in some of its relations to other things, of 
which relations the principal is its position in space. In the previous 
example, the modification which was produced in the antecedent was 
an alteration in its quantity. Let us now suppose the question te- 
be, what influence the moon exerts on the surface of the earth. We 
cannot try an experiment in the absence of the moon, so as to observe 
what terrestrial phenomena her annihilation would put an end to; 
but when we find that all the variations in the position of the moon are 
followed by con-esponding variations in the time and place of high 
water, the place being always either on the side of the earth which is 
nearest to, or on that which is most remote from, the moon, we have 
ample evidence that the moon is, wholly or partially, the cause which 
determines the tides. It very commonly happens, as it does in this 
instance, that the variations of an effect are correspondent, or anal- 
ogous, to those of its cause ; as the moon moves further towards the 
east, the high water point does the same : but this is not an indis- 
pensable condition; as may be seen in the same example, for along 
with that high water point, there is at the same instant another high 
water point diametrically opposite to it, and which, therefore, of 
necessity, moves towards the west as the moon followed by the 
nearer of the tide waves advances towards the east : and yet both 
these motions are equally effects of the moon's motion. 

That the oscillations of the pendulum are caused by the earth, is 
proved by similar evidence. Those oscillations take place between 
equidistant points on the two sides of a line, which, being perpendic- 
ular to the earth, varies with every variation in the earth's position, 
either in space or relatively to the object. Speaking accurately, we 
only know by the method now characterized, that all terrestrial 
bodies tend to the earth, and not to some unknown fixed point 
lying in the same direction. In every twenty-four hours, by the 
earth's rotation, the line drawn from the body at right angles to the 
earth coincides successively with all the radii of a circle, and in the 
course of six months the place of that circle varies by nearly two 
hundred millions of miles; yet in all these changes of the earth's posi- 
tion, the line in which bodies tend to fall continues to be directed to- 
wards it : which proves that terrestrial gravity is directed to the earth, 
and not, as was once fancied by some, to a fixed point of space. 



THE FOUR EXPERIMENTAL METHODS. 233 

The method by which these results -were obtained, may be termed 
the Method of Concomitant Variations : it is regulated by the follow- 
ing canon : — 

Fifth Canon. 

Whatever phenomenon varies in any manner whenever another 
phenomenon varies in some particular manner, is either a cause or an 
effect of that phenomenon^ or is connected with it through some fact 
of causation. 

The last clause is subjoined, because it by no means follows when 
two phenomena accompany each other in their variations, that the 
one is causQ and the other effect. The same thing may, and indeed 
must happen, supposing them to be two different effects of a common 
cause : and by this method alone it would never be possible to ascer- 
tain which of the two suppositions is the true one. The only way to 
solve the doubt would be that which we have so often adverted to, 
viz., by endeavoring to ascertain whether we can produce the one 
set of variations by means of the other. In the case of heat, for 
example, by increasing the temperature of a body we increase its 
bulk, but by increasing its bulk we do not increase its temperature ; 
on the contrary (as in the rarefaction of air under the receiver of an 
air-pump), we generally diminish it : therefore heat is not an effect, 
but a cause, of increase of bulk. If we cannot ourselves produce 
the variation^, we must endeavor, though it is an attempt which is 
seldom successful, to find them produced by nature in some case 
in which the preexisting circumstances are perfectly known to us. 

It is scarcely necessary to say, that in order to ascertain the uniform 
concomitance of variations in the effect with variations in the cause, the 
same precautions must be used as in any other case of the determina- 
tion of an invariable sequence. We must endeavor to retain all the 
other antecedents unchanged, while that particular one is subjected to 
the requisite series of variations ; or in other words, that we may be 
warranted in inferring causation from concomitance of variations, the 
concomitance itself must be proved by the Method of Difference. 

It might at first appear that the Method of Concomitant Variations 
assumes a new axiom, or lavv^ of causation in general, namely, that 
every modification of the cause is followed by a change in the effect. 
And it does usually happen that when a phenomenon A causes a phe- 
nomenon a, any variation in the quantity or in the various relations of 
A, is uniformly followed by a variation in the quantity or relations of 
a. To take a familiar instance, that of gravitation. The sun causes a 
certain tendency to motion in the earth ; here we have cause and effect; 
but that tendency is towards the sun, and therefore varies in direction 
as the sun varies in the relation of position; and moreover the tendency 
varies in intensity, in a certain numerical ratio to the sun's distance 
from the earth, that is, according to another relation of the sun. 
Thus we see that there is not only an invariable connexion between 
the sun and the earth's gi'avitation, but that two of the relations of the 
sun, its position with respect to the earth and its distance from the 
earth, are invariably connected as antecedents with the quantity and 
direction of the earth's gi'avitation. The cause of the earth's gravita- 

G G , 



234 INDUCTION. 

ting at ally is simply the sun; but the cause of her gravitating with a 
given intensity and in a given direction, is the existence of the sun in 
a given direction and at a given distance. It is not strange that a modi- 
fied cause, which is in truth a different cause, should produce a differ- 
ent effect. But as the cause is only different in its quantity, or in some 
of its relations, it usually happens that the effect also is only changed 
in its quantity or its relations. 

Although it is for the most part true that a modification of the cause 
is followed by a modification of the effect, the Method of Concomitant 
Variations does not, however, presuppose this as an axiom. It only 
requires the converse proposition; that anything upon whose modifica- 
tions, modifications of an effect are invariably consequent, must be the 
cause (or connected with the cause) of that effect; a proposition, the 
truth of which is evident; for if the thing itself had no influence on the 
effect, neither could the modifications of the thing have any influence. 
If the stars have no power over the fortunes of men, it is implied in the 
very terms, that the conjunctions or oppositions of different stars can 
have no such power. 

Although the most striking applications of the Method of Concomi- 
tant Variations take place in the cases in which the Method of Differ- 
ence, strictly so called, is impossible, its use is not confined to those 
cases ; it may often usefully follow after the Method of Difference, to 
give additional precision to a solution which that has found. When 
by the Method of Difference it has first been ascertained that a cer- 
tain object produces a certain effect, the Method of Concomitant Va- 
riations may be usefully called in to determine according to what 
law the quantity or the different relations of the effect follow those of 
the cause. 

§ 7. The case in which this method admits of the most .extensive 
employment, is that in which the variations of the cause are variations 
of quantity. Of such variations we may in general affirm with safety, 
that they will be attended not only with Variations, but with similar 
variations, of the effect : the proposition, that moi'e of the cause is 
followed by more of the effect, being a corollary from the principle of 
the Composition of Causes, which, as we have seen, is the general 
rule of causation; cases of the opposite description, in which causes 
change their properties on being conjoined with one another, being, on 
the contrary, special and exceptional. Suppose, then, that when A 
changes in quantity, a also changes in quantity, and in such a manner 
that we can trace the numerical relation which the changes of the one 
bear to such changes of the other as take place within our limits of 
observation. We may then, with certain precautions, safely conclude 
that the same numerical relation will hold beyond those limits. If, for 
instance, we find that when A is double, a is double ; that when A is 
treble or quadruple, a is treble or quadruple ; we may conclude that 
if A were a half or a third, a would be a half or a third, and finally, 
that if A were annihilated, a would be annihilated, and that a is wholly 
the effect of A, or wholly the effect of the same cause with A, And 
so with any other numerical relation according to which A and a would 
vanish simultaneously; as for instance if a were proportional to the 
square of A. If, on the other hand, a is not wholly the effect of A, 
but yet vai'ies when A vai'ies, it is probably (to use a mathematical 



THE FOUR EXPERIMENTAL METHODS. 235 

pbrase) a function not of A alone but of A and sometbing else : it3 
cbanges will be sucb as would occur if part; of it remained constant, 
or varied on some o:ber principle, and tbe remainder varied in some 
numerical relation to tbe variations of A. In tbat case, wben A dimiri- 
isbes, a will seem to approacb not towards zero, but towards some 
other limit : and wben the series of variations is such as to indicate 
what that limit is, if constant, or the law of its variation if variable, 
the limit will exactly measure how much of a is tbe effect of some 
other and independent cause, and tbe remainder will be the effect of A 
(or of the cause of A). ^ 

These conclusions, however, must not be drawn without certain 
precautions. In the first place, the possibility of drawing them at all, 
manifestly supposes that we are acquainted not only with the variations, 
but with the absolute quantities, both of A and a. If we do not know 
the total quantities, we cannot, of course, determine the real numerical 
relation according to which those quantities vary. It is therefore an 
error to conclude, as some have concluded, that because increase of 
heat expands bodies, that is, increases the distance between their 
particles, therefore that distance is wholly the effect of heat, and that 
if we could entirely exhaust the body of its heat, the particles v/ould 
be in complete contact. This can never be more than a guess, and of 
tbe most hazardous sort, not a legitimate induction: for since we 
neither know how much heat there is in any body, nor what is the real 
distance between any two of its particles, we cannot judge whether the 
contraction of the distance does or does not follow the diminution of 
the quantity of heat according to sucb a numerical relation that the two 
quantities would vanish simultaneously. 

In contrast with this, let us consider a case in which the absolute 
quantities are known; the case contemplated in the first law of motion; 
viz., that all bodies in motion continue to move in a straight line with 
uniform velocity until acted upon by some new force. This assertion 
is in open opposition to first appearances; all terrestrial objects, when 
in motion, gradually abate their velocity and at last stop; which 
accordingly the ancients, with their inductio per enumerationem sim- 
plicem, imagined to be the law. Every moving body, however, 
encounters various obstacles, as friction, the resistance of the atmos- 
phere, &c., which we know by daily experience to be causes capable 
of destroying motion. It was suggested that the whole of the retard- 
ation might be owing to these causes. How was this inquired into ] 
If the obstacles could have been, entirely removed, the case would 
have been amenable to the Method of Difference. They could not be 
removed, they could only be diminished, and the case, therefore, 
admitted only of the Method of Concomitant Variations. This accord- 
ingly being employed, it was found that every diminution of the 
obstacles diminished the retardation of the motion : and inasmuch as 
in this case (unlike the case of heat) the total quantities both of the 
antecedent and of the consequent were known ; it was practicable to 
estimate, with an approach to accuracy, both the amount of the retard- 
ation and the amount of the retarding causes, or resistances, and to 
judge how near they both were to being exhausted; and it appeared 
that the effect dwindled as rapidly, and at each step was as far on the 
road towards annihilation, as the cause was. The simple oscillation 
of a weight suspended fi-om a fixed point, and moved a little out of the 



238 ' . INDUCTION. 

perpendicular, wliich in ordinary circumstances lasts but a few minutes, 
was prolonged in Borda's experiments to more than thirty hours, by 
diminishing as much as possible the friction at the point of suspension, 
and by making the body oscillate in a space exhausted as nearly as 
possible of its air. There could therefore be no hesitation in assign- 
ing the whole of the retardation of motion to the influence of the 
obstacles ; and since, after subducting this retardation from the total 
phenomenon, the remainder was an uniform velocity, the result was 
the proposition known as the first law of motion. 

There is also another characteristic uncertainty affecting the infer- 
ence that the law of variation which the quantities observe within our 
limits of observation, will hold beyond those limits. There is of 
course, in the first instance, the possibility that beyond the limits, and 
in circumstances, therefore of which we have no direct experience, 
some counteracting cause might develop itself; either a new agent, or 
a new property of the agents concerned, which lies dormant in the 
circurnstances we are able to observe. This is an element of uncer- 
tainty which enters largely into all our predictions of effects ; but it is 
not peculiarly applicable to the Method of Concomitant Variations. 
The uncertainty, however, of which I am about to speak, is character- 
istic of that method; especially in the cases in which the extreme 
limits, of our observation are very narrow, in comparison with the 
possible variations in the quantities of the phenomena. Any one who 
has the slightest acquaintance with mathematics, is aware that very 
different laws of variation may produce numerical results which differ 
but slightly from one another within narrow limits ; and it is often 
only when the absolute amounts of variation are considerable, that the 
difference between the results given by one law and by another, be- 
comes appreciable. When, therefore, such variations in the quantity 
of the antecedents as we have the means of observing, are but small in 
comparison with the total quantities, there is much danger lest we 
should mistake the numerical law, and be led quite to miscalculate the 
variations which would take place beyond the limits; a miscalculation 
which would vitiate any conclusion respecting the dependence of the effect 
upon the cause, which could be founded upon those variations. Exam- 
ples cire not wanting of such mistakes. " The formulse," says Sir John 
Herschel,* " which have been empirically deduced for the elasticity of 
steam (till very recently), and those for the resistance of fluids, and 
other similar subjects," when relied on beyond the limits of the obser- 
vations from which they were deduced, " have almost invariably failed 
to support the theoretical structures which have been erected on them." 

Under this uncertainty, the conclusion we may draw from the con- 
comitant variations of a and A, to the existence of an invariable and 
exclusive connexion between them, or to the permanency of the same 
numerical relation between their variations when the quantities are 
much greater or smaller than those which we have had the means of 
observing, cannot be considered to rest upon a complete induction. 
All that in such a case can be regarded as proved on the subject of 
causation, is that there is some connexion between the two phenomena ; 
that A, or something which can influence A, must be one of the causes 
which collectively deteiinine a. We may, however, feel assured that 

* Discourse on the Study of Natural Philosophy, p. 179. 



EXAMPLES OF THE FOUR METHODS. 237 

the relation which we have observed to exist between the variations 
of A and a, will hold true in all cases which fall between the same 
extreme limits ; that is, wherever the utmost increase or diminution in 
which the result has been found by observation to coincide with the 
law, is not exceeded. 

The four methods which it has now been attempted to describe, are 
the only possible modes of experimental inquiry, of direct induction 
d posteriori, as distinguished from deduction : at least I know not, nor 
am able to conceive, any others. And even of these, the Method of 
Residues, as we have seen, is not independent of deduction; though, as 
it requires specific experience in addition, it may, without impropriety, 
be included among methods of direct observation and experiment. 

These, then, with such assistance as can be obtained from Deduction, 
compose the available resources of the human mind for ascertaining 
the laws of the succession of phenomena. Before proceeding to point 
out certain circumstances, by which the employment of these methods 
is subjected to an immense increase of complication and of difficulty, 
it is expedient to illustrate the use of the methods, by suitable 
examples, drawn from actual physical investigations. These, accord- 
ingly, will form the subject of the succeeding chapter. 



CHAPTER IX. 

MISCELLANEOUS EXAMPLES OF THE FOUR METHODS, 

§ 1. I SHALL select, as my first example, an interesting speculation 
of one of the most eminent theoretical chemists of the present or any 
age, Dr. Liebig. The object in view, is to ascertain the immediate 
cause of the death produced by metallic poisons. 

Arsenious acid, and the salts of lead, bismuth, copper, and mercury, 
if introduced into the animal organism, except in the smallest doses, 
destroy life. These facts have long been known, as insulated truths of 
the lowest order of generalization ; but it was reserved for Liebig, by 
an apt employment of the first two of our methods of experimental 
inquiry, to connect these truths together by a higher induction, point- 
ing out what property, common to all these deleterious substances, is 
the really operating cause of their fatal effect. 

When solutions of these substances are placed in sufficiently close 
contact with many animal products, albumen, milk, muscular fibre, 
and animal membranes, the acid or salt leaves the water in which 
it was dissolved, and enters into combination with the animal sub- 
stance ; which substance, after being thus acted upon, is found to have 
lost its tendency to spontaneous decomposition, or putrefaction. 

Observation also shows, in cases where death has been produced by 
these poisons, that the parts of the body with which the poisonous 
substances have been brought into contact, do not afterwards putrefy. 

And, finally, when the poison has been supplied in too small a quan- 
tity to destroy life, eschars are produced, that is, certain superficial 
portions of the tissues are destroyed, which are afterwards thrown off 
by the reparative process taking place in the healthy parts. 



238 INDUCTION. 

These three sets of instances admit of being treated according to the 
Method of Agreement. In all of them the metallic compounds are 
brought into contact with the substances which compose the human or 
animal body ; and the instances do not seem to agree in any other cir- 
cumstance. The remaining antecedents are as different, and even 
opposite, as they could possibly be made; for in some the animal sub- 
stances exposed to the action of the poisons are in a state of life, in 
others only in a state of organization, in others not even in that. And 
what is the result which follows in all Ihe cases 1 The conversion of 
the animal substance (by combination with the poison) into a chemical 
compound, held together by so powerful a force as to resist the subse- 
quent action of the ordinary causes of decomposition. Now organic 
life (the necessary condition of sensitive life) consisting in a continual 
state of decomposition and recomposition of the different organs and 
tissues ; whatever incapacitates them for this decomposition destroys 
life. And thus the proximate cause of the death produced by this 
description of poisons, is ascertained, as far as the Method of Agree- 
ment can ascertain it. - 

Let us now bring our conclusion to the test of the Method of Differ- 
ence. Setting out from the cases already mentioned, in which the antece- 
dent is, the presence of substances forming with the tissues a compound 
incapable of putrefaction (and a fortiori incapable of the chemical 
actions which constitute life), and the consequent is death, either of 
the whole organism, or of some portion of it ; let us compare with these 
cases other cases, as much resembling them as possible, but in w^hich 
that effect is not produced. And, first of all, " many insoluble basic 
salts of arsenious acid are known not to be poisonous. The substance 
called alkargen, discovered by Bunsen, which contains a very large 
quantity of arsenic, and approaches very closely in composition to the 
organic arsenious compounds found in the body, has not the slightest 
injurious action upon' the organisna." Now when these substances are 
brought into contact with the tissues in any way, they do not combine 
with them; they do not arrest their progress to decomposition. As far, 
therefore, as these instances go, it, appears that when the effect is 
absent, it is by reason of the absence of that antecedent which we had 
already good ground for considering as the proximate cause. 

But the rigorous conditions of the Method of Difference are not yet 
satisfied ; for we cannot be sure that these unpoisonous bodies agree 
with the poisopous substances in every property, except the particular 
one, of entering into a difficultly decomposable compound with the 
animal tissues. To render the method strictly applicable, we need an 
instance, not of a different substance, but of one of the very same sub- 
stances, under circumstances which would prevent it from forming, 
with the tissues, the sort of compound in question ; and then, if death 
does not follow, our case is made out. Now such instances are afforded 
by the antidotes to these poisons. For example, in case of poisoning 
by arsenious acid, if hydrated peroxide of iron is administered, the 
destructive agency is instantly checked. Now this peroxide is known 
' to combine with the acid, and form a c'ompound, which, being in- 
soluble, cannot act at all on animal tissues. So, again, sugar is 
a well-known antidote to poisoning by salts of copper; and sugar 
reduces those salts either into metallic copper, or into the red sub- 
oxide, neither of which enters into combination with animal matter. 



EXAMPLES OF THE FOUR METHODS. 239 

The disease called painter's colic, so common in manufactories of 
white lead, is unknown where the workmen are accustomed to take, 
as a preservative, sulphuric-acid-lemonade (a solution of sugar ren- 
dered acid by sulphuric acid). Now dilated sulphuric acid has the 
property of decomposing all compounds of lead with organic matter, and 
(of course) of preventing them from being formed. 

There is another class of instances, of the nature required by the 
Method of Difference, which seem at first sight to conflict with the 
theory. Soluble salts of silver, such for instance as the nitrate, have, 
the same stiffening antiseptic effect on decomposing aiiimal, substances 
as corrosive sublimate and the most deadly metallic poisons ; and when 
applied to the external parts of the^ body, the nitrate is a powerful 
caustic, depriving those parts of all active vitality, and^ causing them to 
be thrown off by the neighboring living structures, in the form of an 
eschar. The nitrate and the other- salts of silver ought, then, it would 
seem, if the theory be correct, to be poisonous; yet they may be ad- 
ministered internally with perfect impunity. From this apparent 
exception arises the strongest confirmation which this theory of Liebig 
has yet received. Nitrate of silver, in spite of its chemical properties, 
does not poison when introduced into the stomach ; but in the stomach, 
as in all animal liquids, there is common salt ; and in the stomach 
there is also free muiiatic acid. These substances operate as natural 
antidotes, combining with the nitrate, and if its quantity is not too great, 
immediately converting it into chloride of silver ; a substance very 
slightly soluble, and therefore incapable of combining with the tissues, 
although to the extent of its solubility it has a medicinal influence, 
through an entirely different class of organic actions, 

§ 2. The preceding instances have afforded an induction of a high 
order of conclusiveness, illustrative of the two simplest of our four 
methods ; although not rising to the maximum of certainty which the 
Method of Difference, in its most perfect exemplification, is. capable of 
affording. For (let us not forget) the positive instance and the neg- 
ative one which the rigOr of that method requires, ought to differ only 
in the presence or absence of one single circumstance. Now, in the 
preceding argument, they differ in the presence or absence not of a sin- 
gle circmnstance, but of a single suhstance : and as every substance has 
innumerable properties, there is no knowing what number of real dif- 
ferences are involved in what is nominally and apparently only one - 
difference. It is conceivable that the antidote, the peroxide of iron for 
example, may counteract the poison through some other of its proper- 
ties than that of forming an insoluble compound with it; and if so, the 
theory would fall to the ground, so far as it is supported by that in- 
stance. This source of uncertainty, which is a' serious hindrance to 
all extensive generalizations in chemistry, is however reduced in the 
present case to almost the lowest degree possible, when we find that 
not only one substance, but many substances, possess the capacity of 
acting as antidotes to metallic poisons, and that all these agi'ee in the 
property of forming insoluble compounds with the poisons, while they' 
cannot be ascertained to agree in any other property whatsoever. We 
have thus, in favor of the theory, all the evidence which can be ob- 
tained by what we termed the Indirect Method of Difference, or the 
Joint Method of Agreement and Difference ; the evidence of which, 



240 INDUCTION. 

tliough it never can amount to that of the Method of Difference prop- 
erly so called, may approach indefinitely near to it. 

No similar defect of completeness in proof will be found in the 
following original investigation, for which I am indebted to Mr. Alex- 
ander Bain, at present Lecturer on Moral Philosophy in Marischal 
College, Aberdeen ; one of the men from whom science and philoso- 
phy have most to hope, and who has permitted me to lay his extensive 
knowledge of every department of physical inquiry freely under con- 
tribution, for the purpose of exemplifying and illustrating the doctrines 
of this work. ' - 

§ 3. Let the object be to ascertain the law of what is termed induced 
electricity ; to find under what conditions any electrified body, whether 
positively or negatively electrified, gives rise to a contrary electric 
state in some other body adjacent to it. 

The most familiar exemplification of the phenomenon to be investi- 
gated, is the following. Around the prime conductors of an electrical 
machine, the atmosphere to some distance, or any conducting surface 
suspended in that atmosphere, is found" to be in an electric condition 
opposite to that of the prime conductor itself. Near and around the 
positive prime conductor there is a negative electricity, and near and 
around the negative prime conductor there is positive electricity. 
When pith balls are brought near to either of the conductors, they 
become electrified with the opposite electricity to it ; either receiving 
a share from the already electrified atmosphere by conduction, or 
acted upon by the direct inductive influence of the conductor itself: 
they are then attracted by the conductor to which they are in opposi- 
tion ^ or, if withdrawn in their electrified state, they will be attracted 
by any other oppositely charged body. , In like manner the hand, if 
brought near enough to the conductor, receives or gives an electric 
discharge ; now we have no evidence that a charged conductor can be 
suddenly discharged unless by the approach of a body oppositely elec- 
trified. In the case, therefore, of the electrical machine, it appears 
that the accumulation of electricity in an insulated conductor is always 
accompanied by the excitement of the contrary electricity in the sur- 
rounding atmosphere, and in every conductor placed near the former 
conductor. It does not seem possible, in this case, to produce one 
electricity by itself 

Let us now examine all the other instances which we can obtain, 
resembling this instance in the given consequent, namely, the evolution 
of an opposite electricity in the neighborhood of an electrified body. 
As one remarkable instance we have the Ley den jar ; and after the 
splendid experiments of Faraday in complete and final establishment 
of the substantial identity of magnetism and electricity, we may cite 
the magnet, both the natural and the electro-magnet, in neither of 
which is it possible to produce one kind of electricity by itself, or to 
charge one pole without charging an opposite pole with the contrary 
electricity at the same time. We cannot have a magnet with ohe 
pole : if we break a natural loadstone into a thousand pieces, each 
piece will have its two .oppositely electrified poles complete within 
itself. In the voltaic circuit, again, we cannot have one cunent with- 
out its opposite. In the ordinary elbctric machine, the glass cylinder 
or plate, and the rubber, acquire opposite electricities. 



EXAMPLES OF THE FOUR METHODS. 241 

From all these instances, treated by the Method of Agreement, a 
general law appears to result. The instances -embrace all tlie known 
modes in which a body can become charged with electricity ; and in 
all of them therei is found, as a concomitant Or consequent, the excite- 
ment of the opposite electric state in some other body or bodies. It 
seems, to follow that the two facts are invailably connected, and that 
the excitement of electricity in any body has for one of its necessary 
conditions the possibility of a simultaneous excitement of the opposite 
electricity in some neigliboring body. 

As the two contrary electricities can only be produced togethery sjo 
they can only cease together. This may be shown by an application 
of the Method of Pifference to, the example of the Leyden jar. It 
needs scarcely be here remarked that in the Leyden jar, electricity 
can be accumulated and retained in considerable quantity, by the con- 
trivance of having two conducting surfaces of equal extent, and parallel 
to each other through the whole of that extent, with a non-conducting ■ 
substance such as glass between them. When one side of the jar is 
charged positively, the other is charged negatively, and it was by virtue 
of this fact that the Leyden jar served just now as an instance in our 
employment of the Method of Agi'eement. Now it is impossible to 
discharge one of the coatings unless the other can be discharged at 
the same time. A conductor held to the positive side cannot convey 
away any electricity unless an equal quantity be allowed to pass from 
the negative side : if one coating be perfectly insulated, the charge 
is safe. The dissipation of one must proceed jpari passu with the 
other. 

The law thus strongly indicated admits ' of corroboration by the 
Method of Concomitant Variations. The Leyden jar is capable of 
receiving a much higher charge than can ordinarily be given to the 
conductor of an electncal machine. Now in the case of the Leyden 
jar, the metallic surface which receives the induced electricity is a 
conductor exactly similar to that which receives the primary charge, 
and is therefore as susceptible of receiving and retaining the one elec- 
tricity, as the opposite surface of receiving and retaining the other: 
but in the machine, the neighboring body which is to be oppositely 
electrified is the siuTounding atmosphere, or any body casually brought 
near to the conductor ; and as these are generally much inferior in 
their capacity of becoming electrified, to the conductor itself, their lim- 
ited power imposes a corresponding limit to the capacity of the con- 
ductor for being charged. As the capacity of the neighboring body 
for supporting the opposition increases, a higher charge becomes pos- 
sible : and to this appears to be owing the great superiority of the 
Leyden jar. 

A further and most decisive confirmation by the Method of Differ- 
ence, is to be found in one of Faraday's experiments in the course of 
his researches on the subject of induced electricity. 

Since common or machine electricity, and voltaic electricity, may 
be considered for the present purpose to be identical, Faraday wished 
to know whether, as the prime conductor develops opposite electri- 
city upon a conductor in its vicinity, so a voltaic current running 
along a wire would induce an opposite current upon another wire laid 
parallel to it at a short distance. Now this case is similar to the cases ' 
previously examined, in every circumstance except the one to which 
Hh 



242 INDUCTION. 

we have ascribed the effect. We found in the former instances that 
whenever electricity of one kind was excited in one body, electricity 
of the opposite kind must be excited in a neighboring body ; and the 
interpretation of this, in the language of cause and effect, is, that all 
causes which can excite the one kind of electricity, have the property 
of simultaneously exciting an equal amount of the other. But in 
Faraday's experiment this indispensable opposition exists within the 
wire itself. From the nature of a voltaic charge, the two opposite" 
currents necessary to the existence of each other are both accommo- 
dated in one ^wire ; and there is no need of another wire placed be- 
side it to contain one of them, in the same way as the Leyden jar 
must have a positive and a negative surface. The exciting cause can 
and does produce all the effect which its laws require, independently 
of any electric excitement of a neighboring body. Now the result 
of Faraday's experiment Vith the second wire, was that no opposite 
current was produced. There was an instantaneous effect at the 
closing and breaking of the voltaic circuit; electric inductions ap- 
peared when the two wires were moved to and from one another ; 
but these are phenomena of a different class. There was no in- 
duced electricity in the sense in which this is predicated of the 
Leyden jar; there was no sustained current running up the one wire 
while an opposite cuiTent ran down the neighboring wire; and this 
alone would have been a true parallel case to the other. 

It thus appears by the combined evidence of the Method of Agree- 
ment, the Method of Concomitant Variations, and the most rigorous 
form of the Method of Difference, that neither- of the two kinds of 
electricity can be excited without an equal excitement of the other 
and opposite kind : that both are effects of the same cause, that the 
possibility of the one is a condition of the possibility of the other, and 
the quantity of the one an impassable limit to the quantity of the other. 
A scientific result of considerable interest in itself, and illustrating 
those three methods in a manner both characteristic and easily in- 
telligible. 

§ 4. Our third example shall be extracted from Sir John HerschePs 
Discourse on tlie Study of Natural JPhilosopJiy, a work replete with 
admirably selected exemplifications of inductive processes from almost 
every department of physical science, and in which alone, of all books 
which I have met with, the foar methods of induction are recognized^ 
although not characterized and defined nor their correlation shown, so 
distinctly as has appeared to me desirable. The present example is 
justly described by Sir John Herschel as " one of the most beautiful 
specimens" which can be cited " of inductive experimental inquiry 
lying within a moderate compass;" the theory of dew, first promul- 
gated by the late Dr. Wells, and now universally adopted by scien- 
tific men. 

The passages in inverted commas are extracted verbatim from Sir 
John Herschel, * but to those who possess his work I would strongly 
recommend to read the entire passage in the original, and fully pos- 
sess themselves of the purport of the speculation as a whole, before 
applying themselves, with me, to the logical analysis of the different 
Bteps of the argument. 

» « "" * Discourse, pp. 159—162, 



EXAMPLES OF THE FOUR METHODS. 243 

" Suppose dew were the phenomenon proposed, whose cause we 
would know. In. the first place" we must determine precisely what 
we .mean by dew ; what the fact really is, whose cause we desire to 
investigate. " We must separate dew from rain, and the moisture of 
fogs, and limit the application of the term to what is really meant, 
which is, the spontaneous appearance of moisture on substances 
exposed in the open air when no rain or visible wet is falling." This 
answers to a preliminary operation which will be characterized in the 
ensuing book, treating of operations subsidiary to induction.* The 
state of the question being fixed, we come to the solution. 

" Now, here we have analogous phenomena in the moisture which 
bedews a cold metal or stone when we breathe upon it ; that which 
appears on a glass of water fresh from the well in hot weather ; that 
which appears on the inside of windows when sudden rain or hail 
chills the external air; that which runs down our walls when, after a 
long frost, a warm moist thaw comes on," Comparing these cases, we 
find that they all contain the phenomenon which was proposed as the 
subject of investigation. Now '* all these instances agree in one point, 
the coldness of the object dewed, in comparison with the air in contact 
with it." But there still remains the most important case of all, that 
of nocturnal dew : does the same circumstance exist in this case 1 " Is 
it a fact that the object dewed is colder than the air ] Certainly not, 
one would at first be inclined to say ; for what is to make it so ,^ But .... 
the experiment is easy ; we have only to lay a thermometer in contact 
with the dewed substance, and hang one at a little distance above it, 
out of reach of its influence. The experiment has been therefore 
made; the question has been asked, and the answer has been inva- 
riably in the afiirmative. Whenever an object contracts dew, it is 
colder than the air." 

Here then is a complete application of the Method of Agreement, 
establishing the fact of an invariable connexion between the deposition 
of dew on a surface, and the coldness of that surface compared with the 
external air. But which of these is cause and which effect ; or are they 
both effects of something else ] On this subject the Method of Agree- 
ment can afford us no light: we must call in a more potent method. 

" That dews are accompanied with a chill is a common remark; but 
vulgar prejudice would make the cold the effect rather than the cause. 
We must therefore collect more facts, or which comes to the same thing, 
vary the circumstances ; since every instance in which the circum- 
stances differ is a fresh fact; and especially, we must note the contrary' 
or negative cases, i. e., where no dew is produced :" for we are aware 
that a "comparison between instances of dew, and instances of no dew, 
is the condition necessary to bring the Method of Difference into play. 
' "Now, first, no dew is produced on the surface oi polisliecl metals y 
but' it is very copiously on glass, both exposed with their faces 
upwards, and in some cases the under side of a horizontal plate of 
glass is also dewed."t Here is an instance in which the effect is pro- 

* Vide infra, book iv., chap. ii. On Abstraction, 

t This last circumstance (adds Sir John Herschel) " excludes the fall of moisture from 
the sky in an invisible form, which would naturally suggest itself as a cause." I have 
omitted this passage in the text, as not pertinent to the purpose in hand, the argument 
which it contains being deductive and a priori. The fall of moisture is rejected as a cause, 
because from its laws previously known, we infer that it could not have produced the par- 
ticular phenomenon last mentioned. , " ^ > 



244 • INDUCTION, 

duced, and another instance in wliich it is not produced ; but we cannot 
yet pronounce, as the canon of the Method of Difference requires", 
that the latter instance agrees with the former in all its circumstances 
except one ; for the differences between glass and polished metals are 
manifold, and the only thing we can as yet be sure of is, that the 
cause of dew will be found among the circumstances by which the 
former substance is distinguished from the latter. But if we could be 
sure that glass, and the various other substances on which dew is 
deposited, have only one quality in common, and that polished metals 
and the other substances on which dew is not deposited have also 
nothing in common but the one circumstance, of not having the one 
quality which the others have ; the requisitions of the Method of 
Difference would be completely satisfied, and we should recognize, in 
that quality of the substances, the cause of dew. This, accordingly, 
is the path of inquiry which is next to be pursued. ■, 

"In the cases of polished metal and polished glass, the contrast 
shows evidently that the substance has much to do with the phenome- 
non ; therefore let the substance, alone be diversified as much as . 
possible, by exposing polished surfaces of various kinds. This done, 
a scale of intensity becomes obvious,. Those polished substances are 
found to be most strongly dewed which conduct heat worst; while 
those which conduct well, resist dew most effectually." The compli- 
cation increases ; here is the Method of Concomitant Variations called 
to our assistance ; and no other method was practicable upon this 
occasion ; for, the quality of conducting heat could not be excluded, 
since all substances conduct heat in some degree. The conclusion 
obtained is, that cceteris paribus the deposition of dew is in some 
proportion to the power which the body possesses of resisting the, 
passage of heat ; and that this, therefore, (or something connected with- 
this,) must be at least one of the causes which assist in producing the 
deposition of dew upon the surface. 

"But if we expose rough surfaces instead of pjolished, we some- 
times find this law interfered with. Thus, roughened iron, especially 
if painted over or blackened, becomes dewed sooner than varnished 
paper: the kind o1 surface, therefore, has a great influence. Expose, 
then, the same material in very diversified states as to surface," (that 
is, employ the Method of Difference to ascertain concomitance of 
variations,) "and another scale of intensity becomes at once apparent, - 
those surfaces which 'part with their heat most readily by radiation, are 
found to contract dew most copiously." Here, therefore, are the 
requisites for a second employment of the Method- of Concomitant 
Variations; which in this case also is the only method available, since ^ 
all substances radiate heat in some degree or other. The conclusion 
obtained by this new application of the method is, that caieris paribus 
the deposition of dew is also in some proportion to the power of 
radiating heat ; and that the quality of doing this abundantly (or some 
cause on which that quality depends) is another of the causes which 
promote the deposition of dew upon the substance. 

" Again, the influence ascertained to exist of substance and surface 
leads us to consider that oi texture : and here, again, we are presented 
on trial with remarkable differences, and with a third scale of intensity, 
pointing out substances of a close firai texture, such as stones, metals, 
&c., as unfavorable^ but those of a loose one, as cloth, wool, velvet, eider- 



EXAMPLES OF THi: FOUR METHODS. 245 

dpwn, cotton, &c., as eminently favorable to the contraction of dew." 
The Method of Concomitant Variations is here, for the third time, had 
recourse to; and, as before,, from necessity, since the texture of no 
substance is absolutely firm or absolutely loose. Looseness of texture, 
therefore, or something which is the cause of that quality, is another 
^^circumstance which promotes the deposition of dew ; but this third 
eause resolves itself into the first, viz., the quality of resisting the 
passage of heat : for substances of loose texture " are precisely those 
which are best adapted for clothing, or for impeding the free passage 
of heat from the skin into the air, so as to allow their outer surfaces to 
be very cold while they remain warm within ;" and this last is, there- 
fore, an induction (from fresh instances) simply corroborative of a^ 
former induction. 

It thus appears that the instances in which much dew is deposited, 
which are very various, agree in this, and, so far as we are able to 
observe, in this only, that they either radiate heat rapidly or conduct 
it slowly : qualities between which there is no other circumstance of 
agreement, than that by virtue of either, the body tends to lose heat 
from the surface more rapidly than it can be restored from within. 
The instances, on the contrary, in which no dew, or but a small' 
quantity of it, is formed, and which are also extremely various, agree 
(so far as we can observe) in nothing except in 7iot having this same 
property. We seem, therefore, to have detected the sole difference 
between the substances on which dew is produced, and those on which 
it is not produced. And thus have been realized the requisitions of 
what we have termed the Indirect Method of Difference, or the Joint 
Method of Agreement and Difference. The example afforded of this 
indirect method, and of the manner in which the data are prepared 
for it by the Methods of Agreement and of Concomitant Variations, 
is the most important of all the illustrations of induction afforded by- 
this most interesting speculation. 

We might nOw consider the question, upon what the deposition of 
dew depends, to be completely solved, if we could be quite sure that 
the substances on which dew is produced differ from those on which it. 
is not, in nothing but in the property of losing heat from the surface 
faster than the loss can be repaired from within. And, although we 
never can have that cornplete certainty, this is npt of so much import- 
ance as might at first be supposed ; for we have, at all events, ascer- 
tained that even if there be any other quality hitherto unobserved 
which is present in all the substances which contract dew, and absent 
in thosfe which do not, this other property must be one which, in all 
that great number of substances, is present or absent exactly where the 
property of being a better radiator than conductor is present or absent ; 
an extent of coincidence which affords the strongest presumption of a 
community of cause, and a consequent invariable coexistence between 
the two properties ; so that the property of being a better radiator 
than conductor, if not itself the cause, almost certainly always accom- 
panies the cause, and for purposes of prediction, no en'or will be 
committed by treating it as if it were really such. 

Reverting now to an earlier stage of the inquiry, let us remember 
that we had ascertained that, in every instance where dew is formed, 
there is actual coldness of the surface below the temperature of the 
'surrounding air; but we were not sure whether this coldness was the 



246 , INDUCTION. 

cause of dew, or its effect. This doubt we are now able to resolve. 
We have found that, in every such instance, the substance must be one 
which, by its own properties or laws, would, if exposed in the night, 
become colder than the suiTounding air. But if the dew were the 
cause of the coldness, that effect would be produced in other substances, 
and not solely in those whose own laws suffice to produce it whether 
there were dew or no. That supposition, therefore, is repelled. But 
there were only three suppositions possible ; the dew is the cause of 
the coldness ; both are caused by some third circumstance ; or the 
coldness is the cause of the dew: The first is refuted. The second is 
inapplicable: the cause of the coldness is a known cause; a radiation 
from the surface greater than can be supplied by conduction : now this, 
by its known laws, can produce no direct effect except coldness. There 
remains only the third supposition, that the coldness is the cause of the 
dew : which, therefore, may be considered as completely made out. 

This law of causation, already so amply established, admits, how- 
ever, of most efficient additional corroboration in no less than three 
ways. First, by deduction from the know:n laws of aqueous vapor 
when diffused through air or any other gas ; and although we have 
not yet come to the Deductive Method, we will not omit what is neces- 
sary to render this speculation complete. It is known by direct exper- 
iment that only a limited quantity of water can remain suspended in 
the state of vapor at each degree of temperature, and that this maxi- 
mum grows less and less as the temperature diminishes. From this it 
follows, deductively, that if there is already as much vapor suspended 
as the air will contain at its existing temperature, any lowering of that 
temperature will cause a portion of the vapor to be condensed and 
become water. But, again, we know deductively, from the laws of 
heat, that the contact of the air with a body colder than itself, will 
necessarily lower the temperature of the stratum of air immediately 
applied to. its surface ; and will therefore cause it to part with a portion 
of its water, which accordingly will, by the ordinary laws of gravita- 
tion or cohesion, attach itself to the surface of the body, thereby con- 
stituting dew. This deductive proof, it will have been seen, has the 
advantage of proving at once, causation as wellas coexistence; and it 
has the additional advantage that it also accounts for the exc'eptio7is to 
the occurrence of the phenomenon, the cases in which, although the 
body is colder than the air, yet no dew is deposited ; by showing that 
this will necessarily be the case when the air is so undersupplied with 
aqueous vapor, comparatively to its temperature, that even when some- 
what cooled by the contact of the colder body, it can still continue to 
hold in suspension all the vapor which was previously suspended in it: 
thus in a very dry summer there are no dews, in a very dry winter no 
hoar frost. Here, therefore, is an additional condition of the produc- 
tion of dew, which the methods we previously made use of failed to 
detect, and which might have remained still undetected, if recourse had 
not been had to the plan of deducing the effect from the ascertained 
properties of the agents known to be present. 

The second corroboration of the theory is by direct experiment, 
according to the canon of the Method of Difference. We . can, by 
cooling the surface of any body, find in all cases some temperature 
(more or loss inferior to that of the surrounding air, according to its 
hygromotric condition,) at which dew will begin, to be deposited* 



EXAMPLES OF THE FOUR METHODS. 247 

Here, too, therefore, the causation is directly proved. We can, it is 
true, accomplish this only on a small scale ; but we have ample reason 
to conclude that the same operation, if conducted in Nature's great 
laboratory, w^ould equally produce the effect. 

And, finally, even on that great scale we are able to verify the result. 
The case is one of those (rare cases, as we have shown them to be) in 
which Nature works the experiment for us in the same manner in 
which we ourselves perform it; introducing into the previous state of 
things a single and perfectly definite new circumstance, and manifest- 
ing the effect so rapidly that there is not time for any other material 
change in the preexisting circumstances. Let us quote again Sir John 
Herschel : — " It is observed that dew is never copiously deposited in 
situations mu5h screened from the open sky, and not at all in a cloudy 
night ; but if the clouds withdraw even for a few minutes, and leave a 
clear opening, a deposition of dew presently begins, and goes on increas- 
ing Dew formed in clear intervals will often even evaporate again 

, when the sky becomes thickly overcast." The proof, therefore, is 
coraplete, that the presence or absence of an uninterrupted communi- 
cation with the sky causes the deposition or non-depcjsition of dew. 
Now, since a clear sky is nothing but the absence of clouds, and it is a 
known property of clouds, as of all other bodies between which and 
any given object nothing intervenes but an elastic fluid, that they 
tend to raise or keep up the superficial temperature of the object by 
■radiating heat to it, we see at once that the disappearance of clouds 
will cause the surface to cool ; so that Nature, in this case, produces a 
change in the antecedent by definite and known means, and the con- 
sequent follows accordingly : a natural experiment which satisfies the 
requisitions of the Method of Difference.* 

The accumulated proof of which the Theory of Dew has been found 
susceptible, is a striking example of the fullness of assurance which the 
inductive evidence of laws of causation may attain, in cases in which 
the invariable sequence is by no means obvious to a superficial view. 
It is unnecessary to subjoin Sir John Herschel's summary of the result, 
as it does not contain all the proofs which I have given, and our more 
detailed analysis of each step of the process renders sucji a recapitula- 
tion unnecessary. 

§ 5. This admirable example will have conveyed to any one by 
whom it has been duly followed, so clear a conception of the use and 
practical management of three of the four methods of experimental 

* I must, however, remark, that this example, which seems to militate against the asser- 
tipri we made of the comparative inappUcabih'ty of the Method of Difference to cases of 
pure observation, is really one of those exceptions which, according to a proverbial expres- 
sion, prove the general rule. For, be it observed, in this case iti which Nature, m her 
experiment, seems to have imitated the type of the experiments made by man, she has only 
succeeded in producing the likeness of man's most imperfect experiments, namely, those 
in which, though he succeeds in producing the phenomenon, he does so by employing com- 
plex means, wliich he is unable perfectly to analyze, and can form, therefore, no sufficient 
judgment what portion of the effects may be due, not to the supposed cause, but to some 
unknown agency of the means by which that cause was produced. In the natural experi- 
ment which we are speaking of, the means used was the clearing off a canopy of clouds; 
and we certainly do not know sufficiently in what this process consists, or upon what it 
depends, to be certain a priori that it might not operate upon the deposition of dew inde- 
pendently of any thermometric effect at the earth's surface. Even, therefore, in a case so 
favorable as this to Nature's experimental talents, her experiment is of little value except 
Sfi corroboration of a conclusion already attained through other means. 



248 ^ INDUCTION. 

inquiry, as to supersede 'the necessity of any further exemplification 
of them. The remaining method, that of Residues, not having found 
any place either in this or in the two preceding investigations, I shall 
extract from Sir John Herschel some examples of that method, with 
the remarks by which they are introduced. , . 

*' It is by this process, in fact, that science, in its present advanced 
state, is chiefly promoted. Most of the phenomena which Nature 
presents, are very complicated; and when the effects of all known 
causes are estimated with exactness, and subducted, the residual facts 
are constantly appearing in the form of phenomena altogether new, 
and leading to the most important conclusions. 

"For example : the return of the comet predicted by Professor 
^ncke, a great many times in succession, and the general good agree- 
inent^ of its calculated with its obseiTed place during any one of its 
periods of visibility, would lead us to say that its gravitation towards 
the sun and planets is the sole and sufficient cause of all the phenom- 
ena of its orbitual motion : but when the effect of this cause is strictly 
calculated and subducted from the observed motion, there is found to 
remain behind a residMol j^^'^^i^omenon, which would never have been 
otherwise ascertained to exist, which is a small anticipation of the 
time of its reappearance, or a diminution of its periodic time, which 
cannot be accounted for by gravity, and whose cause is therefore to be 
inquired into. Such an anticipation would be caused by the resistance 
of a medium disseminated through the celestial regions; and as there 
are other good reasons for believing this to be ^ vera catisa,^'' (an 
actually existing antecedent,) "it has therefore been asciibed to such 
E' resistance. 

" M. Arago, having suspended a magnetic needle by a silk thread, 
^ahd set it in vibration, observed, that it came much sooner to a state 
of rest when suspended over a plate of copper, than when no such 
plate was beneath it. Now, in both cases there were two vercBcausce^^ 
(antecedents known to exist) " why it should come at length to rest, 
viz., the resistance of the air, which opposes, and at length destroys, 
all motions performed in it ; and the want of perfect mobility in the 
silk thread. But the effect of these causes being exactly known by 
the observation made in the absence of the copper, and being thus 
allowed for and subducted, a residual phenomenon appeared, in the 
factthat a retarding influence was exerted by the copper itself; and 
this fact, once ascertained, speedily led to the knowledge of an entirely 
liew and unexpected class of relations." This example belongs, how- 
ever, not to the Method of Residues but to the Method of Difference, 
the law being ascertained by a direct comparison of the results of two 
experiments, which differed in nothing but the presence or absence of 
the plate of copper. To have made it exemplify the Method of Res- 
idues, the effect of the resistance of the air and that of the rigidity of 
the silk should have been calculated d jpfiori^ fi"om the laws obtained 
by separate and foregone experiments. 

• " Unexpected and peculiarly striking confirmations of inductive 
laws frequently occur in theform of residual phenomena, in the course 
of investigations of a widely different nature from those which gave rise 
to the inductions themselves. A very elegant example may be cited 
in the unexpected confirmation of the law of the development of heat 
m elastic fluids by compression, \vhich is afforded by the phenomena 



EXAMPLES OF THE FOUR METHODS. 249' 

of sound. The inquiry into tlie cause of sound had led to conchisions 
respecting its mode of propagation, from which its velocity in the air 
could be precisely calculated. The calculations were performed ; 
but, when compared with fact, though the agreement was quite suffi- 
cient to show the general correctness of the causQ and mode of propa- 
■>^ation assigned, yet the Wii^/e velocity could not be shown to arise 
;fi:om this theory. Tliere was still a residual velocity to be accounted 
for, which placed dynamical philosophers for a long. time in a great 
dilemma. --At length Laplace struck' on the ^happy idea, that this 
might arise i. from the heat developed in the acfc of that condensa- 
tion which necessarily takes place at every vibration by which sound 
i^- conveyed. The matter was subjected to- exact calculation, and 
the result was at once the complete explanation of the residual phe- 
nomenon, and a striking confirmation of the general law of the devel- 
opment of heat by compression, under circumstances beyond artificial 
imitation." 

'■ Many of the new elements of chemistry have been detected in the 
investigation of residual phenomena. Thus Arfwedson discovered 
lithia by perceiving an excess of weight in the sulphate produced from 
a small portion of what he considered as magnesia present in a mineral 
he had analyzed. It is on this principle, too, that the small concen- 
trated residues of great operations in the arts are almost sure to be the 
lurking places of new chemical ingredients : witness iodine, brome, 
selenium, and the new metals accompanying platina in the experi- 
ments of Wollaston and Tennant. It was a happy thought of Glauber- 
to examine what everybody else threw away."* 

The disturbing effects mutually produced by the earth and planets 
upon each other's motions were first brought to light as residual phei- 
nomena, by the difference which .appeared between the observed 
places of those bodies, and the places calculated on a consideration 
solely of their gravitation towards the sun^ It was this which deter- 
mined philosophers to consider the law of gravitation as obtaining be- 
tvi^een ail bodies whatever, and therefore between^ all particles of 
matter ; their first tendency having been to regard it as a force acting 
only between each planet or satellite and the central body to whose 
system it belonged. Again, the catastrophists, in geology, be their 
opinion light or wrong, support it upon the plea, that after the effect 
of all causes now in operation has been allowed for, there remains in 
the existing constitution of the earth a large residue of facts, proving 
the existence at former periods either of other forces, or of the, same ' 
forces iii a much greater degree of intensity. To add one more 
example : if it be possible to establish, what is generally rather as- 
sumed than proved, that there is in one human individual, one sex, or 
one race of mankind over another, an inherent and inexplicable supe- 
riority in mental faculties, this must be proved by subtracting from the 
differences of intellect which we in fact see, all that can be traced by 
known laws either to the ascertained differences of physical organiza- 
tion, or to the differences which have existed in the outward circum- 
stances in which the subjects of the comparison have hitherto been 
placed. Wliat these causes might fail to account for, would constitute 
a residual phenomenon, which and which alone "\yould be evidence of' 

* Herschel, wif supra, pp, 78-9, and 86. ^ ■" '■"^■ 

II 



250 INDUCTION. 

an ulterior original distinction, and tlie mfeasuf© pf its amount. But 
the strongest assertors of such supposed differences have hitherto been 
very negligent of providing themselves with these necessary logical 
conditions of the establishment of their doctrine. 

.The spirit of the Method of Residues being, it is hoped, sufficiently 
intelligible from these examples, and the other three methods having 
been so aptly exemplified in the inductive processes which produced 
the Theory of Dew, we may here close our exposition of the four 
methods, considered as employed in the investigation of the simpler 
and more elementarv order of the copibinations of phenomena. • y • 



CHAPTER X. 

OF PLURALITY OF CAUSES; AND OF THE INTERMIXTURE OF EFFECTS. 

§ !.■ In the preceding exposition of the four methods of observation 
and experiment, by which we contrive to distinguish among a mass of 
coexistent phenomena the particular effect due to a given cause, or the 
particular cause which gave birth to a given effect ; it has been neces- 
sary to suppose, in the first instance, for the sake of simjilification, that 
this analytical operation is encumbered by no other difficulties than 
what are essentially inherent in its nature ; and to represent to our- 
selves, therefore, every effect, on the one hand as connected exclu- 
sively with a single cause, and on the other hand as incapable of being 
mixed and confounded with any other coexistent effect. We have re- 
garded ahcde, the aggregate of the phenomena existing at any mo- 
ment, as consisting of dissimilar facts, a, h, c, d, and e, for each of which 
one, and only one, cause needs be sought; the difficulty being only that 
of singling out this one cause from the multitude of antecedent circum- 
stances, A, B, C, D, and E. 

If such were the fact, it would be comparatively an easy task to in- 
vestigate the laws of nature. But the supposition does not hold, iii 
either of its parts. In the first place, it is not true that the same phe- 
nomenon is always produced by the same cause : the effect a may 
sometimes arise from A, sometimes from B. And, secondly, the effects 
of different causes are often not dissimilar, but homogeneous, and 
marked out by no assignable boundaries from one another : A and B 
may produce not a and b, but different portions of an effect a. The 
obscurity and difficulty of the investigation of the laws of phenomena 
is singularly, increased by the necessity of adverting to these two cir- 
cumstances ; 'Intermixture of Effects, and Plurality of Causes. To the 
latter, being the simpler of the two considerations, we shall first direct 
our attention. 

' It is not true, then, that one effect must be connected with only one 
cause, or assemblage of conditions ; that each phenomenon can be pro- 
duced only ill one way. There are often several independent modes 
in which the same phenomenon could have originated. One fact may 
be the consequent in several invariable sequences ; it may follow, with 
equal uniformity, any one of several antecedents, or collections of ante- 
cedents. Man^ causes may produce motion: many causes may pro- 



PLURALITY OF CAUSES. 251 

duce some kinds of sensation : many causes may produce death. A 
given effect may really be produced by a certain cause, and yet be 
perfectly capable of being produced without it. 

§ 2. One of the principal consequences of this fact of Plurality of 
Causes is, to render the first of our inductive methods, that of Agree- 
ment, uncertain. To illustrate that method, we supposed two instances. 
ABC followed hy a be, and A D E followed by a ^ e. From these in- 
stances it might be concluded that A is an invariable antecedent of a; 
and even that it is the unconditional invariable antecedent or cause, if 
we could be sure that there is no other antecedent common to the two 
cases. That this difhculty may not stand in the way, let us suppose 
the two cases positively ascertained to have no antecedent in common 
except A. The moment, however, that we let in the possibility of a plu- 
rality of causes, the conclusion fails. For it involves a tacit suppo- 
sition that a must have been produced in both instances by the same 
cause. If there can possibly have been two causes, those two may, for 
example, be C and E : the one may have been the cause of a in the 
former of the instances, the other in the latter, A ha\ang no influence 
'in either case. 

Suppose, for example, that two great artists, or great philosophers, 
that two extremely selfish, or extremely generous characters, were 
compared together as'to the circumstances of their education and his- 
tory, and the two cases were found to agree only in one circumstance : 
would it follow that this one circumstance was the cause of the quality 
which characterized both those individuals 1 Not at all ; for the 
causes at work to produce any given type of character are innumer- 
able ; and the two persons might equally have agreed in their char- 
acter, although there had been no manner of resemblance in their 
previous history. 

This, therefore, is a characteristic imperfection of the Method of 
Agreement ; from which imperfection the Method of Difference is free. 
For if we have two instances, ABC and BC, of which BC gives be, 
and A being added converts it into a be, it is certain that in this instance 
at, least A was either the cause of a, or an indispensably portion of its 
cause, even though the cause which produces it in other instances may 
be altogether different. Plurality of Causes, therefore, not only does 
not diminish the reliance due to the Method of Difference, but does not 
even render a greater number of observations or experiments necessary : 
two instances, the one positive and the other negative, are still suffi- 
cient for the most complete and rigorous induction. Not so, however, 
with the Method of Agreement. The conclusions which that yields, 
when the number of instances compared is small, are of no real value, 
except as, in the character of suggestions, they may lead either to 
experiments bringing them to the test of the Method of Difference, or 
to reasonings which may explain and verify them deductively. 

It is only when the instances, being indefinitely multiplied, and vaiied, 
continue to suggest the same result, that this result acquires any high 
degree of independent value. If there are but two instances, ABC 
and ADE, although these instances have no antecedent in common 
except A, yet as the effect may possibly have been produced in the 
two cases by different causes, the result is at most only a sUght proba- 
bility in favor of A; there may be causation, l>ut it is almost equally 



252 ' . INDUCTION. 

probable that there was only, as the expression is, a coincidence. But 
the oftener we repeat the observation, varying the circumstances, the 
more we advance towards a solution of this doubt. F-or if we try 
A FG-, AH K, &CC., all entirely unlike one another except in containing 
the' circumstance A, and if we find the effect a entering into the result 
in all these cases, we must suppose one of two things, either that it is 
caused by A, or that it has as many difterent causes cijS thei'e are- in- 
stances. With each addition, therefore, to the number of instances, 
the presumption is strengthened in favor of A. "^ The inquirer, of course, 
will not neglect, if an opportunity present itself, to exclude A from 
some one of these combinations, from AH R for instance, and by trying 
H K separately, appeal to the Method of Difference in aid of the Method 
of Agreement. By the former method alone can it be ascertained that 
A is the cause of a: but that it is either the cause or another effect of 
the same cause, may be placed beyond any reasonable doubt by the 
Method of Agreement, provided the instaiices are very numerous, as 
well as sufficiently various. 

After how great a multiplication, then, of varied instances, all agree- 
ing in no other antecedent except A, is the supposition of a plurality 
of causes sufficiently rebutted, and the conclusion that a is the effect of 
A divested of the characteristic imperfection and reduced to a virtual 
certainty? This is a question, whicji we cannot be exempted fiom 
answering ; but the consideration of it belongs to what is called the 
Theory of Probability, which will form the subject of a chapter here- 
afler. It is seen, however, at once, that the conclusion, does amount to 
a practical certainty after a sufficient number of instances, and that the 
method, therefore, is not radically vitiated by the characteristic imperfec- 
tion. The result of these considerations is only, in the first place, to 
point out a new source of inferiority in the Method of Agreement as 
compared with other modes of investigation, and new reasons for never 
resting contented with the results obtained by it, without attempting to 
confirm them either by the Method of Difference, or by connecting 
them deductively with some law or laws already ascertained by that 
superior method. And, in the second place, we learn from this, the 
true theory of the value of mere nmnher of instances in inductive 
inquiry. The tendency of unscientific inquiries is to rely too much 
upon number, without analyzing the instances ; without looking closely 
enough into their nature, to ascertain what circumstances are or are not 
eliminated by means of them. Most people hold their conclusions 
with a degree of assurance proportioned to the mere mass of the expe- 
rience on which they appear to rest: not considering that by the addi- 
tion of instances to instances, all of the .same kind, that is, differing from 
one another only in points already recognized as immaterial, nothing 
whatever is added to the evidence of the conclusion. A.single instance 
eliminating some antecedent which existed in all the other cases, is of 
more value than the greatest multitude of instances which are reckoned' 
by their number alone. It is necessary, no doubt, to assure ourselves, 
by a repetition of the observation or experiment, that nO error has 
been committed ooncerning the individual facts observed; and until we 
have assured ourselves of this, instead of varying the circumstances, we 
cannot too^ scrupulously repeat the same experiment or observation 
without any change. But when once this assurance has been obtained, 
the multiplication of instances which do not exclude any more cir- 



PLURALITY OF CAUSES. 253 

curastances would be entirely useless, were it not for the Plurality 
©f Causes. 

It is of importance to remark, that the peculiar modification of the 
Method of Agreement which, as partaking in some degree of the na- 
ture of the Method of Difference, I have called the Joint Method of 
Agreement and Difference, is not aifected by the characteristic imper- 
fection now pointed out. For, in the joint method, it is supposed not 
only that the instances in which a is, agree only in containing A, but 
also that the instances in which a is not, agree only in not contain- 
ing A. Now, if this be so, A must be not only the cause of a, but the 
only possible cause: for if there were another, as for example B, 
then in the instances in which a is not, B must have been absent as 
w.eli as A, and it would not be true that these instances agree only 
in" not containing A. This, therefore, constitutes an immense advan- 
tage of the joint method over the simple Method of Agreement. It 
inay seem, indeed, ^that the advantage does not belong so much to the 
j-oint method, as to one of its two premisses (if they may be so 
called), the negative premiss. The Method of Agreement, when 
applied to negative instances, or those in which a phenomenon does 
not take place, is certainly free from the characteristic imperfection 
which affects it in the affirmative case. The negative premiss, it 
might therefore be supposed, could be worked as a simple case of 
the Method of Agreement, without requiring an affirmative premiss to 
be joined with it. But although this is true in principle, it is gen- 
erally altogether impossible to work the Method of Agreement by 
negative instances without positive ones : it is so much more diffi- 
cult to exhaust the field of negation than that of affirmation. For 
instance, let the question be, what is the cause of the transparency of 
bodies : with what prospect of success could we set ourselves to 
inquire directly in what the multifarious substances which are not 
transparent, agree'? But we might hope much sooner to seize some 
point of resemblance among the comparatively few and definite 
species of objects which are transparent; and this being attained, 
we should quite naturally be put upon examining whether the ab- 
sence of this one circumstance be not precisely the point in which 
► all opaque substances will be found to resemble. 

The Joint Method of Agreement and Difference, therefore, or, as 
I have otherwise called it, the Indirect Method of Difference, (be- 
cause, like the Method of Difference properly so called, it proceeds by 
ascertaining how and in what the cases where the phenomenon is. 
present, differ from those in which it is absent) is, after the direct 
Method. of Difference, the most powerful of the remaining instru- 
ments of inductive investigation; and in the sciences which depend 
on pure observation, with little or no aid from experiment, this 
method, so well exemplified in the beautiful speculation on the cause 
of dew, is the primary resource, so far as direct appeals to experi- 
ence are concerned. 

§ 3. We have thus far treated Plurality of Causes only as a possible 
supposition, which, until removed, renders, our inductions uncertain, 
and have only considered by what means, where the plurality does not 
really exist, we may be enabled to disprove it. But we must also con- 
sider it as a case actually occumng in nature, and which, as often as 



254 INDUCTION. 

it does occur, oiir methods of induction ought to be capable of ascer- 
taining and establishing. For this, however, there is required no 
peculiar method. When an effect is really producible by two or more 
causes, the process for detecting them is in no way different from that 
by which we discover single causes. They may (first) be discovered 
as separate sequences, by separate sets of instances. One set of ob- 
servations or experiments shows that the sun is a cause of heat, another 
that friction is a source of it, another that percussion, another that elec- 
tricity, another that chemical action is such a source. Or (secondly) 
the plurality may come to light in the course of collating a number of 
instances, when we attempt to find some circumstance in which they 
all .agi'ee, and fail in doing so. We find it impossible to trace, in all 
the cases in which the effect is met with, any common circumstance. 
We find that we can eliminate all the antecedents ; that no one of them 
is present in all the instances, no one of them indispensable - to the 
effect. On closer scrutiny, however, it appears, that though no one is 
always present, one or other of several always is. If, on further anal- 
ysis, wC/Can detect in these any common element, we may be able to 
ascend from them to some one cause which is the really operative cir- 
cumstance in them all. Thus it might, and perhaps will be, discovered, 
that in the production of heat by friction, percussion, chemical action, &c., 
the ultimate source is one and the same. But if (as continually hap- 
pens) we cannot take this ulterior step, the different antecedents must be 
set down as distinct causes, each sufficient of itself to produce the effect. 
We may here close our remarks on the Plurality of Causes, and pro- 
ceed to ^he still more peculiar and more complex case of the Intermix- 
ture of Effects, and the interference of causes with one another: a 
case constituting the principal part of the complication and difficulty of 
the study of nature ; and with which the four only possible methods 
of directly inductive investigation by observation and experiment, are 
for the most part, as will appear presently, quite unequal to cope. 
The instrument of Deduction alone is adequate to unravel the com- 
plexities proceeding from this source ; and the four methods have little- 
more in their power than to supply premisses for our deductions.* 

§ 4. A concurrence of two or more causes, not separately producing 
each its own effect, but interfering with or modifying the effects of one 
another, takes place, as has already been explained, in two different 
ways. In the one case, which is exemplified by the joint operation of 
different forces in mechanics, the separate effects of all the causes con- 
tinue to be produced, but are comjDOunded with one another, and' dis- 
appear in one total. In the other case, illustrated by the case of chem- 
ical action, the separate effects cease entirely, and are succeeded by 
phenomena altogether different, and governed by different laws. 

Of these cases the former is by far the more frequent, and this case 
it is which, for the most part, eludes the :grasp of our experimental 
methods. The other, and exceptional case is essentially amenable to 
them. When the laws., of the original agents cease entirely, and a 
phenomenon makes its appearance, which, with reference to those 
laws, is' quite heterogeneous; when, for example, two- gaseous sub- 
stances, hydrogen and oxygen, on being brought together, throw off 
their peculiar properties, and produce the substance called water ; in 
euch cases the new fact may be subjected to expeiimental inquiry, like 



INTERMIXTURE OF EFFECTS. 255 

my Other phenoifleraon ; and the elements which are said to compose 
it may be considered as the mere agents of its production ; the condi- 
tions on which it depends, the facts which make up its cause. 

The effects of the new phenomenon, th^ froperties of water, for in- 
stance, are as easily found by experiment as the effects of any other 
cause. But to discover the cause of it, that is, the particular conjunc- 
tion of agents from which it results, is often difficult enough. In the 
first place, the origin, and actual production of the phenomenon, is 
most frequently inaccessible to our observation. If we could not have 
learned the composition of water until we found instances in which it 
was actually produced from oxygen and hydrogen, we should have 
bepn forced to wait until the casual thought, struck some one of passing 
an electric spark through a mixture of the two gases, or inserting a 
lighted taper into it, merely to try what would happen. Further, even 
if we could have ascertained by the Method of Agreement, that oxygen 
and hydrogen were both present when water is produced, no experi- 
mentation on oxygen and hydrogen separately, no knowledge of their 
laws, could have enabled us deductively to infer that they would pro- 
duce water. We require a specific experiment on the two combined. 

Under these difficulties, we should, generally have been indebted for 
our knowledge of the causes of this class of effects, not to any inquiry 
directed specifically towards that end, but either to accident, or to the 
gradual progress of experimentation on the different combinations ot 
which the producing agents are susceptible ; if it were not for a pecu- 
liarity belonging to effects of this description, that they often, under 
some particular combination of circumstances, reproduce their causes. 
If water results from the juxtaposition of hydrogen and oxygen when- 
ever this can be made sufficiently close and intimate, so, on the other 
hand, if water itself be placed in certain situations, hydrogen and oxy- 
gen are reproduced from it : an abrupt termmation is put to the new 
laws, and the agents reappear separately with their own properties as 
at first. What is called chemical analysis is the process of searching 
for the causes of a phenomenon among its effects, or rather among the 
effects produced by the action of some other causes upon^it. 

Lavoisier, by heating mercury to a high temperature in a close vessel 
containing air, found that the mercury increased in weight and became 
what was then called red precipitate, while the air, on being examined 
afi;er the experiment, proved to have lost weight, and to have become 
incapable of supporting life or combustion. When red precipitate was 
exposed to a stilf greater heat, it became mercury again, and gave off 
a gas which did support life and flame. Thus the agents which by 
their combination produced red precipitate, namely, the mercury and 
the gas, reappear as effects resulting from that precipitate when acted 
upon by heat. So, if we decompose water by means of iron filings, 
we produce two effects, rust and hydrogen : now rust is, already known 
by experiments upon the component substances, to be an effect of the 
union of iron and oxygen : the iron we ourselves supplied, but the 
oxygen must have been produced from the water. The result there- 
fore is that the water has disappeared, and hydrogen and oxygen have 
appeared in its stead: or in other words, the original laws of these 
gaseous agents, which had been suspended by the superinduction of 
the new laws called the properties of water, have again started into 
existence, and the causes of water are found among its effects. 



256 INDUCTION. 

; Where two phenomena, between the laws or properties of which 
considered in themselves no connexion can be traced, are thus recipro- 
cally cause and effect, each capable in its turn of being produced from • 
the other, and each, when it produces the other, ceasing itself to exist 
(as- water is produced from oxygen and hydrogen, and oxygen and 
hydrogen are reproduced from water); this causation , of the two 
-phenomena by one another, each of them being generated by thp' 
other's destruction, is properly transformation. The idea of chemical, 
composition is an idea of transformation, but of a transformation which" 
is incomplete ; since we consider the oxygen and hydrogen to be 
present in the water as oxygen and hydrogen, and capable of being 
discovered in it if our senses were sufficiently keen : a supposition (for 
it is no more) grounded solely upon the fact, that the weight of the 
water is the sum of the separate weights of the two ingredients. If 
there had not been this exception to the entire disappearance, in the 
compound, of the laws of the separate ingredients ; if the combined 
agents had not, in this one particular of weight, preserved their own 
laws, and produced a joint result equal to the sum of their separate 
results; we should never, probably, have had the notiou now implied 
by the words chemical composition : and, in the fact of water produced 
from hydrogen and oxygen and hydrogen and oxygen produced from 
water, as the transformation • wotild Have been complete, we should 
have seen only a transformation. ' ■■ ' \ - 

In these cases, then, when the heteropathic effect (as we called it iji ' 
a former chapter) is but a transformation of its cause, or in other 
words, when the effect and its cause are reciprocally such, and 
mutually convertible into each other; the problem of finding the cause 
resolves itself into the far easier one of finding an effect, which is the 
kind of inquiry that admits of being prosecuted by dirfect experiment. 
But there are other cases of heteropathic effects to which this mode of 
investigation is not appUcable, Take, for instance, the heteropathic 
laws of mind; that portion of the phenomena of our mental nature., 
which are analogous to. chemical rather than to dynamical phenomena; 
as when a complex passion is formed by the coalition of several 
elementary impulses, or a complex^emotion by several simple pleasures. 
or pains, of which it is the result, without being the aggregate, or in 
any respect homogeneous with them. The product, in these cases, is' 
generated by its various factors ; but the factors cannot be reproduced 
from the product : just as a youth can grow into an old man, but an 
old man cannot grow into a youth. We cannot ascertain from vrhat 
simple feelings any of our complex states of mind- are generated, as 
we ascertain the ingredients of a chemical compound, by making it, 
in its turn, generate them. We can only, therefore, discover these 
laws by the slow process of studying the simple feelings themselves, 
and ascertaining synthetically, by experimenting on the various com-: 
binations of which they are susceptible, what they, by their mutual 
action upon one another, are capable of generating. 

§ 5. It mig'ht.haYe-fjeen suppos;ed that the other, and apparently 
simpler variety of the mutual interference of causes, where each cause, 
continues to produce its own proper effect. according to the same laws 
to which it conforms in its separate state, would have presented feAver 
difficulties to the inductive inquirer than that of which we have just 



INTERMIXTURE OF EFFECTS. 257 

finished the consideration. It presents, however, so far as direct in- 
duction apart from deduction is concerned, infinitely greater difficul- 
ties. Wlien a concurrence of causes gives rise to a new effect bearing 
no relation to the separate effects of those causes, the resulting phe- 
nomeuon at least stands forth undisguised, inviting attention to its 
peculiarity, and presenting no obstacle to our recognizing its presence 
or absence among any number of surrounding phenomena. It admits 
therefore of being easily brought under the canons of induction, pro- 
vided instances can be obtained such as those canons require: and the 
non-occurrence of such instances, or the want of means to produce 
them artificially, is the real and onl^^ difficulty in such investigations ; 
a difficulty not logical, but in some sort physical. It is otherwise with 
cases of what, in a preceding chapter, has been denominated the 
Composition of Causes. There, the effects of the separate causes do 
not terminate and give place to others, thereby ceasing to form any 
part of the phenomenon to be investigated ; on the contrary they still 
take place, but are intermingled with, and disguised by, the homoge- 
neous and closely-allied effects of other causes. They are no longer 
a, b, Cj d, e, existing side by side, and continuing to be separately dis- 
cernible ; they are + a,'- — a,'^*b, — b, 2 b, &c., some of which cancel 
one another, while many others dp not appear distinguish ably but 
merffe in one sum : forminof altosfether a result, between which and 
the causes whereby it was produced there is often an insurmountable 
difficulty in tracing by observation any fixed relation whatever. 

The general idea of the Composition of Caus.es has been seen to be, 
that although two or more laws interfere with one another, and appa- 
rently frustrate or modify one another's operation, yet in reality all 
are fulfilled, the collective effect being the exact sum total of the 
effects of the causes taken separately. A familiar instance is that of a 
body kept in equilibrium by two equal and contrary forces. One of 
the forces if acting alone would carry it so far to the west, the other if 
acting alone would carry it exactly as far towards the east : and the 
result is the same as if it had been first can'ied to the west as far as 
the one force would carry it, and then back towards the east as far as 
the other would carry it, that is, precisely the same distance ; being 
ultimately left where it was found at first. 

All laws of causation are liable to be in this manner counteracted, 
and seemingly frustrated, by coming into conflict with other laws, the 
separate result of which is opposite to theirs, or more or less incon- 
sistent with it. And hence, with alniost every law, many instances in 
which it really is entirely fulfilled, do not, at first sight, appear to be 
cases of its operation at all. It is so in the example just adduced : a 
force, in mechanics, means neither more nor less than a cause of 
motion, yet the sum of the effects of two causes of motion may be rest. 
Again, a body solicited by two forces in directions making an angle 
with one another, moves in the diagonal; and it seems a paradox to 
say that motion in the diagonal is the sum of two motions in two other 
lines. Motion, how^ever, is but change of place, and at every instant 
the body is in the exact place it would have been in if the forces had 
acted during alternate instants instead of acting in the same instant ; 
(saving that if we suppose two forces to act successively which are in 
truth simultaneous, we must of course allow them double the time.) 
It is evident, therefore, that each force has had, during each instant, 
Kk 



258 INDUCTION. ' 

all the effect which belonged to it ; and that the modifying influence 
which one of two concurrent causes is said to exercise with respect to 
the other, may be considered as exerted not over the action of the 
cause itself, but over the effect after it is completed. For all purposes 
of predicting, calculating, or explaining their joint result, causes which 
compound their effects may be treated as if they produced simultane- 
ously each of them its own effect, and all these effects coexisJ:ed visibly. 

Since the laws of causes are as really fulfilled when the causes are 
said to be counteracted by opposing causes, as when they are left to 
their own undisturbed action, we must be cautious not to express the 
laws in such terms as would render the assertion of their being fulfilled 
in those cases a contradiction. If, for instance, it were stated as a law 
of nature that a body to which a force is applied moves in the direction 
of the force, with a velocity proportioned to the force directly, and to 
its own mass inversely ; when in point of fact some bodies to which a 
force is applied do not move at all, and those which do move are, from 
the very first, retarded by the action of gravity and other resisting 
forces, and at last stopped altogether ; it is clear that the general propo- 
sition, although it would be true under a certain hypothesis, would not 
express the facts as they actually occur. To accommodate the expres- 
sion of the law to the real phenomena, we must say, not that the object 
moves, but that it tends to move in the direction and with the velocity 
specified. We might, indeed, guard our expression in a different mode, 
by saying that the body moves in that manner unless prevented, or except 
in so far as prevented by some counteracting cause. But the body 
does not only move in that manner unless counteracted ; it tends to 
move in that manner even when counteracted ; it still exerts, in the 
original direction, the same energy of movement as if its first impulse 
had been undisturbed, and produces, by that energy, an exactly equiva- 
lent quantity of effect. This is true even when the force leaves the 
body as it found it, in a state of absolute rest ; as when we attempt to 
raise a body of three tons weight with a force equal to one ton. For 
if, while we are applying this fiDrce, the wind or water or any other 
agent supplies an additional force just exceoiiing two tons, the body 
will be raised ; thus proving that the force we applied exerted its full 
effect, by neutralizing an equivalent portion of the weight which it was 
insufficient altogether to overcome. And if, while we are exerting 
this force of one ton upon the object in a direction contrary to that of 
gravity, it be jDut into a scale and weighed, it will be found to have 
lost a ton of its weight, or, in other words, to press downwards with 
a force only equal to the difference of the two fof ces. 

These facts are correctly indicated by the expression tendency. All 
laws of causation, in consequence of their liability to be counteracted, 
require to be stated in words affirmative of tendencies only, and not of 
actual results. In those sciences of causation which have an accurate 
nomenclature, there are special words which signify a tendency to the 
particular effect with which the science is conversant ; thus pressure, in 
mechanics, is synonymous with tendency to motion, and forces are not 
reasoned upon as causing actual motion, bui: as exerting pressure. A 
similar improvement in terminology would be very salutary in many 
other branches of science. 

Tlio habit of neglecting this necessary element in the precise ex- 
pression of the laws of nature, has given birth to the popular prejudice 



INTERMIXTURE OF EFFECTS. 259 

that all general truths have exceptions ; and much unmerited distrust 
has thence accrued to the conclusions of philosophy, when they have 
been submitted to the judgment of persons w^ho were not philosophers. 
The rough generalizations suggested by common observation usually 
have exceptions ; but the principles of science, or in other words, the 
laws of causation, have not. *' What is thought to be an exception to 
a principle," (to quote words used on a different occasion,) " is always 
some other and distinct principle cutting into the former ; some other, 
force which impinges against the first force, and deflects it from its 
direction. There are not a law and an exception to that law, the law 
a^cting in ninety-nine cases and the exception in one. There are two 
laws, each possibly acting in the whole hundred cases, and bringing 
about a common effect by their conjunct operation. If the force which, 
being the less conspicuous, of the two, is called the disturhing force, 
prevails sufficiently over the other force in some one case, to constitute 
that case what is commonly called an exception, the same disturbing 
force probably acts as a modifying cause in many other cases which no 
one will call exceptions. 

" Thus if it were stated to be a law of nature that all heavy bodies 
fall to the ground, it would probably be said that the resistance of the 
atmosphere, which prevents a balloon from falling, constitutes the 
balloon an exception to that pretended law of nature. But the real 
law is, that all heavy bodies tend to fall ; and to this there is no excep- 
tion, not even the sun and moon ; for even they, as every astronomer 
knows, tend towards the earth, with a force exactly equal to that with 
which the earth tends towards them. The resistance of the atmosphere 
might, in the particular case of .the balloon, from a misapprehension of 
what the law of gravitation is, be said to prevail over the law ; but its 
disturbing effect is quite as real in every other case, since, though it 
does not prevent, it retards the fall of all bodies whatever. The rule, 
and the so-called exception, do not divide the cases between them ; 
each of them is a comprehensive rule extending to all cases. To call 
one of these concurrent principles an exception to the other, is super- 
ficial, and contrary to the correct principles of nomenclature and 
arrangement. An effect of precisely the same kind, and arising from 
the .same cause, ought not to be placed in two diffe-rent categories, 
merely as there does or does not exist another cause preponderating 
over it." 

§ 6. We have -now to consider according to what method these 
complex effects, compounded of the effects of many causes, are to be 
studied ; how we are enabled to trace each effect to the concurrence 
of causes in which it originated, and ascertain the conditions of its 
recurrence, the circumstances in which it may bo expected again to 
occur. The conditions of a phenomenon which aiises fi'om a com- 
position of causes, may be investigated either deductively or experi- 
mentally. 

The case, it is evident, is naturally susceptible of the deductive 
mode of investigation. The law of an effect of this description is a 
result of the laws of the separate causes on the combination of which 
it depends, and is therefore in itself capable of being deduced from 
these laws. This is called the method a priori. The other, or a 
posteriori method, professes to proceed according to the canons of 



260 INDUCTION. 

experimental inquiry. Considering the whole assemblage of con- 
cilri'ent causes which produced the phenomenon, as one single cause, 
it attempts to ascertain that cause in the ordinary manner, by a com- 
parison of instances. This second method subdivides itself into two 
different varieties. If it merely collates instances of the effect, it is a 
method of pure observation. If it operates upon the causes, and tries 
different combinations of them in hopes of ultimately hitting the 
precise combination which will produce the given total effect, it is a 
method of experiment. 

In order more completely to clear up the nature of each of these 
three methods, and determine which of them deserves the preference, 
it will be expedient (conformably to a favorite maxim of l^ord Chan- 
cellor Eldon, to which, though it has often incurred philosophical 
ridicule, a deeper philosophy will not refuse its sanction), to "clothe 
them in circumstances." We shall select for this purpose a case 
which as yet furnishes no very brilliant example of the success of any 
of the three methods, but which is all the more suited to illustrate the 
difficulties inherent in them. Let the subject of inquiry be, the condi- 
tions of health and disease in the human body ; or (for greater simpli- 
city), the conditions of recovery from a given disease ; and in order 
to narrow the question still more, let it be limited, in the first instance, 
to this one inquiry : Is, or is not some particular medicament (mer- 
cury, for instance), a remedy for that disease. <• 

Now, the deductive method would set out from known properties 
of mercury, and known laws of the human body, and by reasoning 
from these, would attempt to discover whether mercury will act upon, 
the body when in the morbid condition supposed, in such a manner as 
to restore health. The experimental method would simply administer 
mercury in as many cases as possible, noting the age, sex, tempera- 
ment, and other peculiarities of bodily constitution, the particular form 
or variety of the disease, the particular stage of its progress, &c., re- 
marking in which of these cases it produced a salutary effect, and with 
what circumstances it was on those occasions combined. The method 
of simple observation would compare instances of recovery, to find 
whether they agreed in having been preceded by the administration of 
mercury; or would compare instances of recovery with instances of 
failure, to find cases which, agreeing in all other tespects, differed only 
in the fact that mercury had been administered, or that it had not. 

§ 7. That the last of these three modes of investigation is applicable 
to the case, no one has ever seriously contended. No conclusions of 
value, on a subject of such intricacy, ever were obtained in that way. 
The utmost that could result would be a vague general impression for 
or against the efficacy of mercury, of no real avail for guidance unless 
confirmed by one of the other two methods. Not that the results, 
which this method strives to obtain, would not be of the utmost possi- 
ble value if they could be obtained. If all the cases of recovery which 
presented themselves, in an examination extending to a great number 
of instances, were cases in which mercury had been administered, we 
might generalize with confidence from this experience, and should 
have obtained a conclusion of real value. But no such basis for gene- 
ralization can we, in a case of this description, hope to obtain. The 
reason is that wliich we have. so often spoken of as constituting the 



INTERMIXTURE OF EFFECTS. 261 

characteristic imperfection of the Method of Agreement ; Plurality of 
Causes. Supposing even that mercury does tend to cure the disease, 
so many other causes, both natural and artificial, also tend to cure it, 
that there are sure to be abundant instances of recovery in v^hich 
mercury has not been administered : unless, indeed, the practice be to 
administer it in all cases ; on v^hich supposition it w^ill equally be 
found in the cases of failure. , 

When an effect results from the 'jinion of many causes, the share 
which each has in the determination of the effect cannot in general be 
great: and the effect is not likely, even in its presence or absence, 
still less in its variations, to follow very exactly anyone of the causes. 
' Recovery from a disease is an event to which, in eveiy case,- many influ- 
ences must concur. Mercury may be one such influence; but, from 
the very fact that there are many other such, it will necessarily happen 
that although mercury is administered, the patient, for want of other 
concurring influences, will often not recover, and that he often will 
recover when it is not administered, the other favorable influences 
being sufficiently, powerful VAthout it. Neither, therefore, will the 
instances of recovery agree in the administration of mercury, nor will 
the instances of failure agree in the non- administration of it. It is 
much if, by multiplied and accurate returns from hospitals and the like, 
we, can collect that there are rather more recoveries and rather fewer 
failures when mercury is administered than when it is not ; a result of 
very secondary value even as a guide to practice, and almost worthless 
as a contribution to the theory of the subject. 

§ 8. The inapplicability of the method of simple observation to 
ascertain the conditions of effects dependent on many concurring causes, 
being thus recognized ; we shall next inquire whether any greater 
benefit can be expected from the other branch of the a posteriori 
method, that which proceeds by directly trying different combinations 
of causes, either artificially produced or found in nature, and taking 
notice what is their effect : as, for example, by actually trying the effect 
of' mercury, in as many different circumstances as possible. This 
method differs from the one which we have just examined, in turning 
our attention directly to the causes' or agents, instead of turning it to 
the effect, recovery fi'om the disease. And since, as a general rule, 
the effects of causes are far more accessible to our study than the causes 
of effects, it is natural to think that this method may be successful 
although the former must necessarily fail. 

The method now under consideration is called the Empirical Method; 
and in order to estimate it fairly, we must suppose it to be completely, 
not incompletely, empirical. We must exclude fi'om it everything 
which partakes of the nature not of an experimental but of a deductive 
operation. If for instance we try experiments with mercury upon a 
person in health, in order to ascertain the general laws of its action 
upon the human body, and then reason from these laws to determine 
how it will act upon persons affected with a particular, disease, this 
may be a really effectual method, but this is deduction. The experi- 
mental method does not- derive the law' of a complex case fi'om the 
simpler laws which conspire to produce it, but makes its experiments 
directly upon the complex case. We must make entire abstraction of 
all knowledge of the simpler tendencies; the rPuodi opetandi of mercury 



262 INDUCTION. 

in detail ; our experimentation must aim at obtaining a direct answer 
to the specific question, Does or does not mercury tend to cure tlie 
particular disease 1 

Let us see, therefore, how far this case admits of the observance of 
those rules of experimentation, which it is found necessary to observe 
in other cases. When we devise an experiment to ascertain tho effect 
of a given agent, there are certain precautions which we never, if we 
can help it, omit. In the first place, we introduce the agent into the 
midst of a set of circumstances which we have exactly ascertained. ' It 
needs hardly be remarked how far this condition is from being realized 
in any case connected with the phenomena of life ; how far we are 
from knowing what are all the circumstances which preexist in any 
instance in which mercury is administered to a living being. This 
diflSculty, however, though insuperable in most^ cases, may not be so 
in all ; there are sometimes (though I should think never in physiology) 
concurrences of many causes, in which we yet know accurately what 
the causes are. But when we have got clear of this obstacle we en- 
counter another still more serious. In other cases, when we intend to 
try an experiment, we do not reckon it enough that there be no cir- 
cumstance in the case, the presence of which is unknown to us. We 
require also that none of the circumstances which we do know of, shall 
have effects susceptible of being confounded with those of the agent 
whose properties we wish to study. We take the utmost pains to 
^ exclude all causes capable of composition with the given cause ; or if 
forced to let in any such causes, we take care to make them such, that 
we can compute and allow for their influence, so that the effect of the 
given cause may, after the subduction of those other effects, be appa- 
rent as a residual phenomenon. 

These precautions are inapplicable to such cases as we are now con- 
sidering. The mercury of our experiment being tried with an unknown 
multitude (or even let it be a known multitude) of other influencing 
circumstances, the mere fact of their being influencing circumstances 
implies that they disguise the effect of the mercury, and preclude us 
from knowing whether it has any effect or no. Unless we already knew 
what and how much is owing to every other circumstance (that is, un- 
less we suppose the very problem solved which we are considering the 
means of solving), we cannot tell that those other circumstances may 
not have produced the. whole of the effect, independently or even in 
spite of the mercury. The Method of Difference, in the ordinary mode 
of its use, namely, by comparing the state of things following the ex- 
periment with the state which preceded it, is thus, in the case of inter- 
mixture of effects, entirely unavailing; because other causes than that 
whose effect we are seeking to determine, have been operating during 
the transition. As for the other mode of employing the Method of 
Difference, namely, by comparing, not the same case at two different 
periods, but different cases, this in the present instance is quite chi- 
merical. In phenomena so complicated it is questionable if two cases 
similar in all respects but one ever occurred ; and were they to occur, 
we could not possibly know that they were so exactly similar. 

Anything like a spientific use of the method of experiment, in these 
complicated cases, is therefore out of the question. We can in the 
most favorable cases only discover, by a succession of trials, that a cer- 
tain cause is vert/ often followed by a certain effect. For, in one of 



INTERMIXTURE OF EFFECTS. 263 

these conjunct effects, the portion which is determined by any one of 
the influencing agents, is generally, as we before remarked, but small; 
and it must be a more potent cause than most, if even the tendency 
which it really exerts is not thwarted by other tendencies in nearly as 
many ^^ases as it is fulfilled. 

If so little can be done by the experimental method to determine the 
conditions of an effect of matiy combined causes, in the case of medical 
science, .still less is this method applicable to a class, of phenomena 
-more complicated than even those of physiology, the phenomena of 
politics and history. There, Plurality of Causes exists in almost bound- 
less excess, and the effects are, for the most part, inextricably inter- 
woven with one another. To add to the embarrassment, most of the 
inquiries in political science relate to the production of effects of a 
most comprehensive description, such as the public wealth, public 
security, public mdrality, and the like : results liable to be affected 
directly or indirectly either in 'plus or in'Tninus by nearly every fact 
which exists, or event which , occurs, in human society. The vulgar 
notion, that the safe methods on political subjects are those of Baconian 
induction, that the true guide is not general reasoning but specific 
experience, will one day be quoted as among the. most unequivocal 
marks Qf a low state. of the speculative faculties in any age in which it 
is accredited. What can, be more ludicrous than the sort of parodies 
on experimental reasoning which one is accustomed to meet with, not 
in popular discussion only, but in grave treatises when the affairs of 
nations are the theme. " How," it is asked, '" can an institution be 
bad, when the country has prospered under it ]" '' How can sucL or 
such causes have contributed to the prosperity of one country, when 
another has prospered without them 1" Whoever makes use of an 
argument of this kind, not intending to deceive, should be sent back 
to learn the elements of some one of the more easy physical sciences. 
Such reasoners ignore the fact of Plurality of Causes in the very case 
which affords the most signal example of it. So little could be con- 
cluded, in such a case, from any possible collation of individual instances, 
that even the impossibility, in social phenomena, of making artificial 
experiments, a circumstance otherwise so prejudicial to directly induc- 
tive inquiry, hardly affords, in this case, additional reason of regret. 
For even if we could try ex-periments upon a nation, or upon the 
human race, with as little scruple as M. Majendie tries them upon dogs 
or rabbits, we should never succeed in making two instances identical 
in every respect except the presence or absence of some one definite 
circumstance. The nearest approach to an experiment, in the philo- 
sophical sense, w^hich takes place in politics, is the introduction of a 
new operative element into national affairs by some special and assign- 
able measure of government, such as the enactment or repeal of a 
particular law. But, where there are so many influences grt work, it 
requires some time for the influence of any new cause upon national 
phenomena to become apparent ; and as the causes operaiting in so 
extensive a sphere are not only infinitely numerous, but in a state of 
perpetual alteration, it is always" certain that before the effect of a new 
cause becomes conspicuous enough to be a subject of induction, so 
many of the other influencing circumstances will have changed as to 
vitiate the experiment. 

Two, therefore, of the three possible methods for the study of phe- 



264 INDUCTION. 

nomena resulting from the composition of many causes, being from the 
very nature of the case, inefficient and illusory ; there remains only 
the third — that which considers the causes separately, and computes 
the effect from the balance of the different tendencies which produce 
it : in short, the deductive, or a priori method. The more particular 
consideration of this intellectual process requires a chapter to itself. 



CHAPTER XI. • 

OF THE DEDUCTIVE METHOD. 



§ 1. The mode of investigation which, from the proved inapplicability 
of direct methods of observation and experiment,' remains to us as the 
main source of the knowledge we possess, or can acquire, respecting 
the conditions, and laws of recuiTence, of the more complex phenom- 
ena, is called in its most general expression, the Deductive Method; 
and consists of three operations : the first, one of direct induction ; the 
second, of ratiocination ; and the third, of verification. 

I call the first step in the process an inductive operation, because 
there must be a direct induction as the basis of the whole ; although 
in many particular investigations the place of the induction may be 
supplied by a prior deduction ; but the premisses of this prior deduc- 
tion must have been derived from induction. 

The problem of the Deductive Method is, to find the law of an effect 
from the laws of the different tendencies of which it is the joint result. 
The first requisite, therefore^ is to know the laws of those tendencies ; 
the law of each of the concurrent causes : and this supposes a previous 
process of observation or experiment upon each cause separately; or 
else a previous deduction, which also must depend for its ultimate 
premisses upon observation or experiment. Thus, if the subject be 
social, or historical phenomena, the premisses of the Deductive Method 
must be the laws of the causes which determine that class of phenom- 
ena; and those causes are human actions, together with the general 
outward circumstances under the dominion of which mankind are 
placed, and which constitute man's position in this world. The De- 
ductive Method, applied to social phenomena, must begin, therefore, 
by investigating, or must suppose to have been already investigated, 
the laws of human action, and those properties of outward things by 
which the actions of human beings in society are determined. Some 
of these general truths will naturally be obtained by observation and 
experiment, others by deduction : the more complex laws of human 
action, for example, may be deduced from the simpler ones ; but the 
simple or elementary laws will always, and necessarily have been ob- 
tained by a directly inductive process. 

To ascertain, then, the laws of each separate cause which takes a 
share in producing the effect, is the first desideratum of the Deductive 
Method. To know what the causes are, which must be subjected to 
this process of study, may or may not be difficult. In the case last 
mentioned, this first condition is of easy fulfilment. That social phe- 
nomena depended upon the acts and mental impressions of humai| 



THE DEDUCTIVE METHOD. 265 

beings, never could have been a matter of any doubt, however imper- 
fectly it may have been known either by what laws those impressions 
and actions are governed, or to what social consequences their laws 
naturally lead. Neither, again, after physical science had attained a 
certain development, could there be any real doubt where to look for 
the laws on which the phenomena of life depend, since they must be 
the mechanical and chemical laws of the solid and fluid substances 
composing the organized body and the medium in which it subsists, 
together with the peculiar vital laws of the different tissues constituting 
the organic structure. In other cases, really far more simple than 
these, it was much less obvious in what quarter the causes were to be 
looked for : as in the great case of the celestial phenomena. Until, 
by combining the laws of certain causes, it was found that those laws 
explained all the facts which experience had proved concerning the 
heavenly motions, and led to predictions which it always verified, 
mankind never knew that those were the causes. But whether we 
are able to put the question before dr not until after we have become 
capable of answering it, in either case it must be answered ; the laws 
of the different causes must be ascertained, before we can proceed to 
deduce from them the conditions of the effect. 

The mode of ascertaining these laws neither is, nor can be, any 
other than the fourfold method of experimental inquiry, already dis- 
cussed. A few remarks on the application of that method to cases of 
the Composition of Causes, are all that is requisite. 

It is obvious that we cannot expect to find the law of a tendency, 
by an induction from cases in which the tendency is counteracted. 
The laws of motion could never have been brought to light from the 
observation of bodies kept at rest by the equilibrium of opposing 
forces. Even where the tendency is not, in the ordinary sense of the 
word, counteracted, but only modified, by having its effects compounded 
with the effects arising from some other tendency or tendencies, we 
are still in an unfavorable position for tracing by means of such cases, 
the law of the tendency itself It would have been diflScult to dis- 
cover the law that every body in motion tends to continue moving in a 
straight line, by an induction from instances in which the motion is 
deflected into -a curve, by being compounded with the effect of an 
accelerating force. Notwithstanding the resources afforded in this 
description of cases by the Method of Concomitant Variations, the 
principles of a judicious experimentation prescribe that the law of each 
of the tendencies should be studied, if possible, in cases in which that 
tendency operates alone, or in combination with no agencies but those 
of which the effect can, from previous knowledge, be calculated and 
allowed for. 

Accordingly, in the cases, unhappily very numerous and important, 
in which the causes do not suffer themselves to be separated and 
observed apart, there is much difficulty in laying down, with due 
certainty, the inductive foundation necessary to support the deductive 
method. This diflflculty is most conspicuous in the case of physiological 
phenomena ; it being impossible to separate the different agencies 
which collectively compose an organized body, without destroying the 
very phenomena which it is our object to investigate: 

following life, in creatures we dissect, 

We lose it, in the moment we detect. 
L L 



266 INDUCTION. 

And for this reason I am not quite prepared to agree with M. Comte, 
in deeming the science of Society and government intrinsically a more 
difficult study than the science of organic and animal life. I cannot 
but incline to the opinion, that physiology is embarrassed by greater 
natural difficulties, and is probably susceptible of a less degree of 
ultimate perfection, than the social science; inasmuch as it is possible 
to study the laws of one man's mind and actions apart from other men, 
much less imperfectly than we can study the laws of one organ or 
tissue of the, human body apart from the other organs or tissues. 

It is profoundly remarked by M. Comte, that pathological facts, or, 
to speak in common language, diseases in their different fprms and 
degrees, afford in the case of physiological investigation the nearest 
equivalent to experimentation properly so called ; inasmuch as they 
often exhibit to us a definite disturbance in some one organ or organic 
function, the remaining organs and functions being, in the first instance 
at least, unaffected. It is true that from the perpetual actions and 
reactions which are going on among all the parts of the organic 
economy, there can be no prolonged disturbance in any one function 
without ultimately involving many of the others; and when once it has 
'done so, the experiment for the most part loses its scientific value. All 
depends upon observing the early stages of the derangement ; which, 
unfortunately, are, of necessity the least marked. If, however, the 
organs and functions not disturbed in the first instance, become affected 
in a fixed order of succession, some light is thereby thrown upon the 
action which one organ exercises over another ; and we occasionally 
obtain a series of effects,- which we can refer with some confidence to 
■ the original looal derangement; but for. this it is necessary that we 
should know that the original derangement ivas local. If it was what 
4s termed constitutional, that is, if we dd not know in what part of the 
animal economy it took its rise, or the precise nature of the disturbance 
which took place in that part, we are unable to determine which of the 
various derangements was cause and which effect; which of them 
were produced by one another, and which by the direct, though 
perhaps tardy, action of the original cause. 

' Besides natural pathological facts, we can produce pathological facts 
artificially ; we can try experiments, even in the popular sense of the 
term, by subjecting the living being to some external agent, such as 
the mercury of our former example. As this experimentation is not 
intended to obtain a direct solution of any practical question, but to 
discover general laws, from which afterwards the conditions of any 
particular effect may be obtained by deduction ; the best cases to select 
are those of which the circumstances can be best ascertained: and 
such are generally not those in which there is any practical object in 
view. " The experiments are best tried, not in a state of disease, which 
is essentially a changeable state; but in the condition of health, com- 
paratively a fixed state. In the one, unusual agencies are at work, 
.the results of which we have, no means of "^predicting,; in the other, 
the coarse of the accustomed physiological phenomena would, it may 
generally be presumed, remain undisturbed, were it not for the dis- 
turbing cause which we introduce. 

Such, with the occasional aid of the method of Concomitant Varia- 
tions (the latter not less encumbered than the more elementary 
methods, by the peculiar difficulties of the subject), are our indue- 



THE DEDUCTIVE METHOD. 267 

tive resources for ascertaining the laws of the causes considered sepa- 
rately, when we have it not in our power to make trial of them in a 
state of actual separation. The insufficiency of these^ resources is so 
glaring that no one can be surprised at the backward state of the 
science of physiology ; in which indeed our knowledge of causes is so 
imperfect, that we can neither explain, nor could, without specific 
experience, have predicted many of the facts which are certified to us 
by the most ordinary observation. Fortunately, we are much better 
informed as to the empirical laws -of the phenomena, that, is, the 
uniformities respecting which we cannot yet decide whether they are 
cases of causation or mere results of it. Not only has the order in 
which the facts of organization and life successively manifest them- 
selves, from the first germ of existence to death, been found to be uni- 
foiTn, and Very accurately ascertainable ; but, moreover, ' by a great 
application of the Method of Concomitant Variations to the' entire 
facts of comparative anatomy and physiology, the conditions of or- 
ganic structure corresponding to each class of functions have been 
determined with considerable precision.* Whether these organic 
conditions are the whole of the conditions, and whether they be con- 
ditions at all, or mere collateral effects of some common cause, we are 
quite ignorant : norare we ever likely to know, unless we could con- 
struct an organized body, and try whether it would live. 

Under such disadvantages do we, in cases of this description, at- 
tempt the initial, or inductive step, in the application of the Deductive 
Method to complex phenomena. But such, fortunately, is not the 
common case. In general, the laws of the causes on which the effect 
depends may be obtained by an induction from comparatively simple 
instances, or, at the worst, by deduction from the laws of simpler 
causes so obtained. By simple instances are meant, of course, those 
in which the action of each cause was not intermixed or interfered 
with, or not to any great extent, by other causes Whose laws were 
unknown. And only when the induction which furnished, the prem- 
isses to the Deductive Method rested upon such instances, has the 
application of such a method to the ascertainment of the laws of a 
complex effect, been attended with brilliant results. 

§ 2. Wlien the laws of the causes have been ascertained, and the 
first stage of the great logical operation now under discussion satis- 
factorily accomplished, the second part follows; that of determining, 
from the laws of the causes, what effect any given combination of those 
causes will produce. This is a process of calculation, in the wider 
sense of the term ; and very often involves processes of calculation in 
the narrowest sense. It is a ratiocination ; and when our knowledge 
of the causes is so perfect, as to extend to the- exact numerical laws 
which they observe in producing their effects, the ratiocination may 
reckon among its premisses the theorems of the science of number, in 
the whole immense extent of that science. Not only are the highest 
truths of mathematics often required to enable us to compute an effect, 
the numerical law of which we already know ; but, even by the aid 
of those highest truths^ we can go but a little way. In so simple a 
case as the celebrated^ problern, of three bodies gravitating towards one 

* This great pl^ilosophical operation has been admirably .cha'^acterized in the third vol- 
ume of M, Comte's truly encyclopedical work. ' , 



268 [NDUCTION. 

anotlier, with a force directly as their mass and inversely as the square 
of the distance, all the resources of the calculus have not hitherto 
fiufficed to obtain anything more than an approximate general solution. 
In a case a little more complex, but still one of the simplest w^hich 
arise in practice, that of the motion of a projectile, the causes which 
affect the velocity and range (for example) of a cannon-ball may be all 
known and estimated ; the force of the gunpowder, the angle of eleva- 
tion, the density of .the air, the strength and direction of the sound ; 
but it is one of the most difficult of all mathematical problems to 
combine all these, so as to determine the effect resulting from their 
collective action. 

Besides the theorems of number, those of geometry also come in as 
premisses, where the effects take place in space, and involve motion 
and extension, as in mechanics, optics, acoustics, astronomy. But 
when the complication increases, and the effects are> under the influ- 
ence of so many and such shifting causes as to give no room either for 
fixed numbers, or for straight lines and regular curves, as in the case 
of physiological, to say nothing of mental and social phenomena, the 
laws of number and extension are applicable, if at all, only on that 
large scale on which precision of details becomes imimportant; arid 
although th^se laws play a conspicuous part in the most striking 
examples of the investigation of nature by the Deductive Method, as 
for example in the Newtonian theory of the celestial motions, they are 
by no means an indispensable part of every such process. All that is 
essential in it is the ratiocination from a general law to a particular 
case, that is, the' determination, by means of the particular circum- 
stances of that case, what result is required in that instance to fulfill the 
law. Thus, in the Torricellian experiment, if the fact that air had 
weight had been previously known, it would have been easy, without 
any numerical data, to deduce from the general law of equilibrium, 
that the mercury would stand in the tube at such a height that the 
column of mercury would exactly balance a column of the atmosphere 
of -equal diameter ; because otherwise, equilibrium would not exist. 

By such ratiocinations from the separate laws of the causes, we may, 
to a certain extent, succeed in answering either of the following ques- 
tions : Given a certain combination of causes, what effect will follow? 
and, What combination of causes, if it existed, would produce a given 
effect ? In the one case, we determine the effect to be expected in 
any complex circumstances of which the different elements^ are known: 
in the. other case we learn, according to what law — under what ante- 
cedent conditions- — a given complex effect will recur. 

§ 3. But (it may here be asked) are not the same arguments by 
which the methods of direct observation and experiment were set 
aside as illusory when applied to the laws of complex phenomena, 
applicable with equal force against the Method of Deduction 1 When 
in every single instance a multitude, often an unknown multitude, of 
agencies, are clashing and combining, what security have we that in 
our computation a priori we have taken all these into our reckoning 1 
How many must we not generally be ignorant of? Among those 
which we know, how probable that some have been overlooked; and 
even were all included, how vain the pretence of summing up the 
effects of many causes, unless we know accurately the numerical law 



THE DEDUCTIVE METHOD. .269 

of each,— a condition in most cases not to be fulfilled ; and even when 
fulfilled, to make the calculation transcends, in any but very simple 
cases, the utmost power of mathematical science with its most modem 
improvements. 

These objections truly have much weight, and would be altogether 
unanswerable, if there were no test by which, when we employ the 
Deductive Method, we might judge whether an error of any of the 
above descriptions had been committed or no. Such a test, however, 
there is: and its application forms, under the name of Verification, 
the third essential component part of the Deductive Method ; without 
which all the results it can give have little other value than that of 
guess-work. To warrant reliance upon the general conclusions arrived 
at by deduction, these conclusions must be found, on a careful com- 
parison, to accord with the results of direct observation wherever it 
can, be had. If, when we have experience to compare with them, this 
experience confirms them, we may safely trust to them in other cases 
of which our specific experience is yet to come. But if our deductions 
have led to the conclusion that from a particular combination of causes 
a given effect would result, then in all known cases where that combi- 
nation can be shown to have existed, and where the effect has not 
followed, we must be able to show (or at least to make a probable 
surmise) what frustrated it : if we cannot, the theory is imperfect, and 
not yet to be relied upon. Nor is the verification complete, unless 
some of the cases in which the theory is borne out by the observed 
result, are of at least equal complexity with any other cases in which 
its application could be called for. . 

It needs scarcely be observed, that if direct observation and collation 
of instances have furnished us with any empirical laws of the effect, 
whether true in all observed cases or only true for the most part, the 
most effectual verification of which the theory could be susceptible 
would be, that it led deductively to those empirical laws: that the 
uniformities, whether complete or incomplete, which were observed to 
exist among the phenomena, were accounted for by the laws of the 
causes, were such as could not hut exist if those be really the causes 
by which the phenomena are produced. Thus it was very reasonably 
deemed an essential requisite of any true theory of the causes of the 
celestial motions, that it should lead by deduction to Kepler's laws : 
which, accordingly, the Newtonian theory did. 

In order, therefore, to facilitate the verification of theories obtained 
by deduction, it is important that as many as possible of the empirical 
laws of the phenomena should be ascertained, by a comparison of in- 
stances, conformably to the Method of Agi-eement : as well as (it must 
be added) that the phenomena themselves should be described, in the 
most comprehensive as well as accurate manner possible ; by collect- 
ing from the observation of parts, the simplest possible correct expres- 
sion for the corresponding wholes : as when the series of the observed 
places of a planet was first expressed by a system of epicycles, and 
subsequently by an ellipse. 

It is worth remarking, that complex instances which would have 
been of no use for the discovery of the simple laws into which we 
ultimately analyze their phenomena, nevertheless, when they have 
served to verify the' analysis, become additional evidence of the laws 
themselves. Although we could not have got at the law from com- 



270 INDUCTION. 

plex cases, still when the law, got at otherwise, is found to be in 
accordance with the result of a complex case, that case becomes a 
new experiment on the law, and helps to confirm what it did not 
assist us to discover. It is a new trial of the principle in a different 
set of circumstances ; -'and occasionally serves to eliminate some cir- 
cumstance not previously ' excluded, and to effect the exclusion of 
which, might require an experiment impossible to be executed. This 
was -strikingly conspicuous in the example formerly quoted, in which 
the difference between the observed and the calculated velocity of 
sound was ascertained to result from the heat extricated by the con- 
densation which takes place in each sonorous vibration. This was a 
trial, in new circumstances, of the law of the development of heat by 
compression; and it certainly added materially to the proof of the uni- 
versality of that law. Accordingly any law of nature is deemed to 
have gained in point of certainty, by being found to explain some 
complex case which had not previously been thought of in connexion 
with it ; and this indeed is a consideration to which it is the habit of 
scientific men to attach rather too much value than too little'. 

To the Deductive Method, thus characterized in its three constituent 
parts. Induction, Ratiocination, and Verification, the human mind is 
indebted for its most glorious triumphs in the investigation of nature. 
To it we owe. all the theories by which vast and complicated phenomena 
are embraced under a few simple laws, which, considered as the laws 
of those gi'eat phenomena, could never have been detected by their 
direct study. We may form some conception of what the method has 
done for us, from the case of the celestial motions ; one of the simplest 
among the greater instances of the Composition of Causes, since (ex- 
cept in a few cases not of primary importance) each of the heavenly 
bodies may be considered, without material inaccuracy, to be never at 
one time influenced by the attraction of more than two bodies, the 
sun and one other planet or satellite, making, with the reaction of the 
body itself, and the tangential force, only four different agents on the 
concurrence of which the motions of that body depend ; a mucli smaller 
number, no doubt, than that by which any other of the great phenom- 
ena of nature are determined or modified. Yet how could we ever 
have ascertained the combination offerees upon which the motions of 
th-e earth and planets are dependent, by merely comparing the orbits, 
or velocities, of different planets, or the different velocities or positions 
of the same planet ] Notwithstanding the regularity which manifests 
itself in those motions, in a degree so rare among the effects of a con- 
cuiTence of causes ; although the periodical recurrence of exactly the 
same effect, affords positive proof that all the combinations of causes 
which occur at all, recur periodically ; we should never have known 
what the causes were, if the existence of agencies precisely similai on 
our own earth had not, fortunately, brought the causes themselves 
within the reach of experimentation under simple circumstances. As 
we shall have occasion to analyze, further on, this great example of 
the Method of Deduction, w^e shall not occupy any time with it here, 
but shall proceed to that secondary application of the Deductive 
Method, the result of which is not to prove laws of phenomena but 
to explain them. 



EXPLANATION OF LAWS. 271 



CHAPTER XII. 

OF THE EXPLANATION OF LAWS OF NATURE. 

§ 1. The deductive operation, by which we derive the law of an effect 
from the laws of the causes of which the concurrence gives rise to it, 
may be undertaken either for the purpose of discovering the law, or 
of explaining a law already discovered. The word explanation occurs 
S-O continually, and holds so important a place in philosophy, that a 
little time spent in fixing the meaning of it will be profitably em- 
ployed. 

An individual fact is said to be explained, by pointing out its cause, 
that is, by stating the law or laws of causation, of w^hich its production 
is an instance. Thus, a conflagration is explained, when it is proved 
to have arisen from a spark falling into the midst of a heap of combus- 
tibles. And in a similar manner, a law or uniformity in nature is said 
to be explained, when another law or laws are pointed out, of which 
that law itself is but a case, and from which it could be deduced. 

§ 2. There are three distinguishable sets of circumstances in which 
a law of acusation may be explained from, or, as it also is often ex- 
pressed, resolved into, other laws. 

The first is the case already so fully considered; an intermixture of 
laws, producing a joint effect equal to the sum of the effects of the 
causes taken separately. The law of the complex effe'ct is explained, 
by being resolved into the separate laws of the causes which contribute 
to it. Thus, the law of the motion of a planet is resolved into the law 
of the tangential force, which tends to produce an uniform motion in 
the tangent, and the law of the centripetal force, which tends to pro- 
duce an accelerating motion towards the sun ; the real motion being a 
compound of the two. 

It is necessary here to remark, that in this resolution of the law of a 
complex effect, the laws of which it is compounded are not the only ele- 
ments. It is resolved into the laws of the separate causes, together 
with the fact of their coexistence. The one is as essential an ingredi- 
ent as the other ; whether the object be to discover the law of the effect, 
or only to explain it. To deduce the laws of the heavenly motions, 
we require not only to know the law of a rectilineal and that of a grav- 
itative force, but the existence of both these forces in the celestial 
regions, and even their relative amount. The complex laws of causa- 
tion are thus resolved into two distinct kinds of elements : the one, 
simpler laws of causation, the other (in the aptly selected language of 
Dr. Chalmers) collocations ; the collocations consisting in the existence 
of certain agents or powers, in certain circumstances of place and time. 
We shall hereafter have occasion to return to this distinction, and to 
dwell upon it at such a length as dispenses with the necessity of further 
insisting upon it here. The first mode, then, of the explanation of 
Laws of Causation, is when the law of an effect is resolved into the va- 
rious tendencies of which it is the result, and into the laws of those 
tendencies. 



272 INDUCTION. 

§ 3. A second case is when, between what seemed the cause and 
what was supposed to be its eiFect, further observation detects an in- 
termediate link ; a fact caused by the antecedent, and in its turn caus- 
ing the consequent ; so that the cause at first assigned is but the remote 
cause, operating through the intermediate phenomenon. A seemed 
the cause of C, but it subsequently appeared that A was only the cause 
of B, and that it is B which was the cause of C. For example : man- 
kind were aware that the act of touching an outward object caused a 
sensation. It was, however, at last discovered, that after we have 
touched the object, and before we experience the sensation, some 
change takes place in a kind of thread called a nerve, which extends 
from our outward organs to the brain. Touching the object, therefore, 
is only the remote cause of our sensation; that is, not the cause, prop- 
erly speaking, but the cause of the cause : the real cause of the sensa- 
tion is the change in the state of the nerve. Future experience may not 
only give us more knowledge than we now have of the particular 
nature of this change, but may also interpolate another link : between 
the contact (for example) of the object with our outward organs, and 
the production of the change of state in the nerve, there may take 
place some electric phenomenon. Hitherto, however, no such inter- 
mediate agency has been discovered ; and the touch of the object must 
be considered, provisionally at least, as the proximate cause of the 
affection of the nerve. The sequence, therefore, of a sensation of 
touch upon contact with an object, is ascertained not to be an ultimate 
law; is resolved, as the phrase is, into two other laws — the law, that 
contact with an object produces an affection of the nei-ve ; and the law, 
that an affection of the nerve produces sensation. 

To take another example : the more powerful acids corrode or black- 
en organic compounds. This is a case of causation, but of remote causa- 
tion ; and is said to be explained when it is shown that there is an inter- 
mediate link, namely, the separation of some of the chemical elements of 
the organic structure from the rest, and their entering into combination 
with the acid. The acid causes this separation of the elements, and the 
separation of the elements causes the disorganization, and often the 
chaiTing of the structure. So, again, chlorine extracts coloring mat- 
ters (whence its efficacy in bleaching), and purifies the air from infec- 
tion. This law is resolved into the two following laws. Chlorine has 
a powerful affinity for bases of all kinds, particularly metalhc bases 
and hydrogen. Such bases are essential elements of coloring matters 
and contagious compounds ; which substances, therefore, are decom- 
posed and destroyed by chlorine. 

§ 4. It is of importance to remark, that when a sequence of phe- 
nomena is thus resolved into other laws, they are always laws more 
general than itself The law that A is fi)llowed by C, is less general 
than either of the laws which connect B with C and A with B. This 
will appear from very simple considerations. 

All laws of causation are liable to be counteracted, or frustrated, by 
the non-fulfilment of some negative condition : the tendency, therefore, 
of B to produce C may be defeated. Now the law that A produces 
B, is equally fulfilled whether B is followed by C or not ; but the law 
that A produces C by means of B, is of course only fulfilled when B 
is really followed by C, and is therefore less general than the law that 



EXPLANATION OF LAWS. 273 

A produces B. It is also less general than the law that B produces 
C For B may have other causes besides A ; and as A produces C 
only by means of B, while B produces C whether it has itself been 
produced by A or by anything else, the second law embraces a greater 
number of instances, covers as it were a greater space of ground, than 
the first. 

Thus, in our former example, the law that the contact of an object 
causes a change in the state of the nerve, is more general than the 
law that contact with an object causes sensation, since, for aught we 
know, the change in the nerve may equally take place when, from 
a counteracting cause, as for instance strong mental excitement, the 
sensation does not follow ; as in a battle, where wounds are often re- 
ceived without any consciousness of receiving them. And again, the 
law that change in the state of a nerve produces sensation, is more 
general than the law that contact with an object produces sensation ; 
since the sensation equally follows the change in the nerve when not 
produced by contact with an object, but by some other cause ; as in 
the well knovni case, when a person who has lost a limb feels the very 
Sensation which he has been accustomed to call a pain in the limb. 

Not only are the laws of more immediate sequence into which the 
law of a remote sequence is resolved, laws of greater generality than 
that law is, but (as a consequence of, or rather as implied in, their 
greater generality,) they are more to be relied on ; there are fewer 
chances of their being ultimately found not to be universally true. 
From the moment when the sequence of A and C is shown not to be 
immediate, but to depend upon an intervening phenomenon, then, how- 
ever constant and invariable the sequence of A and C has hitherto been 
found, possibilities arise of its failure, exceeding those which can affect 
either of the more immediate sequences, A B and B C. The tendency 
of*A to produce C may be defeated by whatever is capable of defeat- 
ing either the tendency of A to produce B, or the tendency of B to 
produce C ; it is therefore twice as liable to failure as either of those 
more elementary tendencies ; and the generalization that A is always 
followed by C, is twice as likely to be found erroneous. And so of the 
converse generalization, that C is always preceded and caused by A; 
which will be erroneous not only if there should happen to be a second 
immediate mode of production of C itself, but moreover if there be a 
second mode of production of B, the immediate antecedent of C in the 
sequence. 

The resolution of the one generalization into the other two, not 
only shows that there are possible limitations of the former, from 
which its two elements are exempt, but shows also where these are to 
be looked for. As soon as we know that B intervenes between A and 
C, we also know that if there be cases in which the sequence of A 
and C does not hold, these are most likely to be found by studying the 
effects and the conditions of the phenomenon B. 

It appears, then, that in the second of the three modes in which a 
law may be resolved into other lav^^s, the latter are more general, that 
is, extend to more cases, and are also less likely to require limitation 
from subsequent experience, than the law which they serve to explain. 
They are more nearly unconditional ; they are defeated by fewer con- 
tingencies ; they are a nearer approach to the universal tiiith of nature. 
The same obsei-vations are still more evidently true with regard to the 
Mm 



274 INDUCTION. 

first of the three modes of resolution. When the law of an effect of 
combined causes is resolved into the separate laws of the causes, the 
nature of the case implies that the law of the effect is less general than 
the law of any of the causes, since it only holds when they are com- 
bined; while the law of any one of the causes holds good both then, 
and also when that cause acts apart from the rest. It is also manifest 
that the complex law is liable to be oftener unfulfilled than any one 
of the simpler laws of which it is tjie result, since every contingency 
which defeats any of the laws prevents so much of the effect as 
depends upon it, and thereby defeats the complex law. The mere 
rusting, for example, of some small part of a great machine, often 
suffices entirely to prevent the effect which ought to result from the 
joint action of all the parts. The law of the effect of a combination 
of causes is always subject to the whole of the negative conditions 
which attach to the action of all the causes severally. 

There is another and a still stronger reason why the law of a complex 
effect must be less general than the laws of the causes which conspire 
to produce it. The same causes, acting according to the same laws, 
and differing only in the proportions in which they are combined, often 
produce effects which differ not merely in quantity, but in kind. The 
combination of a tangential with a centripetal force, in the proportions 
which obtain in all the planets and satellites of our solar system, gives 
rise to an elliptical motion ; but if the ratio of the two forces to each 
other were slightly altered, it is demonstrable that the motion produced 
would be in a circle, or a parabola, or an hyperbola: and it has been 
supposed that in the case of some comets one of these is really the 
fact. Yet the law of the parabolic motion would be resolvable into 
the very same simple laws into which that of the elliptical motion is 
resolved, namely, the law of the permanence of rectilineal motion, 
and the law of an uniform centripetal force. If, therefore, in the 
course of ages, some circumstance were to manifest itself which, 
without defeating the law of either of those forces, should merely 
alter their proportion to one another, (such as the shock of a comet, 
or even the accumulating effect of the resistance of the medium in 
which astronomers have been led to sufmise that the motions of the 
heavenly bodies take place;) the elliptical motion might be changed 
into a motion in some other curve ; and the complex law of the heav- 
enly motions, as at present understood, would be deprived of its 
universality, although the discovery would not at all detract from the 
universality of the simpler laws into which that complex law is resolved. 
The law, in short, of each of the concurrent causes remains the same, 
however their collocations may vary; but the law of their joint effect 
varies with every difference in the collocations. There needs no more 
to show how much more general the elementary laws must be, than 
any of the complex laws which are derived fi-om them. 

§ 5. Besides the two modes which have been treated of, there is a 
third mode in which laws are resolved into one another; and in this it 
is self-evident that they are resolved into laws more general than them- 
selves. This third mode is the subsumj>tion (as it has been called) of 
one law under another; or (what comes to the same thing) the gather- 
ing up of several laws into one more general law which includes them 
all. The most splendid example of this operation was, when terres- 



EXPLANATION OF LAWS. 275 

trial gravity and the central force of the Bolar system were brought 
together under the general law of gravitation. It had been proved 
antecedently that the earth and the other planets tended to the sun ; 
and it had been known from the earliest times that all terrestrial bodies 
tend towards the earth. These were similar phenomena; and to enable 
them both to be subsumed under one law, it was only necessary to 
prove that, as the effects were similar in quality, so also they, as to 
quantity, conform to the same rules. This was first shown to be true 
of the moon, which agreed with terrestrial objects not only in tending 
to a centre, but in the fact that this centre was the earth. The tendency 
of the moon to the earth was already known to vary as the inverse 
square of the distance ; and it was deduced from this, by direct calcu- 
lation, that if the moon were as near to the earth as terrestrial objects 
are, and the tangential force were suspended, the moon would fall 
towards the earth through exactly as many feet in a second as those 
objects do by virtue of their weight. Hence, the inference was irre- 
sistible, that the moon also tends to the earth by virtue of its weight : 
and that the two phenomena, the tendency of the moon to the earth 
and the tendency of terrestrial objects to the earth, being not only 
similar in quality, but, when under the same circumstances, identical 
in quantity, are cases of one and the same law of causation. But the 
tendency of the moon to the earth and the tendency of the earth and 
planets to the sun, were already known to be cases of the same law of 
causation : and thus the law of all these tendencies, and the law of 
terrestrial gravity, were recognized as identical, or, in other words, 
were subsumed under one general law, that of gravitation. 

In a similar manner, the laws of magnetic phenomena have recently 
been subsumed under known laws of electricity. It is thus that the 
most general laws of nature are usually arrived at : we mount to them 
by successive steps. For, to arrive by correct induction at laws which 
hold under such an immense variety of circumstances, laws so general 
as to be independent of any varieties of space or time which we are 
able to observe, requires for the most part many distinct sets of experi- 
ments or observations, conducted at different times and by different 
people. One part of the law is first ascertained, afterwards another 
part: one set of observations teaches us that the law holds good under 
some conditions, another that it holds good under other conditions, by 
combining which observations v/e find that it holds good under con- 
ditions much more general, or even universally. The general law, in 
this case, is literally the sum of all the partial ones ; it is the recog- 
nition of the same sequence in different sets of instances ; and may, in 
fact, be regarded as merely one step in the process of elimination. 
That tendency of bodies towards one another, which we new call 
gravity, had at first been observed only upon the earth's surface, where 
it manifested itself only as a tendency of all bodies towards ihe earth, 
and might, therefore, be ascribed to a peculiar property rf the earth 
itself: one of the circumstances, namely, the proximity ct' the earth, 
had not been eliminated. To eliminate this circumstance required a 
fresh set of instances in other parts of the universe : chese we could 
not ourselves create ; and though nature had created them for us, we 
were placed in very unfavorable circumstances for observing them. 
To make these observations, fell naturally to the lot of a different set of 
persons from those who studied terrestrial phenomena, and had, in- 



276 INDUCTION. 

deed, been a matter of great interest at a time when the idea of 
explaining celestial facts by terrestrial laws, was looked upon as the 
confounding of an indefeasible distinction. When, however, the celes- 
tial motions were accurately ascertained, and the deductive processes 
performed from which it appeared that their laws and those of terres- 
trial gravity corresponded, those celestial observations became a set of 
instances which exactly eliminated the circumstance of proximity to 
the earth ; and proved that in the original case, that of terrestrial ob- 
jects, it was not the earth, as such, that caused the motion or the pres- 
sure, but the circumstance common to that case with the celestial 
instances, namely, the presence of some great body within certain 
limits of distance. 

§ 6. There are, then, three modes of explaining laws of causation, 
or, which is the same thing, resolving them into other laws. First, 
when the law of an effect of combined causes is resolved into the sepa- 
rate laws of the causes, together with the fact of their combination. 
Secondly, when the law which connects any two links, not proximate, 
in a chain of causation, is resolved into the laws which connect each 
with the intermediate links. Both of these are cases of resolving one 
law into two or more ; in the third, two or more are resolved into one : 
when, after the law has been shown to hold good in several different 
classes of cases, we decide that what is true in each of these classes of 
cases, is true under some more general supposition, consisting of what 
all those classes of cases have in common. We may here remark that 
this last operation involves none of the uncertainties attendant upon 
induction by the Method of Agreement, since we need not suppose 
the result to be extended by way of inference to any new class of cases, 
different from those by the comparison of which it was engendered. 

In all these three processes, laws are, as we have seen, resolved into 
laws more general than themselves, laws extending to all the cases 
which the former extend to, and others besides. In the first two 
modes they are also resolved into laws more certain, in other words, 
more universally true than themselves ; they are, in fact, proved not 
to be themselves laws of nature, the character of which is to be 
universally true, but results of laws of nature, which may be only true 
conditionally, and for the most part. No difference of this sort exists 
in the third case ; since here the partial laws are, in fact, the very 
same law as the general one, and any exception to them would be an 
exception to it too. 

By all the three processes, the range of deductive science is 
extended ; since the laws, thus resolved, may be thenceforth deduced 
demonstratively from the laws into which they are resolved. As 
abeady remarked, the same deductive process which proves a law or 
fact of causation, if unknown, serves to explain it when known. 

The w(ird explanation is here used in a somewhat peculiar sense. 
What is called explaining one law of nature by another, is but sub- 
stituting ouG mystery for another ; and does nothing to render the 
general course of nature other than mysterious : we can no more assign 
a why for the more extensive laws than for the partial ones. The 
explanation may substitute a mystery which has become familiar, and 
has giown to seem not mysterious, for one which is still strange. And 
this is the meaning of explanation, in common parlance. But the 



EXAMPLES OF THE EXPLANATION OF LAWS. 277 

process with which we are here concerned often does the very con- 
trary ; it resolves a phenomenon with which we are faraihar, into one 
of which we previously knew little or nothing ; as when the common 
fact of the fall of heavy bodies is resolved into a tendency of all par- 
ticles of matter towards one another. It must be kept constantly in 
view, therefore, that when philosophers speak of explaining any of 
the phenomena of nature, they always mean, pointing out not some 
more familiar but merely some more general phenomenon of which it 
is a partial exemplification, or some laws of causation which produce 
it by their joint or successive action, and from which, therefore, its 
conditions may be determined deductively. Every such operation 
brings us a step nearer towards answering the question, which was 
stated some time ago as comprehending the whole problem of the 
investigation of nature viz., What are the fewest assumptions which 
being granted, the order of nature as it exists would be the result 1 
What are the fewest general propositions from which all the uniformities 
existing in nature could be deduced ? 

The laws, thus explained or resolved, are sometimes said to be 
accounted Jor ; but the expression is incorrect, if taken to mean any- 
thing more than what has been already stated. In minds not habituated 
to accurate thinking, there is often a confused notion that the general 
laws are the causes of the partial ones ; that the law of general gravita- 
tion, for example, causes the phenomenon of the fall of bodies to the 
earth. But to assert this, would be a misuse of the word cause : 
terrestrial gi'avity is not an effect of general gravitation, but a case of 
it ; that is, one kind of the particular instances in which that general 
law obtains. To account for a law of nature means, and can mean, no 
more than to assign other laws more general, together with collocations, 
which laws and collocations being supposed, the partial law follows 
without any additional supposition. 



CHAPTER XIII. 

MISCELLANEOUS EXAMPLES OF THE EXPLANATION OF LAWS OF NATURE. 

^ § 1. Some of the most remarkable instances which have occuiTed 
since the great Newtonian generalization, of the explanation of laws 
of causation subsisting among complex phenomena, by resolving them 
into simpler and more general laws, are to be found among the recent 
speculations of Liebig in organic chemistry. These speculations, 
although they have not yet been sufficiently long before the world to 
entitle us positively to assume that no well-grounded objection can be 
made to any part of them, afford, however, so admirable an example 
of the spirit of the Deductive Method, that I may be permitted to pre- 
isent some specimens of them here. 

It had been observed in certain cases, that chemical action is, as it 
were, contagious ; that is to say, a substance which would not of itself 
yield to a particular chemical attraction, (the force of the attraction 
not being sufficient to overcome cohesion, or to destroy some chemical 
combination in which the substance was already held,') v/ill neverthe- 



278 INDUCTION. 

less do so if placed in contact with some other body which is in the 
act of yielding to the same force. Nitric acid, for example, does not 
dissolve pure platinum, which may " be boiled with this acid without 
being oxidized by it, even when in a state of such fine division that it 
no longer reflects light," But the same acid easily dissolves silver. 
Now if an alloy of silver and platinum be treated with nitric acid, the 
acid does not, as might naturally be expected, separate the two metals, 
dissolving the silver, and leaving the platinum ; it dissolves both : the 
platinum as well as the silver becomes oxidized, and in that state com- 
bines with the undecomposed portion of the acid. In like manner, 
*' copper does not decompose water, even when boiled in dilute sul- 
phuric acid, but an alloy of copper, zinc, and nickel, dissolves easily 
in this acid with evolution of hydrogen gas." These phenomena can- 
not be explained by the laws of what is termed chemical aflinity. 
They point to a peculiar law, by which the oxidation which one body 
suffers, causes another, in contact with it, to submit to the same change. 
And not only chemical composition, but chemical decomposition, is 
capable of being similarly propagated. The peroxide of hydrogen, a 
compound formed by hydrogen with a greater amount of oxygen than 
the quantity necessary to form water, is held together by a chemical 
attraction of so weak a nature, that the slightest circumstance is suflS- 
cient to decompose it; and it even, though very slowly, gives off oxygen 
and is reduced to water spontaneously (being, I presume, decomposed 
by the tendency of it^ oxygen to absorb heat and assume the gaseous 
state). Now it has been observed, that if this decomposition of tlie 
peroxide of hydrogen takes place in contact with some metallic oxides, 
as those of silver, and the peroxides of lead and manganese, it super- 
induces a corresponding chemical action upon those substances ; they 
also give forth the whole or a portion of their oxygen, and are reduced 
to the metal or to the protoxide ; although they do not undergo this 
change spontaneously, and there is no chemical affinity at work to 
make them do so. Other similar phenomena are mentioned by Dr. 
Liebig. "Now no other explanation," he observes, *' of these phe- 
nomena can be given, than that a body in the act of combination or 
decomposition enables another body, with which it is in contact, to 
enter into the same state." 

Here, therefore, is a law of nature of great simplicity, but which, 
owing to the extremely special and limited character of the phenomena 
in which alone it can be detected experimentally (because in them 
alone its results are not intermixed and blended with those of other 
laws), had been very little recognized by chemists, and no one could 
have ventured, on experimental evidence, to affirm it as a law common 
to all chemical action ; owing to the impossibility of a rigorous employ- 
ment of the Method of Difference where the properties of different kinds 
of substance are involved, an impossibility which we noticed and char- 
acterized in a previous chapter.* Now this extremely special and ap- 
parently precarious generalization has, in the hands of Liebig, been 
converted by a masterly employment of the Deductive Method, into a 
law pervading all nature, in the same way as gravitation assumed that 
character in the hands of Newton ; and has been found to explain, in 
the most unexpected manner, numerous detached generalizations of a 

* Supra, p. 239. 



EXAMPLES OF THE EXPLANATION OF LAWS. 279 

more limited kind, reducing the phenomena concerned in those gener- 
alizations into mere cases of itself. 

The contagious influence of chemical actipn is not a powerful force, 
and is only capable of overcoming weak affinities : we may, therefore, 
expect to find it principally exemplified in the decomposition of sub- 
stances which are held together by weak chemical forces. Now the 
force which holds a compound substance together is generally weaker, 
tiie more compound the substance is ; and organic products are the most 
compound substances known, those which have the most complex 
atomic constitution. It is, therefore, upon such substances that the 
self-propagating power of chemical action is likely to exert itself in 
the most marked manner. Accordingly, first, it explains the remark- 
able laws of fermentation, and some of those of putrefaction. "A little 
leaven," that is, dough in a certain state of chemical action, impresses 
a similar chemical action upon " the whole lump." The contact of any 
decaying substance, occasions the decay of matter previously sounds 
Again, yeast is a substance actually in a process of decomposition from 
the action of air and water, evolving carbonic acid gas. Sugar is a 
substance which, from the complexity of its composition, heis no great 
energy of coherence in its existing form, and is capable of being easily 
converted (by combination with the elements of water) into carbonic 
acid and alcohol. Now the mere presence of yeast, the mere proxim- 
ity of a substance of which the elements are separating from each 
other, and combining with the elements of water, causes sugar to un- 
dergo the same change, giving out carbonic acid gas, and becoming 
alcohol. It is not the elements contained in the yeast which do this. 
" An aqueous infusion of yeast may be mixed with a solution of sugar, 
and preserved in vessels from which the air is excluded, without either 
experiencing the slightest change." Neither does the insoluble resi- 
due of the yeast, after being treated with water, possess the power 
of exciting fermentation. It is not the yeast itself, therefore ; it is 
the yeast in a state of decomposition. The sugar, which would not 
decompose and oxidize by the mere presence of oxygen and water, 
is induced to do so when another oxidation is at work in the midst 
of it. 

By the same principle Liebig is enabled to explain malaria; the 
pernicious influence of putrid substances ; a variety of poisons; conta- 
gious diseases ; and other phenomena. Of all substances, those com- 
posing the animal body are the most complex in their composition, and 
in the least stable condition of union. The blood, in particular, is the 
most imstable compound known. What, therefore, can be less sur- 
prising than that gaseous or other substances, in the act of undergoing 
the chemical changes which constitute, for instance, putrefaction, 
should, when brought into contact with the tissues by respiration or 
otherwise, and still more when introduced by inoculation into the blood 
itself, impress upon some of the particles a chemical action similar to 
its own ; which is propagated in like manner to other particles, until 
the whole system is placed in a state of chemical action more or less 
inconsistent w^itli the chemical conditions of vitality. 

Of the three modes in which we observed in the last chapter that the 
resolution of a special law into more general ones may take place, this 
speculation of Liebig exemplifies the second. The laws explained 
are such as this, that yeast puts sugar into a state of fennentation» 



280 INDUCTION. 

Between the remote cause, the presence of yeast, and the consequent 
fermentation of the sugar, there has been interpolated a proximate 
cause, the chemical actioij between the particles of the yeast and the 
elements of air and water. The special law is thus resolved into two 
others, more general than itself: the first, that yeast is decomposed by 
the presence of air and water ; the second, that matter undergoing 
chemical action has a tendency to produce similar chemical action in 
other matter in contact with it. But while the investigation thus aptly 
exhibits the second mode of the resolution of a complex law, it no less 
happily exemplifies the third ; the subsumption of special laws under 
a more general law, by gathering them up into one more comprehen- 
sive expression which includes them all. For the curious fact of the 
contagious nature of chemical action was only raised into a law of all 
chemical action by these very investigations ; just as the Newtonian 
attraction was only recognized as a law of all matter when it was 
found to explain the phenomena of terrestrial gravity. Previously to 
Liebig's investigations, the property in question had only been observed 
in a few special cases of chemical action ; but when his deductive 
reasonings had established that innumerable effects produced upon 
weak compounds, by substances none of whose known peculiarities 
would account for their having such a power, might be explained by 
considering the supposed special property to exist in all those cases, 
these numerous generalizations on separate substances were brought 
together into one law of chemical action in general: the peculiarities 
of the various substances being, in fact, eliminated, just as the New- 
tonian deduction eliminated from the instances of terrestrial gravity 
the circumstance of proximity to the earth. 

§ 2. Another of Liebig's speculations, which, if it should ultimately 
be found to agree with all the facts of the extremely complicated 
phenomenon to which it relates, will constitute one of the finest 
examples of the Deductive Method upon record, is his theory of respi- 
lation. 

The facts of respiration, or in other words the special laws which 
Liebig has attempted to explain from, and resolve into, more general 
ones, are, that the blood in passing through the lungs absorbs oxygen 
and gives out carbonic acid gas, changing thereby its color from a 
blackish purple to a brilliant red. The absorption and exhalation are 
evidently chemical phenomena ; and the carbon of the carbonic acid 
must have been derived from the body, that is, must have been ab- 
sorbed by the blood from the substances with which it came into 
contact in its passage through the organism. Required to find the 
intermediate links, the precise nature of the two chemical actions which 
take place ; first, the absorption of the carbon or of the carbonic acid 
by the blood, in its circulation through the body ; next, the excretion 
of the carbon, or the exchange of the carbonic acid for oxygen, in its 
passage through the lungs. 

Dr. Liebig believes himself to have found the solution of this vcxata 
qucKstio in a class of chemical actions in which scarcely any less acute 
and accurate inquirer would have thought of looking for it. 

Blood is composed of two parts, the serum and the globules. The 
serum absorbs and holds in solution carbonic acid in great quantity, 
but has no tendency either to part with it or to absorb oxygen. The 



EXAMPLES OF THE EXPLANATION OF LAWS. 281 

globules, therefore, are conGlrided to he the portion of the blood which 
is ojjerative in respiration. These globules contain a certain quantity 
of iron, which from chemical tests is inferred to be in the state of 
oxide. 

Dr. Liebig recognized, in the known chemical properties of the 
oxides of iron, laws which, if followed out deductively, would lead to 
the prediction of the precise series of phencmena which respiration 
exhibits. 

There are two oxides of iron, a protoxide and a peroxide. In the 
arterial blood the iron is in the form of peroxide : in the venous blood 
we have no direct evidence which of the oxides is present, but the 
considerations to be presently stated will prove that it is the protoxide. 
As arterial and venous blood are in a perpetual state of alternate con- 
version into one another, the question arises, under what circumstances 
the protoxide of iron is capable of being converted into the peroxide, 
and vice versd. Now the protoxide readily combines with oxygen in 
the presence of water, fo^-ming the hydrated peroxide : these condi- 
tions it finds in passing through the lungs ; it derives oxygen from the 
air, and finds water in the blood itself. This would already explain 
one portion of the phenomena of respiration. But the arterial blood, 
in quitting the lungs, is charged with hydrated peroxide : in what 
manner is the peroxide brought back to its former state 1 

The chemical conditions for the reduction of the hydrated peroxide 
into the state of protoxide, are precisely those which the blood meets 
with in circulating through the body ; namely, contact with organic 
compounds. 

Hydrated peroxide of iron, when treated with organic compounds 
(where no sulphur is present) gives forth oxygen and water, which 
oxygen, attracting the carbon from the organic substance, becomes 
carbonic acid ; while the peroxide, being reduced to the state of prot- 
oxide, combines with the carbonic acid, and becomes a carbonate. 
Now this carbonate needs only come again into contact with oxygen 
and water to be decomposed ; the carbonic acid being given off, and 
the protoxide, by the absorption of oxygen and water, becoming again 
the hydrated peroxide. 

The mysterious chemical phenomena connected with respiration 
can now, by a beautiful deductive process, be completely explained. 
The arterial blood, containing iron in the form of hydrated peroxide, 
passes into the capillaries, where it meets with the decaying tissues, 
receiving also in its course certain non-azotized but highly carbonized 
animal products, in particular the bile. In these it finds the precise 
conditions required for decomposing the peroxide into oxygen and the 
protoxide. The oxygen combines with the carbon of the decaying 
tissues, and forms carbonic acid, which, although insuflScient in amount 
to neutralize the whole of the protoxide, combines with a portion (one- 
fourth) of it, and returns in the form of a carbonate, along with the 
other three-fourths of the protoxide, through the venous system into 
the lungs. There it again meets with oxygen and water : the free 
protoxide becomes hydrated peroxide ; the carbonate of protoxide 
parts with its carbonic acid, and by absorbing oxygen and water, enters 
also into the state of hydrated peroxide. The heat evolved in the 
transition from protoxide to peroxide, as well as in the previous oxida- 
tion of the carbon contained in the tissues, is considered by Liebig as 
Nn 



282 INDUCTION. 

the cause whicli sustains the temperature of the body. But into this 
portion of the speculation we need not enter.* 

This example displays the second mode of resolving complex laws, 
by the interpolation of intermediate links in the chain of causation ; 
and some of the steps of the deduction exhibit cases of the first mode, 
that which mfers the joint effect of two or more causes from their 
separate effects ; but to trace out in detail these exemplifications may 
be left to the intelligence of the reader. The third mode is not em- 
ployed in this example, since the simpler laws into which those of 
respiration are resolved (the laws of the chemical action of the oxides 
of iron) were already known laws, and did not acquire any additional 
generality from their employment in the present case. 

§ 3. The property which salt possesses of preserving animal sub- 
stances from putrefaction is resolved by Liebig into two more general 
laws, the strong attraction of salt fOr water, and the necessity of the 
presence of water as a condition of putrefaction. The intermediate 
phenomenon which is interpolated between the remote cause and the 
effect, can here be not merely inferred but seen ; for it is a familiar 
fact, that flesh upon which salt has been thrown is speedily found 
swimming in brine. 

The second of the two factors (as they may be termed) into whicli 
the preceding law has been resolved, the necessity of water to putre- 
faction, itself affords an additional example of the Resolution of Laws. 
The law itself is proved by the Method of Difference, since flesh com- 
pletely dried and kept in a dry atmosphere does not putrefy, as we 
see in the case of dried provisions, and human bodies in very dry 
climates, A deductive explanation of this same law results from 
Liebig's speculations. The putrefaction of animal and other azotized 
bodies is a chemical process, by which they are gradually dissipated in 
a gaseous form, chiefly in that of carbonic acid and ammonia ; now to 
convert the carbon of the animal substance into carbonic acid requires 
oxygen, and to convert the azote into ammonia requires hydrogen, 
which are the elements of water. The extreme rapidity of the putre- 
faction of azotized substances, compared with the gradual decay of 
non-azotized bodies (such as wood and the like) by the action of 
oxygen alone, is explained by Liebig from the general law that 
substances are much more easily decomposed by the action of two 
different affinities upon two of their elements, than by the action of 
only one. 

The purgative effect of salt with alkaline bases, when administered 
in concentrated solutions, is explained by Liebig from the two follow- 
ing principles : Animal tissues (such as the stomach) do not absorb 
concentrated solutions of alkaline salts ; and such solutions do dissolve 
the solids contained in the intestines. The simpler laws into which 
the complex law is here resolved, are the second of the two foregoing 

* As corroborating the opinion of Liebig that the protoxide of iron in the venous blood 
is only partially carbonated, the fact has been suggested that the system shows, graet readi- 
npss to absorb an extra quantity of carbonic acid, as furnished in effervescing drinks. In 
such cases the acid must combine with something, and that something is probably the free 
protoxide. It would be worth ascertaining whether the protoxide itself or its carbonate 
has the greater facility in absorbing oxygen and turning itself into hydrated peroxide in 
the lungs. If the carbonate, then the beneficial effect, on the animal economy, of drinks 
which give an artificial supply of carbonic acid to the system, would be, to that extent 
deductively demonstrated. 



EXAMPLES OF THE EXPLANATION OF LAWS. 283 

principles combined with a third, namely, that the peristaltic contrac- 
tion acts easily upon substances in a state of solution. The negative 
general proposition, that animal substances do not absorb these salts, 
contributes to the explanation by accounting for the absence of a 
counteracting cause, namely, absorption by the stomach, which in the 
case of other substances possessed of the requisite chemical properties, 
interferes to prevent them from reaching the substances which they 
are destined to dissolve. 

§ 4. From the foregoing and similar instances, we may see the im- 
portance, when a law of nature previously unknown has been brought 
to light, or when new light has been thrown upon a known law by 
experiment, of examining all cases which present the conditions neces- 
sary for bringing that law into action ; a process necessarily fertile in 
demonstrations of special laws previously unsuspected, and explana- 
tions of others already empirically known. 

For instance, Faraday discovered by experiment, that voltaic elec- 
tricity could be evolved from a natural magnet, provided a conducting 
body were set in motion at right angles to the direction of the magnet; 
and this he found to hold not only of small magnets, but of that great 
magnet, the earth. The law being thus established experimentally, 
that electricity is evolved, by a magnet, and a conductor moving at 
right angles to the direction of its poles, we may now look out for fresh 
instances in which these conditions meet. Wherever a conductor 
moves or revolves at right angles to the direction of the earth's magnetic 
poles, there we may expect an evolution of electricity. In the northern 
regions, where the polar direction is nearly perpendicular to the hori- 
zon, all horizontal motions of conductors will produce electricity ; hori- 
zontal wheels, for example, made of metal ; likewise all running streams 
will evolve a current of electricity which will circulate round them ; 
and the air thus charged with electricity may be one of the causes of 
the Aurora Borealis. In the equatorial regions, on the contrary, upright 
wheels placed parallel to the equator will originate a voltaic circuit, 
and waterfalls will naturally become electric. 

For a second example ; it has recently been found, chiefly by the 
researches of Professor Graham, that gases have a strong tendency to 
permeate animal membranes, and diffuse themselves through the spaces 
which such membranes enclose, notwithstanding the presence of other 
gases in those spaces. Proceeding from this general law, and review- 
ing a variety of cases in which gases lie contiguous to membranes, we 
are enabled to demonstrate or to explain the foUow^ing more special 
laws : 1st. The human or animal body, when surrounded with any gas 
not already contained within the body, absoi'bs it rapidly ; such, for 
instance, as the gases of putrefying matters : which helps to explain 
malaria. 2d. The carbonic acid gas of effervescing drinks, evolved 
in the stomach, permeates its membranes, and rapidly spreads through 
the system, where, as suggested in a former note, it probably combines 
v/ith the iron contained in the blood. 3d. Alcohol taken into the 
stomach (the temperature of the stomach is above the boiling point of 
pure alcohol,) passes into vapor and spreads through the system with 
great rapidity; (which combined with the high combustibility of alco- 
hol, or in other words its ready combination with oxygen, may perhaps 
help to explain the bodily warmth immediately consequent on drinking 



284 INDUCTION. 

spirituous liquors.) 4th. lu any state of the body in which peculiar 
gases are formed within it, these will rapidly exhale through all parts 
of the body; and hence the rapidity with which, in certain states of 
disease, the surrounding atmosphere becomes tainted. 5th. The putre- 
faction of the interior parts of a carcass will proceed as rapidly as that of 
the exterior, from the ready passage outwards of the gaseous products. 
6th. The exchange of oxygen and carbonic acid in the lungs is not pre- 
vented but rather promoted, by the intervention of the membrane of 
the lungs and the coats of the blood vessels between the blood and the 
air. It is necessary, however, that there should be a substance in the 
blood with which the oxygen of the air may immediately combine, 
otherwise, instead of passing into the blood, it would permeate the 
\vhole organism ; and it is necessary that the carbonic acid, as it is 
formed in the capillaries, should also find a substance in the blood with 
which it can combine ; otherwise it would leave the body at all points, 
instead of being discharged through the lungs. 

§ 5. The following is a deduction which confirms, by explaining, the 
old but not undisputed empirical generalization that soda powders 
weaken the human system. These powders, consisting of a mixture 
of tartaric acid with bicarbonate of soda, from which the carbonic acid 
is set free, must pass into the stomach as tartrate of soda. Now, 
neutral tartrates, citrates, and acetates of the alkalis are found, in their 
passage through the system, to be changed into carbonates ; and to 
convert a tartrate into a carbonate requires an additional quantity of 
oxygen, the abstraction of which must lessen the oxygen destined for 
assimilation with the blood, and to the quantity of which the vigorous 
action of the human system is proportional. 

The instances of new theories agreeing with and explaining old em- 
piricisms, are innumerable. All the just remarks made by experienced 
persons on human character and conduct, are so many special laws, 
which the general laws of the human mind explain and resolve. The 
empirical generalizations on which the operations of the arts have 
usually been founded, are continually justified and confirmed on the 
one hand, or rectified and improved on the other, by the discoveiy of 
the simpler scientific laws on which the efficacy of those operations 
depends. The effects of the rotation of crops, of the various manures, 
and the other processes of improved agriculture, have been, for the 
first time, resolved in our own day into known laws of chemical and 
organic action, by Davy and Liebig. The processes of the healing 
art are even now mostly empirical ; their efficacy is concluded, in each 
instance, from a special and most precarious experimental genei-aliza,- 
tion : but as science advances, in discovering the simple laws of chem- 
istry and physiology, progress is made in ascertaining the intermediate 
links in the series of phenomena, and the more general laws on which 
they depend : and thus, while the old processes are either exploded, 
or their efficacy, in so far as real, explained, improved processes, 
founded on the knowledge of proximate causes, are continually sug- 
gested and brought into use.* Many even of the truths of geometry 

* It was an old generalization in surgery, that tight bandaging had a tendency to prevent 
or dissipate local inflammations. This sequence being, in the progress of physiological 
knowledge, resolved into more general laws, led to the important surgical invention 
recently made by Dr. Arnott, the treatment of local inflammation and tumors by means of 



EXAMPLES OF TIIE EXPLANATION OF LAWS. 285 

were generalizations from experience before they were deduced from 
first principles. The quadrature of the cycloid was first effected by 
measurement, or rather by weighing a cycloidal card, and comparing 
its weight with that of a piece of similar card of known dimensions. 

§ 6. To the foregoing examples from physical science, let us add an- 
other from mental. The following is one of the simple laws of mind : 
Ideas of a pleasurable or painful character form associations more easily 
and strongly than other ideas, that is, they become associated after fewer 
repetitions, and the association is more durable. This is an experi- 
mental law, grounded upon the Method of Difference. By deduction 
from this law, many of the more special laws which experience shows 
to exist among particular mental phenomena may be demonstrated 
and explained : — the ease and rapidity, for instance, with which thoughts 
connected with our passions or our more cherished interests are exci- 
ted, and the firm hold which the facts relating to them have on our 
memory ; the vivid recollection we retain of minute circumstances 
which accompanied any object or event that deeply interested us, and 
of the times and places in which we have been very happy or very 
miserable ; the horror with which we view the accidental instru- 
ment of any occurrence which shocked us, or the locality where it 
took place, and the pleasure we derive from any memorial of past 
enjoyment ; all these effects being proportional to the sensibility of 
the individual mind, and to the consequent intensity of the pain or 
pleas\jre from which the association originated. It has been suggested 
by the able writer of a biographical sketch of Dr. Priestley, in one of 
our monthly periodicals, that the same elementary law of our mental 
constitution, suitably followed out, would explain a variety of mental 
phenomena hitherto inexplicable, and in particular some of the funda- 
mental diversities of human character and genius. Our associations 
being of two sorts, either between synchronous, or between successive 
impressions ; and the influence of the law which renders associations 
stronger in proportion to the pleasurable or painful character of the 
impressions, being felt with peculiar force in the synchronous class of 
associations ; it is remarked by the writer referred to, that in minds of 
strong organic sensibility synchronous associations will be likely to 
predominate, producing a tendency to conceive things in pictures and 
in the concrete, clothed in all their attributes and circumstances, a 
mental habit which is commonly called Imagination, and is one of the 
peculiarities of the painter and the poet ; while persons of more moder- 
ate susceptibility to pleasure and pain will have a tendency to asso- 
ciate facts chiefly in the order of their succession, and if they possess 
mental superiority, will addict themselves to history or science rather 
than to creative art. This interesting speculation the author of the 
present work has endeavored, on another occasion, to pursue further, 
and to explain, by means of it, the leading peculiarities of the poetical 
temperament. It is at least an example which may serve, instead of 
many others, to show tlie extensive scope which exists for deductive 

an equable pressure, produced by a bladder partially filled with air. The pressure, by 
keeping back the blood from the part prevents the inflammation, or the tumor, from being 
nourished : in the case of inflammation, it removes the stimulus, which the organ is unfit 
to receive : in the case of tumors, by keeping back the nutritive fluid, it causes the absorp- 
tion of matter to exceed the supply, and the diseased mass is gradually absorbed and dis- 
appears. 



286 INDUCTION. 

investigation in the important and so eminently imperfect Science of 
Mind. 

§ 7. The copiousness with which I have exempHfied the discovery 
and explanation of special laws of phenomena by deduction from sim- 
pler and more general ones, was prompted by a desire to characterize 
clearly, and place in its due position of importance, the Deductive 
Method ; which, in the present state of knowledge, is destined irrevo- 
cably to predominate in the course of scientific investigation from this 
time forward. A revolution is peaceably and progressively effecting 
itself in philosophy, the reverse of that to which Bacon has attached his 
name. That great man changed the method of the sciences from 
deductive to experimental, and it is now rapidly reverting from experi- 
mental to deductive. But the deductions which Bacon abolished were 
from premisses hastily snatched up, or arbitrarily assumed. The prin- 
ciples were neither established by legitimate canons of experimental 
inquiry, nor the results tested by that indispensable element of a 
rational Deductive Method, verification by specific experience. Be- 
tween the primitive Method of Deduction and that which I have 
attempted to define, there is all the difference which exists between 
the Aristotelian physics and the Newtonian theory of the heavens. 

That the advances henceforth to be expected even in physical, and 
still more in mental and social science, will be chiefly the result of 
deduction, is evident from the general considerations already adduced. 
Among subjects really accessible to our faculties, those which still 
remain in a state of dimness and uncertainty (the succession of their 
phenomena not having yet been brought under fixed and recognizable 
lav/s) are mostly those of a very complex character, in which many 
agents are at work together, and their effects in a constant state of 
blending and intermixture. The disentangling of these crossing threads 
is a task attended with difficulties which, as we have already shown, 
are susceptible of solution by the instrument of deduction alone. 
Deduction is the great scientific work of the present and of future 
ages. The portion henceforth reserved for specific experience in the 
achievements of science, is mainly that of suggesting hints to be fol- 
lowed up by the deductive inquirer, and of confirming or checking his 
conclusions. 



CHAPTER XIV. 

op THE LIMITS TO THE EXPLANATION OF LAWS OF NATURE ; AND OF 
HYPOTHESES. 

§ 1. The preceding considerations have led us to recognize a dis- 
tinction between two kinds of laws, or observed uniformities in nature : 
ultimate laws, and what may be termed derivative laws. Derivative 
laws are such as are deducible from, and may, in any of the modes 
which we have pointed out, be resolved into, other and more general 
ones. Ultimate laws are those which cannot. We are not sure that 
any of the uniformities which we are yet acquainted with are ultimate 
laws ; but we know that there must be ultimate laws ; and that every 



HYPOTHESES. 287 

resolution of a derivative law into more general laws, brings us nearer 
to them. 

Since we are continually discovering that uniformities, not previously 
known to be other than ultimate, are derivative, and resolvable into 
more general laws; since (in other words) we are continually discover-, 
ing an explanation of some sequence, which was previously known only 
as a fact ; it becomes an interesting question whether there are any ne- 
cessary limits to this philosophical operation, or whether it may proceed 
until all the uniform sequences in nature are resolved into some one 
universal law. For this seems, at first sight, to be the ultimatum 
towards which the progress of induction, by the Deductive Method 
resting on a basis of observation and experiment, is progressively 
tending. Projects of this kind were universal in the infancy of philo- 
sophy; any speculations which held out a less brilliant prospect, being 
in those early times deemed not worth pursuing. And the idea 
receives so much apparent countenance from the nature of the most 
remarkable achievements of modern science, that speculators are even 
now constantly rising up (more often on the continent of Europe than 
in this island) who profess either to have solved the problem, or to 
suggest modes in which it may one day be solved. Even where pre- 
tensions of this magnitude are not made, the character of the solutions 
which are given, or sought, of particular classes of phenomena, often 
involves such conceptions of what constitutes explanation, as would 
render the notion of explaining all phenomena whatever ,by means of 
.some one cause, or law, perfectly admissible. 

§ 2. It is, therefore, useful to remark, that the ultimate Laws of Na 
ture cannot possibly be less numerous than the distinguishable sensations 
or other feelings of our nature ;-^those, I mean, which are distinguishable 
from one another in quality, and not merely in quantity or degree. For 
example ; since there is a phenomenon sui generis, called color, which 
our consciousness testifies to be not a particular degree of some other 
phenomenon, as heat, or odor, or motion, but intrinsically unlike all 
others, it follows that there are ultimate laws of color ; that, although 
the facts of color may admit of explanation, they never can be ex- 
plained from laws of heat or odor alone, or of motion alone, but that 
however far the explanation may be carried, there will always remain 
in it a law of color. I do not mean that it might not possibly be shown 
that some other phenomenon, some chemical or mechanical action, for 
example, invariably precedes, and is the cause of, every phenomenon 
of color. But although this, if proved, would be an important exten- 
sion of our knowledge of nature, it would not explain how or why a 
motion, or a chemical action, should produce a sensation of color ; and 
however diligent might be our scrutiny of the phenomena, whatever 
number of hidden links we might detect in the chain of causation 
terminating in the color, the last link would still be a law of color, not 
a law of motion, nor of any other phenomenon whatever. Nor does this 
observation apply only to color, as compared with any other of the great 
classes of sensations ; it applies to every particular color, as compared 
with others. White color can in no manner be explained exclusively 
by the laws of the production of red color. In any attempt to explain it, 
we cannot but introduce, as one element of the explanation, the prop- 
osition that some antecedent or other produces the sensation of white. 



288 INDUCTION. 

The ideal limit, therefore, of the explanation of natural phenomena 
(towards which as towards other ideal limits we are constantly tending, 
without the prospect of ever completely attaining it,) would be to show 
that each distinguishable variety of our sensations, or other states of 
consciousness, has only one sort of cause ; that, for example, whenever 
we perceive a white color, there is some one condition or set of con- 
ditions which is always present, and the presence of which always 
produces in us that sensation. As long as there are several known 
modes of production of a phenomenon, (several different substances, 
for instance, which have the property of whiteness, and between 
which we cannot trace any other resemblance) so long it is not im- 
possible that one of these modes of production may be resolved 
into another, or that all of them may be resolved into some more 
general mode of production not hitherto recognized. But when the 
modes of production are reduced to one, we cannot, in point of sim- 
plification, go any further. This one may not, after all, be the ultimate 
mode ; there may be other links to be discovered between the sup- 
posed cause and the effect ; but we can only further resolve the known 
law, by introducing some other law hitherto unknown ; which will not 
diminish the number of ultimate laws. 

In what cases, accordingly, has science been most successful in 
explaining phenomena, by resolving their complex laws into laws of 
greater simplicity and generality? Hitherto chiefly in cases of the 
propagation of various phenomena through space : and, first and prin- 
cipally, the most extensive and important of all facts of that description, 
the fact of motion. Now this is entirely what might be expected from 
the principles which I have laid down. Not only is motion one of the 
most universal of all phenomena, it is also (as might be expected 
from the former circumstance) one of those which, apparently at least, 
are produced in the greatest number of ways ; but the phenomenon 
itself is always, to our sensations, the same in every respect but degree. 
Differences of duration, or of velocity, are evidently differences in 
degree only ; and differences of direction in space, which alone has 
any semblance of being a distinction in kind, entirely disappear (so far 
as our sensations are concerned) by a change in our own position ; 
indeed the very same motion appears to us, according to our position,, 
to take place in every variety of direction, and motions in every 
different direction to take place in the same. And, again, motion in 
a straight line and in a curve are no otherwise distinct than that the 
one is motion continuing in the same direction, the other is motion 
which at each instant changes its direction. There is, therefore, 
according to the views I have stated, no absurdity in supposing that 
all motion may be produced in one and the same way ; by the same 
kind of cause. Accordingly, the greatest achievements in physical 
science have consisted in resolving one observed law of the production 
of motion into the laws of other known modes of production, or the 
laws of several such modes into one more general mode ; as when the 
fall of bodies to the earth, and the motions of the planets, were brought 
under the one law of the mutual attraction of all particles of matter; 
when the motions said to be produced by magnetism were shown to be 
produced by electricity ; when the motions of fluids in a lateral direc- 
tion, or even contrary to the direction of gravity, were shown to be 
produced by gravity ; and the like. There is an abundance of distinct 



HYPOTHESES. 289 

causes of motion still unresolved into one another ; gravitation, heat, 
electricity, chemical action, nervous action, and so forth; but however 
improbable it may be that these different modes of production of mo- 
tion should ever actually be resolved into one, the attempt so to resolve 
them is perfectly legitimate. For though these various causes produce, 
in other respects, sensations intrinsically different, and are not, there- 
fore, capable of being resolved into one another, yet in so far as they 
all produce motion, it is quite possible that the immediate antecedent 
of the motion may in all these different cases be the same ; that the 
other causes may produce motion through the intermediate agency of 
heat, for instance, or of electricity, or of some common medium yet 
to be discovered. 

We need not extend our illustration to other cases, as for instance 
to the propagation of light, sound, heat, electricity, &c., through space, 
or any of the other phenomena w^hich have been found susceptible of 
explanation by the resolution of their observed law^s into more general 
laws. Enough has been said to display the difference between the 
kind of explanation and resolution of laws which' is chimerical, and 
that of which the accomplishment is the great aim of philosophy ; and 
to show into what sort of elements the resolution must be effected,, 
if at all. ■" ,. - " , ; _ . ' ■. 'w-^ • .-•-.. 

§ 3. As, however, there is scarcely any of the principles of a true 
method of philosophizing which does not require to be guarded against 
errors on both sides, I must enter a caveat against another misapprehen- 
sion, of a kind directly contrary to the preceding, and against which 
there is th'^' more necessity to be on our guard, as it has the appear- 
ance of being countenanced (for I am persuaded that it is only the 
appearance) by so great a thinker as M. Auguste Comte. That phi- 
losopher, among other occasions on which he has condemned, with 
some asperity, any attempt to explain phenomena which are " evidently 
primordial" (meaning, apparently, no more than that every such phe- 
nomenon must have at least one peculiar and inexplicable law,) has 
spoken of the attempt to furnish any explanation of the color belonging 
to each substance, "la couleur elementaire propre a chaque substance," 
as essentially illusory. " No one," says he, " in our time, attempts to 
explain the particular specific gravity of each substance or of each 
structure. Why should it be otherwise as to the specific color, the 
notion of which is undoubtedly no less primordial]"* 

Now although, as M. Comte elsewhere observes, a color must al- 
ways remain a different thing from a weight or a sound, it ought not, 
to be forgotten, and notwithstanding these expressions, cannot possibly 
be forgotten by M. Comte, that varieties of color might nevertheless 
follovv^, or correspond to, given varieties of weight, or sound, or some 
other phenomenon as different as these are from color itself It is one 
question what a thing is, and another w^hat it depends upon ; and 
although to ascertain the conditions of an elementary phenomenon is 
not to obtain any new insight into the nature of the phenomenon itself, 
that is no reason against attempting to discover the conditions. M. 
Comte's interdict against endeavoring to reduce distinctions of color to 
any common principle, would have held equally good against a like 

* Cours de Philosophie Positive, ii. 656. 

Oo 



290 INDUCTION. 

attempt on the subject of distinctions of sound ; whicli nevertheless 
have been found to be immediately preceded and caused by distin- 
guishable varieties in the vibrations of elastic bodies : although a sound, 
no doubt, is quite as different as a color is from any motion of particles, 
vibratory or otherwise. We might add, that, in the case of colors, 
there are strong positive indications that they are not ultimate proper- 
ties of the different kinds of substances, but depend upon conditions 
capable of being superinduced upon all substances ; since there is no 
substance which cannot, according to the kind of light thrown upon it, 
*be made to assume any color we think fit ; and since almost every 
change in the mode of aggregation of the particles of the same sub- 
stance, is attended with alterations in its color, and in its optical prop- 
erties generally. 

The real defect in the attempts which have been made to account 
for, colors by the vibrations of a fluid, is not that the attempt itself is 
unphilosophical, but that the existence of the fluid, and the fact of its 
vibratory motion, are not proved ; but are assumed, on no other ground 
than the facility they are supposed to afford of explaining the phenom- 
ena. And these considerations lead us to the important question of 
^he proper use of scientific hypotheses ; a subject the connexion of 
which with that of the explanation of the phenomena of nature, and of 
the necessary limits to that explanation, needs not be pointed out. 

§ 4. An hypothesis is any supposition which we make (either witli- 
cut actual evidence, or upon evidence avowedly insufficient), in order 
ta endeavor to deduce from it conclusions in accordance with facts 
Vhich are known to be real; under the idea that if the conclusiopB 
to which the hypothesis leads are known truths, the hypothesis itself 
either must be, or at least is likely to be, true. If the hypothesis relates 
to the cause, or mode of production of a phenomenon, it will serve, if 
.'admitted, to explain such facts as are found capable of being deduced 
from it. And this explanation is the purpose of many, if not most 
hypotheses. Since explaining in the scientific sense means resolving 
an uniformity which is not a law of causation, into the laws of causa- 
tion from which it results, or a complex law of causation into simpler 
and more general ones from which it is capable of being deductively 
inferred ; if there do not exist any known laws which fulfill this re(]uire- 
ment, we may feign or imagine some which would fulfill it ; and this is 
making an hypothesis,' 

An hypothesis being a mere supposition, there are no other limits 
to hypotheses than those of the human imagination ; we may, if we 
please, imagine, by way of accounting for an effect, some cause of a 
kind utterly unknown, and acting according to a Ielw altogether fic- 
titious. But as hypotheses of this sort would not have any of the 
plausibility belonging to those which ally themselves by analogy with 
known laws of nature, and besides would not supply the want whicfh 
^arbitrary hypotheses are genera,lly invented to satisfy, by enabling the 
imagination to represent to itself an obscure phenomenon in a familiar 
light ; there is probably no hypothesis in the history of science in which 
both the agent itself and the law of its operation were fictitious. Either 
the phenomenon assigned as the cause is real, but the law according to 
which it acts merely supposed ; or the cause is fictitious, but is sup- 
posed to produce its effects according to laws similar to those of some 



. HYPOTHESES. 291 

known class of phenomena. An instance of the first kind is afforded 
by the different suppositions respecting the law of the planetary cen- 
tral force, anterior to the discovery of the true law, that the force varies 
as the inverse square of the distance ; which was itself suggested by 
Newton, in the first instance, as an hypothesis, and was verified by 
proving that it led deductively to Kepler's laws. Hypotheses of the 
second kind are such as the vortices of Descartes, which were fictitious, 
but were supposed to obey the known laws of rotatory motion ; or the 
two rival hypotheses respecting the nature of light, the one ascribing 
the phenomena to a fluid emitted from all luminous bodies, the other 
(now more generally received) attributing them to vibratory motions 
among the particles of an ether pervading all space. Of the existence 
of either fluid there is no evidence, save the explanation they are cal- 
culated to afford of some of the phenomena ; but they are supposed to 
produce their effects according to known laws ; the ordinary laws of 
continued locomotion in the one case, and in the other, those of the 
propagation of undulatory movements among the^ particles of an elastic 
fluid. . ■' 

According to the foregoing remarks, hypotheses are invented to en- 
able the Deductive Method to be earlier applied to phenomena. But* 
in order to discover the cause of any phenomena by the Deductive 
Method, the process must consist of three parts; induction, ratiocin- 
ation, and verification. Induction, (the place of which, however, may 
be supplied by a prior deduction,) to ascertain the laws of the causes; 
ratiocination, to compute from those laws, how the causes will oper- 
ate in the particular combination known to exist in the case in hand; 
verification, by comparing this calculated effect with the actual phe- 
nomenon. No one of these three parts of the process can be dis- 
pensed with. In the great deduction which proves the identity of 
gravity and the central force of the solar system, all the three are 
found. First, it is proved from the moon's motions, that the earth 
attracts her with a force varying as the inverse square of the distance. 
This (though partly dependent on prior deductions) corresponds to 
the first, or purely inductive step, the ascertainment of the law of the 
cause. Secondly, from this law, and from the knowledge previously 
obtained of the moon's mean distance from the earth, and of the actual 
amount of her deflexion from the tangent, it is ascertained with what 
rapidity the earth's attraction would cause her to fall, if she were no 
further off, and no more acted upon by extraneous forces, than terres- 
ti'ial bodies are : this is the second step, the ratiocination. Finally, 
this calculated velocity being compared with the observed velocity 
with which all heavy bodies fall, by mere gi'avity, towards the surface 
of the earth, (namely sixteen feet in the first second, forty-eight in the 
second, and so forth, in the ratio of the odd numbers, 1, 3, 5, &c.,) the 
two quantities were found to agree. The order in which I have here 
presented the three steps was not ,the exact order of their discovery ; 
but it is their correct logical order, as portions of the proof that the 
same attraction of the earth which causes the moon's motion, causes 
also the fall of heavy bodies to the earth : a proof which is thus com- 
plete in all its parts. 

Now, the Hypothetical Method suppresses the first of the three steps, 

' . . * Vide supra, p. 264. , . ,, , 



292 INDUCTION. . 

the induction to ascertain the law ; and contents itself with the other 
two operations, ratiocination and verification ; the law, which is rea- 
soned from, being assumed, instead of proved. 

This process may evidently be legitimate upon one supposition, 
namely, if the nature of the case be such that the final step, the verifi- 
cation, shall amount to, and fulfill the conditions of, a complete induc- 
tion. We want to be' assured that the law, we have hypothetically 
assumed is a true one ; and its leading deductively to true results will 
afford this, assurance, |)rovided the case be such that a false law can- 
pot lead to a true result ; provided no law, except the very one which 
we have assumed, can lead deductively to the same conclusions which 
that leads toJ And this proviso is very often realized. For example, 
in tjiat perfect specimen of deduction which we just cited, the original 
major premiss of the ratiocination, the law of the attractive force, was 
ascertained in this very mode ; by this legitimate employment of the 
Hypothetical Method. Newton began by an assumption, that the 
force which at each instant deflects a planet from its rectilineal course, 
and makes it describe a curve round the sun, is a force tending directly 
towards the sun. He then proved that if this be so, the planet will de- 
scribe, as we know by Kepler's first law that it does describe, equal 
areas in equal times ; and, lastly, he proved that if the force acted in 
any other direction whatever, the planet would not describe equal 
areas in equal times. It being thus shown that no other hypothesis 
could accord with the facts, the assumption was proved; the hypothe- 
sis became a law, established by the Method of Difference. Not only* 
did Newton ascertain, by this hypothetical process, the direction of the 
deflecting force ; he proceeded in exactly the same manner to ascer- 
tain the law of variation of the quantity of that force. He assume^ 
that the force varied inversely as the square of the distance ; showed 
that from this assumption the remaining two of Kepler's laws might be 
deduced ; and, finally, that any other law of variation would give re- 
sults inconsistent with those laws, and inconsistent, therefore, vidth the- 
r-eal motions of the planets, of which Kepler's laws were known td be 
a correct expression. ' 

It is thus perfectly possible, and indeed is a very common occur- 
rence, that what is an hypothesis at the beginning of the inquiry 
becomes a proved law of nature before its close. But this can only 
happen when the inquiry has for its object, not to detect an ui^known 
cause, but to determine the precis6 law of a cause already ascertained. 
If it had not been already known that the planets were hindered from 
moving in straight lines by some force tending towards the interior, of 
their orbit, though the exact direction was doubtful ; or if it had not 
been known that the force increased in some proportion or other as the 
distance diminished, and diminished as it increased ; Newton's argu- 
ment would not have proved his conclusion. These facts, however, 
being already certain, the range of admissible suppositions was limited 
to the various possible directions of a line, and the various possible 
numerical relations between the variations of the distance and the 
variations of the attractive force : now among, these it was easily 
shown that different suppositions could not lead to identical conse- 
quences. 

Accordingly, Newton could not have performed his second great 
philosophical operation, that of identifying tenestrial gravity with the 

E E 



HYPOTHESES. 293 

central force of the solar system, by the same hypothetical method. 
When the law of the moon's attraction had been proved from the data 
of the moon itself, then on finding the same law to accord with the phe- 
nomena of terrestrial gravity, he was warranted in adopting it as the 
law of those phenomena likewise : but it would not have been allow- 
able for him, without any lunar data, to assume that the moon was 
attracted towards the earth with a force as the inverse square of the 
distance, merely because that ratio would enable him to account for 
gravity by a similar attraction : for it would have been impossible for 
him to prove that the observed law of the fall of heavy bodies to the' 
earth could not result from any force, save one extending to the moon, 
and proportional to the inverse square. 

It appears, then, to be a condition of a genuinely scientific hy- 
pothesis, that it be not destined always to remain an hypothesis, ' 
but be certain to be either proved or disproved by that comparison % 
with observed facts which is termed Verification. In hypotheses of 
this character, if they relate to causation at all, the effect must be al- 
ready known to depend upon the very cause supposed, and the hypo- 
thesis must relate only to the precise mode of dependence ; the law of 
the variation of the effect according to the variations in the quantity or 
in the relations of the cause. . With these may be classed the hypo- 
theses which do not make any supposition with regard to causation, 
but only with regard to the law of correspondence between facts which 
accompany each other in their variations, though there may be no rela- 
tion of cause and effect between them. Such are the different false 
hypotheses which Kepler made respecting the law of the refraction of 
light. It was known that "the direction of the line of refraction varied 
with every variation in the direction of the line of incidence, but it was 
not known how ; that is, what changes of the one corresponded to the 
different changes of the other. In this case any law, different from the' , 
true one, must have led to false results. And, lastly, we must add to 
these, all hypothetical modes of merely describing phenomena ; such as 
the hypothesis of- the ancient astronomers that the heavenly bodies 
moved in circles; the various hypotheses of eccentrics, deferents, and 
epicycles, which were added to that original hypothesis ; the nineteen , 
false hypotheses which Kepler' made and abandoned respecting the 
form of the planetary orbits ; and even the true doctrine in which he 
finally rested, that those orbits are ellipses, which was but an hypo- 
thesis like tlie rest until verified by facts. 

In all these cases, verification is proof; if the supposition accords 
with the phenomena there needs no other evidence of it. But in 
order that this may be the case,, it is (as we have seen) necessary, 
^hen the hypothesis relates to causation, that the supposed cause 
should not only be a real phenomenon, something actually existing in 
nature, bijt should be already knoyra to have some influence upon the 
supposed effect ; the precise degi^ee and manner of the influence being 
the only point undetermined. In any other case, it is no evidence of 
the truth of the hypothesis that we are able to deduce the real phe- 
nomena from it. 

Is it, then, never allowable, in a scientific hypothesis, to assume a 
cause; but only to ascribe an assumed law to a known cause? I do, 
not assert this. I only say, that in the latter case alone can the hypo- - 
da^sis be received as true merely becajise it explains the phenomena: 



294 INDUCTION. 

in the former case it is only useful by suggesting a line of investigation 
which may possibly terminate in obtaining real proof For this pur- 
pose, asvis justly remarked by M. Comte (who of all philosophers 
seems to me to have" approached the nearest to a sound view of this 
important subject), it is indispensable that the cause suggested by the 
hypothesis should be in its own nature susceptible of being proved by 
other evidence. This seems to be the philosophical import of Newton's 
maxim (so often cited with approbation by subsequent writers), that 
the cause assigned for any phenomenon must not only be such as if 
admitted would explain the phenomenon, but must also be u.vera causa. 
What he meant by a vera causa Newton did not indeed very explicitly 
define ; and Mr. Whewell, who dissents from the propriety of any such 
restriction upon the latitude of framing hypotheses, has had little diffi- 
culty in showing* that his conception of it was neither precise nor con- 
sistent with itself: accordingly his optical theory was a signal instance 
of the violation of his own rule. And Mr. Whewell is clearly right in 
denying it to be necessary that the cause assigned should be a cause 
already known ; else how could we ever become acquainted with any 
new cause 1 But what is true in the maxim is, that the cause, although 
not known previously, should be capable of being known thereafter ; 
that its existence' should be capable of being detected, and its con- 
nexion with the effect ascribed to it, susceptible of being proved, by 
independent evidence. The hypothesis, by suggesting observations 
and experiments, puts us upon the road to that independent evidence 
if it be really attainable ; and till it be attained, the hypothesis ought 
not to count for more than a suspicion. .■ > 

§ 5. This function, however, of hypotheses, is one w&ch must be 
reckoned absolutely indispensable in science. When Newton said, 
*' Hypotheses non fingo," he did not mean that he deprived himself of 
the facilities of investigation afforded by assuming in the first instance 
what he hoped ultimately to be able to prove. Without such assump- 
tions, science could never have attained its present state : they are 
necessary steps in the progress to something more certain ; and nearly 
everything which is now theory was once hypothesis. Even in purely 
experimental science, some inducement is necessary for trying one 
experiment rather than another ; and although it is abstractedly possi- 
ble that all the experiments which have been tried, might have been 
produced by the mere desire to ascertain what would happen in certain 
circumstances, without any previous conjecture as to the result ; yet 
in point of fact those unobvious, delicate, and often cumbrous and 
tedious processes of experiment, which have thrown most light upon 
the general constitution of nature, would hardly ever have been under- 
taken by the persons or at the time they were, unless it had seemed 
to depend upon them whether some general doctrine or theory which 
had been suggested, but not yet proved, should be admitted or not.. 
If this be true even of merely experimental inquiry, the conversion of 
experimental into deductive truths could still less have been effected 
without large temporary assistance from hypotheses. The process of 
tracing regularity in any complicated and at first sight confused set of 
appearances, is necessarily tentative : we begin by making any suppo- 

* Philosophy of the Inductive Sciences, vol. ii., pp. 441-6. 



HYPOTHESES. - 295 

sition, evfen a false one, to see what consequences will follow from it; 
and by observing how these differ from the real phenomena, we learn 
what corrections to make in our assumption. The simplest supposition 
which accords with any of the most obvious facts, is the best to begin 
with ; because its consequences are the most easily traced. This rude 
hypothesis is then rudely corrected, and the operation repeated; and 
the comparison of the consequences deducible from the corrected hypo- 
thesis, with the observed facts, suggests still further correction, until 
the deductive results are at last made to tally with the phenomena. 
**Some fact," says M. Comte,* "is as yet little understood, or some 
law is unknown: we frame on the subject an hypothesis as accordant 
as possible with the whole of the data already possessed; and the 
science, being thus enabled to move forward freely, always ends by 
leading to new consequences capable of observation, which either con- 
firra or refute, unequivocally, the first supposition." Neither induction 
nor deduction, he justly remarks, would enable- us to understand even 
the simplest phenomena, " if we did not often commence by anticipa- 
ting on the results ; by making a provisional supposition, at first essen- 
tially conjectural, as to some of the very notions which constitute the 
final object of the inquiry."! Let any one watch the manner in which 
he himself unravels any complicated mass of evidence ; let him observe 
how, for instance, he elicits the true history of any occurrence from 
the involved statements of one or of. many witnesses : he will find that 
he does not take all the items of evidence into his mind at once, and 
attempt to weave them together : the human faculties are not equal to 
such an undertaking : he extemporizes, from a few of the particulars, 
a first rude theory of the mode in which the facts took place, and then 
looks at the other statements one by one, to try whether they can be 
reconciled with that provisional theory, or what corrections or additions 
it requires to make it square with them. In this way, which, as M. 
Comte remarks, has some resemblance to the Methods of Approxima- 
tion of mathematicians, we arrive, by means of hypotheses at conclu.- 
sions not hypothetical.! 

Cours de Philosophie Positive, ii,, p. 437 t Ibid, p. 434. 

:{: As an example of a legitimate hypotnesis according to the test here laid down, M. 
Comte cites that of Broussais, who, proceeding on the very rational principle that every 
disease must originate in some definite part or other of the organism, boldly assumed that 
certain fevers, which not being known to be local were called constitutional, had their 
origin in the mucous membrane of the alimentary canal. The supposition was indeed, as 
there is strong ground to believe, erroneous ; but he was justified in makmg it, since by 
deducing the consequences of the supposition, and compariiig them with the facts of those 
maladies, he might be certain of disproving his hypothesis in case it was ill founded, and 
might expect that the comparison would materially aid him in framing another more con- 
formable to the phenomena. 

The doctrine, now universally received, that the earth is a great natural magnet with 
two poles, was originally an hypothesis of the celebrated Gilbert. 

Another hypothesis, to the legitimacy of which no objection can lie, and one which is 
well calculated to light the path of scientific inquiry, is that suggested both by Dr. Arnott 
and Sir John Herschel, that the brain is a voltaic pile, and that each of its pulsations is a 
discharge of electricity through the system. It has been remarked that the sensation felt 
by the hand from the beating of a brain, or even of the great arteries, bears a strong resem- 
blance to a voltaic shock. And the hypothesis, if followed to its consequences, might 
afford a plausible explanation of many physiological facts, while there is nothing to dis- 
courage the hope that we may in time sufficiently understand the conditions of voltaic 
phenomena to render the truth of the hypothesis amenable to observation and experiment. 

The attempt to localize, in difterent regions of the brain, the physical organs of our dif- 
ferent mental faculties and propensities, was, on the part of its original author, a strictly 
jegitimate example of a scientific hypothesis ; and we ought not, therefore, to blame him 
for the extremely slight grounds on which he often proceeded, in an ooeration which 



296 INDtJCTION. 

§ 6. It is perfectly consistent with the spirit of the method, to assume 
in this provisional manner not only an hypothesis respecting the law of 
what we already know to be the cause, but an hypothesis respecting 
the cause itself. It is allowable, useful, and often even necessary, to 
begin by asking ourselves what cause may have produced the effect, 
in order that we may know in what direction to look out for evidence 
to determine whether it actually did. The vortices of Descartes would 
have been a perfectly legitimate hypothesis, if it had been possible, by 
any mode of exploration which we could entertain the hope of ever 
possessing, to bring the question, whether such vortices exist or not, 
within the reach of our observing faculties. The hypothesis was vicious, 
simply, because it could not lead to any course of investigation capable 
of converting it from an hypothesis into a proved fact. The prevailing 
hypothesis of a luminiferous ether I cannot but consider, with M. Comte, 
to be tainted with the same vice. It can never be brought to the test 
of observation, because the ether is supposed wanting in all the pjoper- 
ties by means of which our senses take cognizance of external phe- 
nomena. It can neither be seen, heard, smelt, tasted, nor touched. 
The possibility of deducing from its supposed laws a considerable 
number of the phenomena of light, is the sole evidence of its existence 
that we have ever to hope for ; and this evidence cannot be of the 
smallest value, because we cannot have, in the case of such an hypoth- 
esis, the assurance that if the hypothesis be false it must lead to results 
at variance with the true facts. 

Accordingly, most thinkers of any degree of sobriety allow, that an 
hypothesis of this kind is not to be received as probably true because 
it accounts for all the known phejiomena ; since this is a condition 
often fulfilled equally well by two conflicting hypotheses ; and if we 
give ourselves the license of inventing the causes themselves as well as 
their laws, a person of fertile imagination might devise a hundred 
modes of accounting for any given fact, while there are probably a 
thousand more" which are equally possible, but which, for want of 
anything analogous in our experience, our minds are unfitted to con- 
ceive. But it seems to be thought that an hypothesis of the sort in 
question is entitled to a more favorable reception, if besides account- 
ing for all the facts previously known, it has led to the anticipation and 
prediction of others which experience afterwards verified; as the un- 
dulatory theory of light led to the prediction, subsequently realiized by- 
experiment, that two luminous rays might meet each other in such a 
manner as to produce darkness. Such predictions and their fiilfilment 
are, indeed, well calculated to strike the ignorant vulgar, whose faith 
in science rests solely upon similar coincidences between its prophe- 
cies and what comes to pass. But it is strange that any considerable 
stress should be laid upon such a coincidence by scientific thinkers. If 
the laws of the propagation of light accord with those of the vibra- 

could only be tentative, thx),ugh we may regret that materials barely sufficient for a first 
rude hypothesis shpuld have been hastily worked up by his successors into the vain sem- 
blance of a science. Whatever there may be of reality in the connexion between the 
scale of mental endowments and the various degrees of complication in the ceiel)ral system 
(and that there is some such connexion comparative anatomy seems strongly to indicate), 
it was in no other way so likely to be brought to light as by framing, in the first instance, 
an hypothesis similar to that of Gall. But the verification of any such hypothesis is at- 
tended, from the peculiar nature of the phenomena, with difficulties which phrenologists 
have not hitherto shown themselves even cpmpetent. to appreciate, much less to over* 
come. . -' ■ 



HYPOTHESES.* 297 

tions of an elastic fluid in as many respects as is necessary to make the 
hypothesis a plausible explanation of all or most of the phenomena 
known at the time, it is nothing strange that they should accord with 
each other in one respect more. Though twenty such coincidences 
should occur, they woiild not prove the reality of the undulatory ether ; 
it would not follow that the phenomena of light were results of the laws 
of elastic fluids, but at most that they are governed by laws in some 
measure analogous to these ; which, we may observe, is already cer- 
tain, from the fact that the hypothesis in question could be for a mo- 
ment tenable., There are many such harmonies running through th^- 
laws of phenomena in other respects radically distinct. The remark-; 
able resemblance between the laws of light and many of the laws of 
heat (while others are as remarkably different), is a case in point.^ 
There is an extraordinary similarity running through the properties, ■ 
considered generally, of certain substances, as chlorine, iodine, and 
brome, or sulphur and phosphorus; so much so that when chemists 
discover any new property of the one, they not only are not surprised, 
but expect, to find that the other or others have a property analogous 
to it. But the hypothesis that chlorine, iodine, and brome, or that 
sulphur and phosphorus, are the same substances, would, no doubt, 
be quite inadmissible. 

I do not, like M. Comte, altogether condemn those who employ them- 
selves in working out into detail this sort of hypotheses ; it is useful to 
ascertain what are the known phenomena to the laws of which those 
of the subject of inquiry bear the greatest, or even a great analogy, 
since this may suggest (as in the case of the luminiferous ether it ac- 
tually did) experiments. to determine whether the analogy which goes 
so far does not extend still further. But that in doing this, men should 
imagine themselves'to be seriously inquiring whether the hypothesis of 
an ether, an electric fluid, or the like, is true; that' they should fancy 
it possible to obtain the assurance that the phenomena are produced 
in that way and no other ; seems to me, I confess, as unworthy of the 
present improved conceptions of the methods of physical science, as it 
does to M. Comte. And at the risk of being charged w^ith want of 
modesty, I cannot help expressing astonishment that a philosopher of 
the extraordinary attainments of Mr. Whewell, should have written an 
elaborate treatise on the philosophy of induction, in which he recog- 
nizes absolutely no mode of induction except that of trying hypothesis 
after hypothesis until one is found which fits the phenomena; which 
one, when found, is to be assumed as true, with no other reservation 
than that if on reexamination it should appear to assume more than is 
needful for explaining the phenomena, the superfluous part of the as- 
sumption should be cut off". It is no exaggeration to say that the pro- 
cess which we have described in these few words, is the beginning, 
middle, and end of the philosophy of induction as Mr. Whewell con- 
ceives it. And this witliout the slightest distinction between the cases 
in which it may be known beforehand that two diflferent hypotheses 
cannot lead to the same result, and those in which, for aught we can 
ever know, the range of suppositions, all equally consistent wdth the 
phenomena, may be infinite. 

§ 7. It is necessary, before quitting the subject of hypotheses, 'to 
guard against the appearance of reflecting upon the philosophical cer- 
Pp 



298 INDUCTION. 

tainty of several branches of physical inquiry, which, although only in" 
their infancy, I hold to be strictly inductive. There is a great differ- 
ence between inventing laws of nature to account for classes of phe- 
nomena, and merely endeavoring, in conformity with known laws, to 
conjecture what collocations, now gone by, may have given birth to 
individual facts still in existence. The latter is the strictly legitimate 
operation of inferring from an observed effect, the existence, in time 
past, of a cause similar to that by which we know it to be produced in 
all cases in which we have actual experience of its origin. This, for 
example, is the scope of the inquiries of geology ; and they are no 
more illogical or visionary than judicial inquiries, which also aim at 
discovering a past event by inference from those of its effects which- 
still subsist. As we can ascertain whether a man was murdered or 
died a natural death, from the indications exhibited by the corpse, 
the presence or absence of signs of struggling on the ground or on the 
adjacent objects, the marks of blood, the footsteps of the supposed 
murderers, and so oh, proceeding throughout upon uniformities ascer- 
tained by a perfect induction without any mixture of hypothesis ; so if 
we find, on and beneath the surface of our planet, masses exactly 
similar to deposits frOm water, or to results of the cooling of matter 
melted by fire, we may justly conclude that such has been their origin j 
and if the effects, though similar in kind, are on a far larger scale thaii 
any which are produced now, we may rationally, and without hypoth- 
esis, conclude that the causes existed formerly with greater intensity. 
Further than this no geologist of authority has, since the rise of the 
present enlightened school of geological speculation, attempted to go. , 

In many geological inquiries it doubtless happens, that although the 
laws to which the phenomena are ascribed are known laws, and the 
agents known agents, those agents are not, known to have been pres- 
ent in the particular case. Thus in the speculation respecting the 
igneous orig-in of trap or granite, the fact does not admit of direct, 
proof, that those substances have been actually subjected to intense 
heat. But the same thing might be said of all judicial inquiries which 
proceed upon circumstantial evidence. We can conclude that a man 
was murdered, although it is not proved by the testimony of eye-wit- 
nesses that a man w^ho had the intention of murdering him was present , 
on the spot. It is enough if no other known cause could have gener- ^ 
ated the effects shown to have been produced. And so, in geology ,- 
it is enough that no other known agent than heat could, according to 
any known law, have produced the unstratified rocks, while there is 
the strongest reason to believe that any terrestrial agent capable of 
operating on so large a scale would not have remained unknown. 

The celebrated speculation of Laplace, now very generally received 
as probable by astronomers, concerning the origin of the earth and 
{)lanets, participates essentially in the strictly inductive character of 
modern geological theory. The speculation is, that the atmosphere of 
the sun originally extended to the present limits of the solar system ; 
from which, by the process of cooling, it has contracted to its present 
dimensions ; and since, by the general principles of mechanics, the 
rotation of the sun and of its accompanying atmosphere must increase 
in rapidity as its volume diminishes, the increased centrifugal force 
generated by the more rapid rotation, overbalancing the action of grav- 
itation, would cause the sun to abandon successive rings of vaporous 



HXFOTHfiSES. 299 

matter, which are supposed to have condensed by- cooling, and to have 
become our planets. There is in this theory no unknown substance 
introduced upon supposition, nor any unknown property or law ascribed 
to a known substance. The known laws of matter authorizie us to 
suppose that a body which is constantly giving out so large an amount 
of heat as the sun is, must be progressively cooling, and that by the 
process of cooling it must contract ; if, therefore, we endeavor, from 
the present state of that luminary, to infer its state in a time long past, 
we must necessarily suppose that its atmosphere extended much fur- 
ther than at present, and we are entitled to suppose that it extended as 
far as we can trace those effects which it would naturally leave behind 
it on retiring ; and such the planets ai'e. These suppositions being 
made, it follows from known laws that successive zones of the solar 
atmosphere would be abandoned ; that these would continue to revolve 
round the sun with the same velocity as when they formed part of his 
substance ; and that they would cool down, long before the sun him- 
self, to any given temperature, and consequently to that at which the 
greater part of the vaporous matter of which they consisted would 
become liquid or solid. The known law of gravitation would then 
cause them to agglomerate in masses, which would assume the. shape 
our planets actually exhibit ; would acquire, each round its own axis, 
a rotatory movement ; and would in that state revolve, as the planets 
actually do, about the sun, in the same direction with the sun's rota- 
tion, but with less velocity, and each of them in the same periodic time 
which the sun's rotation occupied when his atmosphere extended to 
that point; and this also M. Comte has, by the necessary calculations, 
ascertained to be true within certain small limits of error.* There is, thus, 
in Laplace's theory, nothing hypothetical : it is an example of legitimate 
reasoning from a present effect to its past cause, according to the known 
laws of that cause ; it assumes nothing more than that objects which 
really exist, obey the laws which are known to be obeyed by all ter- 
restrial objects resembling them. The theory therefore is, as I have 
sai4, of a similar character to the theories of geologists; inferior to 
them in certainty, in about the same ratio as those are inferior to facts 
conclusively established by a judicial inquiry. For, the uncertainty 
whether the laws of nature which prevail on our earth prevail in the 
whole solar system, is about equal to the uncertainty whether the laws 
which prevail in our earth to-day prevailed there a thousand ages ago. 
Laplace's theory requires both these assumptions, geology the latter 
only, and judicial inquiries require neither.f 

* Cours de Philosophie Positive, ii., pp. 378-383, 

t See, for an interesting exposition of this theory of Laplace, the Architecture of the 
Heavens, by Professor Nichol, of Glasgow ; a book professedly popular rather than scien- 
tific, but the production of a thinker who, both in this and in other departments, is capable 
of much more than merely expounding the speculations of his predecessors. 



300 HJDUCTiON.' ' 

CHAPTER XV. ; : 

OP PROGRESSIVE EFFECTS; AND OF THE CONTINUED ACTION OF CAUSES. 

§ 1. In the last four chapters, we have traced the general outlines 
of the theory of the generation of derivative laws from ultimate 
ones. In the present chapter our attention will be directed to a 
particular case of the derivation of laws from other laws, but a case 
so general, and so important, as not only to repay but to require a 
separate examination. This is, the case of a complex phenomenon 
resulting from one simple lavv^, by the continual addition of an effect to 
itself. 

There are some phenomena, some bodily sensations for example, 
which are essentially instantaneous, and whose existence can only be 
prolonged by the prolongation of the existence of the cause by which 
they are produced. But most phenomena are in their own nature 
permanent ; having begun to exist, they would exist for ever unless 
some cause intervened having a tendency to alter or destroy them. 
Such, for example, are all the facts or phenomena which we call bodies.. 
Water once produced, will not of itself relapse into the state of hydro- 
gen and oxygen ; such a change requires some agent having the power 
of decomposing the compound. Such, again, are the positions in 
space, and the movements, of bodies. No object at rest alters its 
position without the intervention of some conditions extraneous to 
itself; and when once in motion, no object returns to a state of rest, 
or alters either its direction or its velocity, unless some new external ' 
conditions are superinduced. It, therefore, perpetually happens that 
a temporary cause gives rise to. a permanent effect. The contact of 
iron with moist air for a few hours, produces a rust which may endure 
for centuries; or a projectile force which launches a cannon ball into 
space, produces a motion which would continue for ever unless some 
other force counteracted it. ' ,^ 

Between the two examples which we have here given, there is at- 
difference worth pointing out. In the foiTner, (in which the plienom- ' 
enon produced is a substance, and not a motion of a substance,) 
since the rust remains for ever and unaltered unless some new caiuse 
supervenes, we may speak of the cojitact of air a hundred years ago 
as even. the proximate cause of the rust which has existed from that 
time until no\Y- But when the effect is motion, which is itself a change, 
we must use a different language. The permanency of the effect is 
now only the permanency of a series of changes. The second foot, 
or inch, or mile of motion, is not the mere prolonged duration of^ 
the first foot, or inch, or mile, but another fact which succeeds, and. 
which may in some respects be very unlike' the former, since it 
carries the body through a different region of space. Now, the 
original projectile force which set the body moving is the remote 
cause of all its motion, however long continued, but the proximate 
cause of no motion except that which took place at the, first instant. 
The motion at any subsequent instant is proximately caused by the 
motion which took place at the instant preceding. It is on that, 
and not on the original moving cause, that the motion^ at any given. 



PROGRESSIVE EFFECTS. 301 

moment depends.' For, suppose that the body passes through some 
resisting medium, which partially counteracts the effect of the original 
impulse, and by so doing retards the motion : this counteraction (it 
needs scarcely here be repeated) is as strict an example of obedience 
to the law of the impulse, as if the body had gone, on moving with its 
original velocity ; but the motion which results is different, being now 
a compound of the effects of two causes acting in contrary directions, 
instead of the one effect of one cause. Now, what cause does the 
body- obey in its subsequent motion 1 The original cause of motion, 
or the actual motion at the preceding instant? The latter : for when 
the object issues from the resisting medium, it continues moving not 
with its original, but with its retarded, velocity. The motion having 
"once been diminished, all that which follows is diminished. The 
effect changes, because the cause which it really^ obeys, the proximate 
'cause, the real cause infact, has changed. • .This principle is recognized 
by mathematicians when they enumerate among the causes by which 
the motion of a body is at any instant determined, the force generated, 
by the previous motion; an expression which would be absurd if 
taken to imply that this " force" was an intermediate link between the 
cause and the effect, but which really means only the previous motion 
itself, considered as a cause of further motion. We must, therefore, 
if we would speak with .perfect precision, consider each .link in the 
succession of motions as the effect of the link preceding it. But if, 
for the convenience of discourse, we speak of the whole series as one 
effect, it must be as an effect produced by. the original impelling force; 
a permanent effect produced by an instantaneous cause, and possessing 
the property of self-perpetuation. 

Let us now suppose that the original agent or cause, instead of 
being instantaneous, is permanent. Whatever effect has been pro- 
duced up to a given time, would (unless prevented by the intervention 
of some new cause) subsist permanently, even if the cause were to. 
perish. Since, however, the cause does not perish, but continues to 
exist and to operate, it must go on producing more- and more of the 
effect; and instead of an uniform effect, we havp a, progressive series 
of effects, arising from the accumulated influence of a permanent cause. 
Thus, the contact of iron with the atmosphere causes a portion of it to 
rust ; and if the cause ceased, the effect already' produced would be 
permanent, but .no further effect would be added. If, however, the 
cause, namely, exposure to moist air, continues, more and more of the 
iron becomes rusted, until it is all converted into a red powder, when 
one of the conditions of the production of rust, namely, the presence 
of unoxidized iron, has ceased, and the effect cannot any longer be 
produced. Again, the earth causes bodies to fall towards it, that is, 
the existence of the earth at a given instanty causes an unsupported 
body to move towards it at the succeeding instant : and if the earth 
were instantly annihilated, as much of the effect as is already produced 
would continue ; the object would go on moving in the same direction, 
with its acquired velocity, until intercepted by some body or deflected 
by some other force. The earth, however, not being annihilated, goes 
on producing in the second instant an effect similar and of equal 
amount to the first, which two effects being added together, there 
results an accelerated velocity; and this operation being repeated at 
each successive instant, the mere permanence of the cause, although 



302 INDUCTION. 

without increase, gives rise to a constant progressive increase of the 
effect, so long as all the conditions, negative and positive, of the pro- 
duction of that effect continue to be realized. - 

It must be obvious that this state of things is merely a case of the 
Composition of Causes. A cause which continues in action, must on 
B strict analysis be considered as a number of causes exactly similar, 
successively introduced, and producing by their combination the sum 
of the effects which they would severally produce if they acted singly. 
The progressive rusting of the iron is in strictness the sum of the 
effects of many particles of air acting in succession upon correspond- 
ing particles of iron. The continued action of the earth upon a falling 
body is equivalent to a series of forces, applied in" successive instants, 
^ach tending to produce a certain constant quantity of motion : and 
the motion at each instant is the sum of the effects of the new force 
applied at the preceding instant, and of the motion already acquired. 
In each instant, a fresh effect of which gravity is the proximate cause, 
is added to the effect of which it was the remote cause : or (to express 
thfe same thing in another manner) the effect produced by the earth's 
influence at the instant last elapsed, is added to the sum of the effects 
of which the reiriote causes were the influences exerted by the earth 
a,t all the previous instants since the motion began. The case, there- 
fpre, comes under the principle of a concurrence of causes producing 
an effect equal to the sum of their separate effects. But as the causes 
€ome into play not all at once, but successively, and as the effect at 
each instant is the sum of the effects of those causes only which have 
■come into action up to that instant, the result assumes the form of an 
ascending series; a succession of sums, each greater than that which 
preceded it ; and we have thus a progressive effect, from the continued 
action of a cause. 

Since the continuance of the cause influences the effect only by 
adding to its quantity, and since the addition takes place according to 
a fixed law (equal quantities in equal times),, the result is capable of 
being computed on mathematical principles. In fkct, this case, being 
that of infinitesimal increments, is precisely the case which the differ- 
ential calculus was invented to meet. The questions, what effect will 
result from the continual addition of a given cause to itself? and, what 
amount of the cause, being continually added to itself, will produce a 
given amount of the effect 1 are evidently mathematical questions, and 
to be treated, therefore, deductively. If, as we have seen, cases of the 
■Composition of Causes are seldom adapted for any other than deduc- 
tive investigation, this is especially true in the case now examined,, the 
continual composition of a cause with its own previous effects ; since 
euch a case is peculiarly amenable to the deductive method, while the 
undistinguishable manner in which the effects are blended with ona 
anpther and with the causes, must make .the treatment of such an 
instance esxperim^nt-ally, ^till-more cliimerical than in .any otiier case. 

§ 2. We shairnext advert to a rather more intricate operalion of the 
same principle, namely, when thb Cctuse" does not merely continue in 
action, but undergoes, during the same time, a progi'essive chan'ge in 
those of its circumstances which contribute to determine the eflect. In 
this case, as in the former, the total effect goes on accumulating, by 
the continual addition of a fresh effect to that already produced, but 



PROGRESSIVE EFFECTS. " , 303 

it is no longer by the addition of equal quantities in equal times ; the 
quantities added are unequal, and even the quality may now b^ differ- 
ent. If the change in the state of the permanent cause be progressive} 
the effect w^ill go through a double series of changes, arising partly 
from the accumulated action of the cause, and partly from the changes 
in its action. The effect is still a progressive effect, produced, how- 
ever, not by the mere continuance of a cause, but by its continuance 
and its progressiveness combined. 

■ A familiar example is afforded by the increase of the temperature 
as summer' advances, that is, as the sun draws nearer to a vertical 
position, and remains a greater number of hours above the horizon. 
This instance exemplifies in a very interesting manner the twofold 
operation on the effect, arising from the continuance of the cause and 
from its progi^essive change. When once the sun has come near 
enough to the zenith, and remains above the horizon long enough, to 
give more warmth during one diurnal rotation than the counteracting 
cause, the earth's radiation, can cany off, the mere continuance of the 
cause would progressively increase the effect, even if the sun came no 
nearer and the days grew no longer ; but in addition to this, a change 
takes place in the accidents of the cause (its series of diurnal posi- 
tions), tending to increase the quantity of the effect. When the sum- 
mer solstice has passed, the progressive change in the cause begins to 
take place the reverse way; but, for some time, the accumulating 
effect of the mere- continuance of the cause exceeds the effect of the 
changes in it, and the temperature continues to increase. 

Again, the motions of a planet are a progressive effect, produced 
by causes at once permanent and progressive. The oi-bit of a planet 
is determined (omitting perturbations) by two causes : first, the action 
of the central body, a permanent cause, which alternately increases 
and diminishes as the planet draws nearer to or goes further from its 
perihelion, and which acts moreover at every point in' a different direc- 
tion; and, secondly, the tendency of the planet to continue moving in 
the direction and with the velocity which it has already acquired. 
This force also grows greater as the planet draws nearer to its perihe- 
lion, because as it does so its velocity increases ; and less, as it recedes 
from its perihelion : and this force as well as the other acts at each point 
in a different direction, because at every point the action of the central 
force, by deflecting the planet from its previous direction, alters the 
line in which it tends to continue moving. The motion at each instant 
is determined by the amount and direction of the motion and the 
amount and direction of the sun's action at the previous instant : and 
if we speak of the entire revolution of the planet as one phenomenon 
(which, as it is periodical and similar to itself, we often find it conve- 
nient to do), that phenomenon is the progressive effect of two perma- 
nent and progi'essive causes, the central force and the acquired motion. 
Those causes happening to be progressive in the particular way which 
is called periodical, the effect necessarily is so too; because,- the quan- 
titiies to be added together returning in a regular order, the same sums" 
must also regularly re turfi. • * • , ■ /^ ■' ' - 

This example, is well worthy of consideration also in another respect. 
Although the causes themselves are permanent, and independent of all 
conditions known to us, the changes which take place in the quantities 
and relations of the causes are actually caused by the periodical changes 



304 ' INDUCTION. 

in. the effects. The causes, as they exist at any moment, having pro- 
duced a certain motion, that motion, becoming itself a cause, reacts on 
the causesj and produces a change in them. By altering the distance 
and direction of the central bpdy relatively to the pla,net, and the direc- 
tion and quantity of the tangential force, it alters the elements which 
determine the motion at the next succeeding instant. This change 
renders the next motion somev^hat different ; and this difference, by a 
fresh reaction upon the causes, renders the next motion still more dif- 
ferent, and so on. The original state of the causes might Jiave been 
such,, that this' series of actions modified by reactions would not have 
been periodical. The sun's action, and the original impelling force, 
might have beein in. such a ratio to one another, that the reaction of the 
effect would have been such as to alter the causes more and more, 
without ever bringing them back . to what they were at any former, 
time. The planet would then have moved in a parabola, oi: an hyper- 
bola, curves not returning into themselves. The; quantities of the two 
forces were, however, originally such, that the successive reactions of 
the effect bring back the causes, after a certain time, to what they were 
before ; and from that time all the variations continue to recur again 
and again in the same periodical order, and must so continue while the 
causes subsist and are not counteracted. ," -■ •',;... \ 

§ 3. In all cases of progressive effects, whether arising from the ac- 
cumulation of an unchanging or of changing elements, there is an uni- 
fdrmity of succession not merely between the cause and the effect, but 
between the first staged of the effect and its subsequent stages. That 
a body in vacuo falls sixteen feet in the first second, forty-eight in the 
second, and so on in the ratio of the odd numbers, one, three, five, &c., 
is as much an uniform sequence as that when the supports, are removed 
the body falls. The sequence of spring and summer is as regular and 
invariable as that of the approach of the sun and spring : but we do 
not consider spring to be the cause of summer, it is evident that they 
are both effects of the increased heat received from the sun, and if that 
cause did not exist, spring might continue for ever, without having 
the slightest tendency to produce summer. As we have so often re- 
marked, not the conditional, but the unconditional invariable antece-t 
dent, is termed the cause. That which would not be. followed by the 
effect unless something else had preceded, is not the cause, however 
invariable the sequence may in fact be. 

It is in this way that most of these uniformities of succession are , 
generated, which are not cases of causation. Wlien a phenomenon 
goes on increasing, or periodically increases and diminishes, or goes 
through any continued and unceasing process of variation reducible to 
an uniform i-ule or law of succession, we do not on this account presume 
that any two successive terms of the series are cause and effect. We 
presume the contrary ; we expect to find that the whole series originate? 
either from the continued action of fixed causes or from causes which go 
through a corresponding process of continuous change. A tree grows 
from half an inch high to an hundred feet 5 -and some trees will gener- 
ally grovt' to that height unless prevente'd by some counteracting cause. 
■JBut we do. not call the .seedling the cause of the full grown tree ; the 
invariable antecedent it certainly is, and we know very imperfectly 
upon what other antecedents the sequence is contingent, but we are 



EMPIRICAL LAWS. 305 

convinced that it is contingent upon something ; because the homoge- 
neousness of the antecedent with the consequent, the close resemblance 
of the seedling to the tree in all respects except magnitude, and the 
graduality of the gi'owth, so exactly resembling the progressively accu- 
mulating effect produced by the long action of some one cause, leave 
scarcely a possibility of doubting that the seedling and the tree are 
really two terms in a series of that description, the first term of which 
is yet to seek. The conclusion is further confirmed by this, that we 
are able to prove by strict induction the dependence of the growth of 
the tree, and even of the continuance of its existence, upon the con- 
tinued repetition of certain processes of nutrition, the rise of the sap, 
the absorptions and exhalations by the leaves, &c., and the same ex- 
periments would probably prove to us that the gi'owth of the tree is 
the accumulated sum of the effects of these continued processes, were 
we not, for want of sufficiently microscopic eyes, unable to observe 
correctly and in detail what those effects are. 



CHAPTER XVI. 

OF EMPIRICAL LAWS, 

§ 1. Experimental philosophers usually give the name of Empirical 
Laws to those uniformities which observation or experiment has shown 
to exist, but upon which they hesitate to rely in cases varying much 
from those which have been actually observed, for want of seeing any 
reason why such a law should exist. It is implied, therefore, in the 
notion of an empirical law, that it is not an ultimate law ; that if true 
at all, its truth is capable of being, and requires to be, accounted for. 
It is a derivative law, the derivation of which is not yet known. To 
state the explanation, the why of the empuical law, would be to state 
the laws fi'om which it is derived ; the ultimate causes upon which 
it is contingent. And if we knew these, we should also know what 
are its limits ; under what conditions it .would cease to be fulfilled. 

The periodical return of eclipses, as originally ascertained by the 
persevering observation of the early eastern astronomers, was an em- 
pirical law, until the general laws of the celestial motions had 
accounted for it. The following are empirical laws still waiting to be 
resolved into the simpler laws fi'om which they are derived. The local 
laws of the flux and reflux of the tides in different places : the succes- 
sion of certain kinds of weather to certain appearances of sky : the ap- 
parent exceptions to the almost universal truth that bodies expand by 
mcrease of temperature]: the law that breeds, both animal and vegeta- 
ble, are improved by crossing: that gases have a strong tendency to 
permeate animal membranes : that opium and alcohol intoxicate : that 
substances containing a very high proportion of niti'ogen (such as hy- 
drocyanic acid and morphia) are powerful poisons : that when different 
metals are fused together the alloy is harder than the various elements: 
that the number of atoms of acid required to neutralize one atom of 
any base, is equal to the number of atoms of oxygen in the base : that 



306 INDUCTION. 

the solubility of substances in one another, depends* (at least in some 
degree) on the similarity of their elements. 

An empirical law, then, is an observed uniformity, presumed to be 
resolvable into simpler laws, but not yet resolved into them. The as- 
certainment of the empirical laws of phenomena, often precedes by a 
long interval the explanation of those laws by the Deductive Method : 
and the verification of a deduction usually consists in the comparison 
of its results with empirical laws previously ascertained. 

§ 2. From a limited number of ultimate laws of causation, there are 
necessarily generated a vast number of derivative uniformities, both 
of succession and of coexistence. Some are laws of succession or of 
coexistence between different effects of the same cause : of these we 
had abundant examples in the last chapter. Some are laws of suc- 
cession between effects and their remote causes ; resolvable into the 
laws which connect each with the intermediate link. Thirdly, w^hen 
causes act together and compound their effects, the laws of those 
causes generate the fundamental law of the effect, namely, that it de- 
pends upon the coexistence of those causes. And, finally, the ordei 
of succession or of coexistence which obtains among effects, necessa- 
rily depends upon their causes. If they are effects of the same cause, 
it depends upon the laws of that cause ; if. of different causes, it de- 
pends upon the laws of those causes severally, and upon the circum- 
stances which determine their coexistence. If we inquire further when 
' and how the causes will coexist, that, again, depends upon their causes : 
and we may thus trace back the phenomena higher and higher, until 
the different series of effects meet in a point, and the whole is shown 
to have depended ultimately upon some common cause ; or until, in- 
stead of converging to one point, they terminate in different points, 
and the order of the eflects is proved to have arisen from the original 
collocation of some of the primeval causes, or natural agents. For 
example, the order of succession and of coexistence among the 
heavenly motions, which is expressed by Kepler's laws, is derived 
from the coexistence of two primeval causes, the sun, and the original 
impulse or projectile force impressed upon each planet.f Kepler's 
laws are resolved into the laws of these causes and the fact of their 
coexistence. 

Derivative laws, therefore, do not depend solely upon the ultimate 
laws into which they are resolvable : they mostly depend upon those 
ultimate laws and an ultimate fact ; namely, the mode of coexistence 
of some of the original elements of the universe. The ultimate laws 
of causation might be the same as at present, and yet the derivative 
laws completely different, if the causes coexisted in different propor- 
tions, or with any difference in those of their relations by which the 
effects are influenced. If, for example, the sun's attraction, and the 

* Thus, water, of which eight-ninths in weight are oxygen, dissolves most bodies which 
contain a high proportion of oxygen, such as all the nitrates, (which have more oxygen . 
than any others of the common salts,) most of the sulphates, many of the carbonates, &c. 
Again, bodies largely composed of combustible elements, like hydrogen and carbon, are 
soluble in bodies of similar composition ; rosin, for instance, will dissolve in alcohol, tar in 
oil of turpentine. This empirical generalization is far from being universally true ; no 
doubt because it is a remote, and therefore easily defeated, result of general laws too deep 
for us at present 1o penetrate: but it will probably in time suggest processes of inquiry, 
leading to the discovery of these laws. 

t Or (according to. Laplace's theory) the sun, and the sun's rotation. 



EMriKlCAL LAWS. 307 

original projectile foxxe, had existed in some other ratio to one another 
than they did (and we know of no reason why this should not have 
been the case), the derivative laws of the heavenly motions might 
have been quite different from what they are. The proportions which 
exist happen to be such as to produce regular elliptical motions ; any 
other proportions would have produced different ellipses, or circular, 
or parabolic, or hyperbolic motions, but still regular ones ; because the 
effects of each of the agents accumulate according to an uniform law; 
and two regular series of quantities, when their corresponding terms 
are added, must produce a regular series of some sort, whatever the 
quantities themselves are. 

§ 3. Now this last mentioned element in the resolution of a deriva- 
tive law, the element which is not a law of causation but a collocation 
of causes, cannot itself be reduced to any law. There is (as formerly 
remarked*) no uniformity, no norma, principle, or rule, perceivable in 
the distribution of the primeval natural agents through the universe. 
The different substances composing the earth, the powers that pervade 
the universe, stand in no constant rel^^tion to one another. One sub- 
stance is more abundant than others, one power acts through a larger 
extent of space than others, without any pervading analogy that we 
can discover. We not only do not know of any reason why the 
sun's attraction and the tangential force coexist in the exact propor- 
tion they do, but we can trace no coincidence between it and the 
proportions in which any other elementary powers in the universe are 
intermingled. The utmost disorder is apparent in the combination of 
the causes ; which is consistent with the most perfect order in their 
effects ; for when each agent carries on its own operations according to 
ah uniform law, even the most capricious combination of agencies will 
generate a regularity of some sort, as we see in the kaleidoscope, 
where any casual arrangement of colored bits of glass produces by 
the laws of reflection a beautiful regularity in the effect. 

§ 4. In the above considerations lies the justification of the limited 
degi^ee of reliance which philosophers are accustomed to place in em- 
pirical laws. 

A derivative law which results wholly from the operation of some 
one cause, will be as universally true as the laws of the cause itself; 
that is, if -wall always be true except where some one of those effects 
of the cause, on vv^hich the derivative law depends, is defeated by a 
counteracting cause. But when the derivative law results not from 
different effects of one cause, but from effects of several causes, we 
cannot be certain that it will be ti'ue under any variation in the mode 
of coexistence of those causes, or of the primitive natural agents on 
which the causes ultimately depend. The proposition that coal beds 
rest upon certain descriptions of strata exclusively, though true on 
the earth so far as our observation has reached, cannot be extended to 
the moon or the other planets, supposing coal to exist there ; because 
we cannot be assured that the original constitution of any other planet 
was such as to produce the different depositions in the same order as 
in our globe. The derivative law in this case depends not solely 

* Supra, p. 206. 



308 iNnuoTioN. 

upon laws but upon a collocation ; and collocations cannot be reduced 
to any law. 

Now it is the very nature of a derivative law which has not yet been 
resolved into its elements, in other words, an empirical law, that we 
do not know whether it results from the different effects of one cause 
or fi'om effects of different causes. We cannot tell whether it depends 
wholly upon laws, or partly upon laws and partly upon a collocation. 
If it depends upon a collocation, it will be true in all the cases in which 
that particular collocation exists. But since we are entirely ignorant, in 
case of its depending upon a collocation, what the collocation is, we are 
not safe in extending the law beyond the limits of time and place in, 
which we have actual experience of its truth. Since within those limits 
the law has always been found true, we have evidence that the colloca- 
tions, whatever they are, upon which it depends, do really exist within 
those limits. But knowing of no rule or principle to which the collo- 
cations themselves conform, we cannot conclude that because a collo- 
cation is proved to exist within certain limits of place or time, it will 
exist beyond those limits. Empirical laws, therefore, can only be held 
true within the limits of time and place in which they have been found 
true by observation : and not merely the limits of time and place, but 
of time, place, and circumstance : for since it is the very meaning of an 
empirical law that we do not know the ultimate laws of causation upon , 
which it is dependent, we cannot foresee, without actual trial, in what 
manner or to vy^hat extent the introduction of any new circumstance 
may effect it. 

§ 5. But how are we to know that an uniformity, ascertained by 
experience, is only an empirical law 1 Since, by the supposition, we 
have not been able to resolve it into higher laws, how do we know 
that it is not an ultimate law of causation ] 

I answer, that no generalization amounts to more than an empirical 
law when the only proof upon which it rests is that of the Method of 
Agreement. For it has been seen that by that method alone we never 
can arrive at causes. All that the Method of Agreement can do i^, to 
ascertain the whole of the circumstances common to all cases in which 
a phenomenon is produced : and this of course includes not only the 
cause of the phenomenon, but all phenomena with which it is con- 
nected by any derivative uniformity, whether as being collateral 
effects of the same cause, or effects of any other cause which, in all the 
instances we have been able to observe, coexisted with it. The method 
affords no means of determining which of these uniformities are laws of 
causation, and which are merely derivative laws resulting from those 
laws of causation and from the collocation of the causes. None of 
them, therefore, can be received in any other character than that of 
derivative laws, the derivation of which has not been traced ; in other 
words, empirical laws : in which light, all results obtained by the 
Method of Agreement (and therefore almost all the truths obtained by 
simple observation without experiment) must be considered, until 
either confirmed by the Method of Difference, or explained deduc- 
tively, in other words, accounted for a priori. 

These empirical laws may be of greater or of less authority, accord- 
ing as there is reason to presume that they are resolvable into laws 
only, or into laws and collocations together. The sequences which we 



EMPIRICAL LAWS. 309 

t>bserve in tlie production and subsequent life of an animal or a vege- 
table, resting upon the Method of Agreement only, are mere empirical 
laws ; but though the antecedents in those sequences may not be the 
causes of the consequents, both the one and the other are probably, in 
the main, successive stages of a progressive effect originating in a 
common cause, and therefore'independent of collocations. The unifor- 
mities, on the other hand, in the order of superposition of strata on the 
earth, are empirical laws of a much weaker kind, since they are not 
only not laws of causation, but there is no reason to believe that they 
depend upon any common cause : all appearances are in favor of 
their depending upon the particular collocation of natural agents which 
primitively existed on our globe, and from which no inference can be 
drawn as to the collocation which exists or has existed in any other 
portion of the universe. 

6. Our definition of an empirical law including not only those 
uniformities which are not known to be laws of causation, but also 
those which are, provided there be reason to presume that they are 
not ultimate laws ; this is the proper place to consider by what signs 
we may judge that even if an observed uniformity be a law of causa- 
tion, it is not an ultimate but a derivative law. 

The first sign is, if between the antecedent a and the consequent h 
there be evidence of some intermediate link ; some phenomenon of 
which we can collect the existence, although from the imperfection of, 
our senses or of our instruments we are unable to ascertain its precise 
nature and laws. If there be such a phenomenon (which may be 
denoted by the letter x), it follows that even if a be the cause of Z>, it 
is but the remote cause, and that the law, a causes h, is resolvable into 
at least two laws, a causes x, and x causes h. This is a very frequent 
case, since the operations of nature mostly take place on so minute a 
scale, that many of the successive steps are either imperceptible, or 
very indistinctly perceived. 

Take, for example, the laws of the chemical composition of substan- 
ces ; as that, hydrogen and oxygen being combined water is produced. 
All we see of the process is, that the two gases being mixed in certain 
proportions, and heat or electricity being applied, an explosion takes 
place, the gases disappear, and water remains. There is no doubt 
about the law, or about its being a law of causation. But between the 
antecedent (the gases in a state of mechanical mixture, heated or elec- 
trified), and the consequent (the production of water), there must be 
an inteimediate process which we do not see. For if we take any 
portion whatever of the water, and subject it to analysis, we find that 
it always contains some hydrogen and some oxygen : nay, the very 
same proportions of them, namely, two-thirds, in volume, of hydrogen, 
and one-third oxygen. This is true of a single drop ; it is true of the 
minutest portion which our instruments are capable of appreciating. 
Since, then, the smallest perceptible portion of the water contains both 
those substances, portions of hydrogen and oxygen smaller than the 
smallest perceptible must have come together in every such minute 
portion of space ; must have come closer together than when the gases 
were in a state of mechanical mixture, since (to mention no other 
reasons) the water occupies far less space than the gases. Now as we 
cannot see this contact or close approach of the minute particles, w© 



310 INDUCTION. 

cannot observe with what circumstances it is attended, or according to 
what laws it produces its effects. The production of water, that is, of 
the sensible phenomena which characterize the compound, may be a 
very remote effect of those laws. There may be innumerable inter- 
vening links ; and we are sure that there must be some. Having full 
proof that corj^uscular action of some kind takes place previous to any 
of the great transformations in the sensible properties of substances, 
we can have no doubt that the laws, of chemical action, as at present 
known, are not ultimate but derivative laws; however ignorant we 
may be, and even though we should for ever remain ignorant, of the 
nature of the laws of corpuscular action from which they are derived. 

In like manner all the processes of vegetative life, whether in the 
vegetable properly so called or in the animal body, are corpuscular 
processes. Nutrition is the addition of particles to one another, in 
part replacing other particles separated and excreted, in part occasion- 
ing an increase of bulk or weight, so gradual, that only after a long 
continuance does it become perceptible. Various' organs, by means 
of peculiar vessels, secrete from the blood, fluids, the component par- 
ticles of which must have been in the blood, but which differ from it 
most widely both in mechanical properties and in chemical composition. 
Here, then, are abundance of unknov^Ti links to be filled up; and there 
can be no doubt that the laws of the phenomena of vegetative qv organic 
life are derivative laws, dependent upon properties of the corpuscles, 
and of those elementary tissues which are comparatively simple com- 
binations of corpuscles. 

The first sign, then, from which a law of causatiori, though hitherto 
unresolved, may be inferred to be a derivative law, is any indication 
of the existence of an intermediate link or links between the antece- 
dent and the consequent. The second is, when the antecedent is an 
extremely complex phenomenon, and its effects, therefore, probably, in 
part at least, compounded of the effects of its different elements ; since 
we know that the case in which the effect of the whole is -not made up 
of the effects of its parts, is exceptional, the Composition of Causes 
being by far the more ordinary case. 

, We will illustrate this by two examples, in one of which the anter 
cedent is the sum of many homogeneous, in the other of heterogeneous, 
parts. The weight of a body is made up of the weights of its minute 
particles ; a truth which astronomers express in its most general terms, 
when they say that bodies, at equal distances, gravitate to one another 
in proportion to their quantity of matter. All true propositions, there- 
fore, which can be made concerning gravity, are derivative laws; the 
ultimate law into which they are all resolvable being that every par- 
ticle of matter attracts every other. As our second example, we may 
take any of the sequences observed in meteorology : for instance, that 
a diminution of the pressure of the atmosphere (indicated by a fall of 
the barometer) is followed by rain. The antecedent is here a com- 
plex phenomenon, made up of heterogeneous elements; the column 
of the atmosphere over any particular place consisting of two parts, a 
column of air, and a column of aqueous vapor mixed with it; and the 
change in the two together, manifested by a fall of the barometer, and 
followed by rain, must be either a change in one of these, or in the 
other, or in both. We might, then, even in the absence of any other 
evidence, form a reasonable presumption, from the invariable presence 



EMPIRICAL LAWS. 311 

of both these elements in the antecedent, that the sequence is proba- 
bly not an ultimate law, but a result of the laws of the two different 
agents : a presumption only to be destroyed when we had made 
ourselves so well acquainted with the laws of both, as to be able to 
affirm that those laws could not by themselves produce the observed 
result. 

§ 7. There are but few known cases of succession from very complex 
antecedents, which have not either been actually accounted for from 
simpler laws, or inferred with great probability (from the ascertained 
existence of intermediate links of causation not yet understood) to be 
capable of being so accounted fgv. " It is, therefore, highly probable 
that all sequences from complex antecedents are thus resolvable, and 
that ultimate laws are . in all cases comparatively simple. If there 
were not the other reasons already mentioned for believing that the 
laws of organized nature are resolvable into simpler laws, it would be 
almost a sufficient reason that the antecedents in most of the sequences 
are so very complex. 

There are appearances strongly favoring the suspicion, that these 
phenomena are really resolvable into much simpler laws than might at 
first be expected. The growth of an animal from infancy to maturity, 
of a plant from infancy till death, and even that process of decay 
which is but a slow death, bear a most striking resemblance to the 
progressive effect of the continued action of some cause, proceeding 
until it tneets agencies which overpower it, or until its accumulated 
effects give rise to conditions inconsistent with its own existence. 
This supposition by no ' means requires that the effect should not, 
during its progress, undergo many modifications besides those of 
quantity, or that it should not sometimes appear to undergo a very 
marked change of character. This may be, either because the unknown 
cause consists of several component elements or agents, whose effects, 
accumulating according to different laws, are compounded in different 
proportions at different periods in the existence of the organized 
being ; or because, at certain points in its progress, fresh causes or 
agencies come in, or are evolved, which intermix their laws with 
those of the prime agent. 

This great problem, the most difficult in all physics, the ascertain- 
ment of the ultimate laws of organized nature, is one which natural 
science in its progress seems now at least to have fairly come up to; 
and a beginning has been made at the point where the phenomena 
appear most accessible to experiment, namely, in separating the effects 
of partial from those of general causes. The result, as far as it goes, 
fully accords with the above surmise. I allude to the new and infant 
science of morphology, created with respect to animals by the genius 
of Cuvier and St. Hilaire, and with respect to vegetables by that of 
the illustrious Goethe, to whom the world owes so much in quite a 
different field of intellect, and whose researches on the ** Metamor- 
phoses of Plants" have met with a more favorable reception from the 
{Scientific world than his speculations on colors. It seems to be now 
considered by natural philosophers as sufficiently estabhshed, that 
plants and animals, in the process of gi'owing up from their germs, 
have a tendency to develop themselves in a much more uniform man- 
ner than they in fact do; that the differences, for example of leaf. 



31'2 INDUCTION. 

flower, and fruit, are mere modifications of one general phenomenon; 
or (which is only another expression for the same idea) joint results of 
one common tendency and of several partial causes combining with it. 

§ 8. In the preceding discussion we have recognized two kinds of 
empirical laws : those known to be laws of causation, but presumed 
to be resolvable into simpler laws ; and those not known to be laws of 
causation at all. Both these kinds of laws agree in the demand which 
they make for being explained by deduction, and agree in being the 
appropriate means of verifying such deduction, since they represent 
the experience with which the result of the deduction must be com- 
pared. They agree, further, in this, that until explained, and con- 
nected with the ultimate laws from which they result, they have not 
attained the highest degree of certainty of which laws are susceptible. 
It has been shown on a former occasion that laws of causation which 
are derivative, and compounded of simpler laws, are not only, as the 
nature of the case implies, less general, but even less certain, than the 
simpler laws from which they result ; not so positively to be relied upon 
as universally true. The inferiority of evidence, however, which 
attaches to this class of laws, is trifling compared with that which is 
inherent in unifomiities not known to be laws of causation at all. So- 
long as these are unresolved, we cannot tell upon how many colloca- 
tions, as well as laws, their truth may be dependent ; and can never, 
therefore, extend them with perfect confidence to cases in which we 
have not assured ourselves, by trial, that the necessary collocation of 
causes, whatever it may be, exists. It is to this class of laws alone 
that the property, which philosophers usually consider as characteristic 
of empirical laws, belongs in all its strictness ; the property of being 
unfit to be relied on beyend the limits of time, place, and circumstance, 
in which the observations have been made. These are empirical laws 
in a more emphatic sense; and when I employ that term (except 
where the context manifestly indicates the reverse) I shall generally 
mean to designate those uniformities only, whether of succession or 
of coexistence, which are not known to be laws of causation. 



CHAPTER XVII. 

OF CHANCE, AND ITS ELIMINATION. 



§ 1. Considering, then, as empirical laws only those observed uni- 
formities respecting which the question whether they are laws of causa- 
tion must remain undecided until they can be explained deductively, 
or until some means are found of applying the Method of Difference to 
the case ; it has been shown in the preceding chapter, that until an 
uniformity can, in one or the other of these modes, be taken out of the 
class of empirical laws, and brought either into that of laws of causa- 
tion or of the demonstrated results of laws of causation, it cannot with 
any assurance be pronounced true beyond the local and other limits 
within which it has been found so by actual obsei'vation. It remains to 
consider how we are to assure ourselves of its ti-uth even within tliose 



CHANCE, AND ITS ELIMINATION. 313 

limits ; after what quantity of experience a generalization which rests 
solely upon the Method of Agreement, can be considered sufficiently 
established, even as an empirical law. In a former chapter, when 
treating of the Methods of Direct Induction, we expressly reserved this 
question,* and the time is now come for endeavoring to solve it. 

We found that the Method of Agi'eement has the defect of not 
proving causation, and can therefore only be employed for the ascer- 
tainment of empirical laws. But we found, moreover, that besides this 
deficiency, it labors under a characteristic imperfection, tending to 
render uncertain even such conclusions as it is in itself adapted to 
prove. This imperfection arises from Plurality of Causes. Although 
two or more cases in which the phenomenon a has been met with, may 
have no common antecedent except A, this does not prove that there 
is any connexion between a and A, since a may have many causes, and 
may have been produced, in these different instances, not by anything 
which the instances had in common, but by some of those elements in 
them which were different. We, nevertheless, observed, that in propor- 
tion to the multiplication of instances pointing to A as the antecedent, 
the characteristic uncertainty of the method diminishes, and the exist- 
ence of a law of connexion between A and a more nearly approaches 
to certainty. It is now to be determined, after what amount of expe- 
rience this certainty may be deemed to be practically attained, and the 
connexion between A and a may be received as an empirical law. 

This question may be otherwise stated in more familiar terms : — 
After how many and what sort of instances may it be concluded, that 
an observed coincidence between two phenomena is not the effect of 
chance % 

It is of the utmost importance for understanding the logic of induc- 
tion, that we should form a distinct conception of what is meant by 
chance, and how the phenomena which common language ascribes to 
that a^bstraction are really produced. 

§ 2. Chance is usually spoken of in direct antithesis to law ; what-" 
ever (it is supposed) cannot be ascribed to any law, is attributed to 
chance. It is, however, certain, that whatever happens is the result 
of some law; is an effect of causes, and could have been predicted 
from a knowledge of the existence of those causes, and from their laws. 
If I turn up a particular card, that is a consequence of its place in the 
pack. Its place in the pack was a consequence of the manner in 
which the cards were shuffled, or of the order in which they were 
played in the last game ; which, again, were the effects of prior causes. 
At every stage, if we had~ possessed an accurate knowledge of the 
causes in existence, it would have been abstractedly possible to foretell 
the effect. 

An event occurring by chance, may be described as a coincidence 
from which we have no ground to infer an uniformity : the occurrence 
of a phenomenon in certain circumstances, without our having reason 
on that account to infer that it will happen again in those circum- 
stances. This, however, when looked closely into, implies that the ' 
enumeration of the circumstances is not complete. Whatever the fact 
be, since it has occuiTed once, we may be sure that if all the same cir- 

* Supra, p. 252. 



314 INDUCTION. 

cumstances were i:epeated, it would occur again ; and not only if all, 
but there is some particular portion of those circumstances upon which 
the phenomenon is invariably consequent. With most of them, how- 
ever, it is not connected in any permanent manner : its conjunction 
with those is said to be the effect of chance, to be merely casual. 
Facts casually conjoined are separately the effects of causes, and 
therefore of laws ; but of different causes, and causes not connected 
by any law. 

It is incorrect, then, to say that any phenomenon is produced by 
chance ; but we may say that two or more phenomena are conjoined 
by chance, that they coexist, or succeed one another only by chance ; 
meaning that they are in no way related through causation ; that they are 
neither cause and effect, nor effects of the same cause, nor effects of 
causes between which there subsists any law of coexistence, nor even 
effects of the same original collocation of primeval causes. 

If the same casual coincidence never occurred a second time, we 
should have an easy test for distinguishing such from the coincidences 
which are results of a law. As long as the phenomena had been found 
together only once, so long, unless we knew some more general laws 
from which the coincidence might have resulted, we could not distin- 
guish it from a casual one ; but if it occurred twice, we should know 
that the phenomena so conjoined must be in some way connected 
through their causes. 

There is, however, no such test. A coincidence may occur again 
and again, and yet be only casual. Nay, it would be inconsistent with 
what we know of the order of nature, to doubt that every casual coin- 
cidence will sooner or later be repeated, as long as the phenomena 
between which it occurred do not cease to exist, or to be produced. 
The recun-ence, therefore, of the same coincidence more than once, 
or even its frequent recurrence, does not prove that it is an instance of 
any law; does not prove that it is not casual, or, in common language, 
the effect of chance. 

.| And yet, when a coincidence cannot be deduced from known laws, 
nor proved by experiment to be itself a case of causation, the frequency 
of its occurrence is the only evidence from which we can infer that it 
is the result of a law. Not, however, its absolute frequency. The 
question is not whether the coincidence occurs often or seldom, in the 
ordinary sense of those terms ; but whether it occurs more often than 
chance will account for; more often than might rationally be expected 
if the coincidence were casual. We have to decide, therefore, what 
degree of frequency in a coincidence chance will account for. And to 
this there can be no general answer. We can only state the principle 
by which the answer must be determined : the answer itself will be 
different in every different case. 

1^ Suppose that one of the phenomena, A, exists always, and the other 
phenomenon, B, only occasionally : it follows that every instance of B 
will be an instance of its coincidence with A, and yet the coincidence 
will be merely casual, not the result of any connexion between them. 
The fixed stars have been constantly in existence since the beginning 
of human experience, and all phenomena that have come under human 
observation have, in every single instance, coexisted with them; yet 
this coincidence, although equally invariable with that which exists 
between any of those phenomena and its own cause, does not prove 



CHANCE, AND ITS ELIMINATION. 815 

that the stars are its cause, nor that they are in anywdse connected 
with it. As strong a case of coincidence, therefore, as can possibly 
exist, and a much stronger one in point of mere frequency than most 
of those which prove laws, does not here prove a law : why 1 because, 
since the stars exist always, they must coexist with every other phe- 
nomenon, whether connected with them by causation or not. The 
uniformity, great though it be, is no greater than would occur on the 
supposition that no such connexion exists. 

On the other hand, suppose that we were inquiring whether there 
be any connexion between rain and any particular wind. Rain, we 
know, occasionally occurs with every wind; therefore the connexion, 
if it exists, cannot be, an actual law; but still, rain may be connected 
with some particular wind through causation; that is, although they 
cannot be always effects of the same cause (for if so they would always 
coexist), there may be so?ne causes common to the two, so that iii so 
far as either is produced by those common causes, they will, from the 
laws of the causes, be found to coexist. How, then, shall we ascertain 
this 1 The obvious answer is, by observing whether rain occurs with 
one wind more frequently than with any other. That, however, is not 
enough ; for perhaps that one wind blows more frequently than any 
other; so that its blowing more fi-equently in rainy weather is no m6re 
than would happen, although it had no connexion with the causes of 
rain, provided it were not connected with causes adverse to rain. In 
England, westerly winds blow during about twice as great a portion 
of the year as easterly. If, therefore, it rains only twice as often with 
a westerly, as with an easterly wind, we have no reason to infer that 
any law of nature is concerned in the coincidence. If it rains more 
than twice as often, we may be sure that some law is concerned ; 
either there is some cause in nature tending to produce both rain and 
a westerly wind, or a westerly wind has itself some tendency to pro- 
duce rain. But if it rains less than twice as often, we may draw a 
directly opposite inference ; the one, instead of being a cause, or con- 
nected with causes of the other, must be connected with causes ad- 
verse to it, or with the absence of some cause which produces it ; and 
although it may still rain much oftener with a westerly wind than with 
an easterly, so far would this be from proving any connexion between 
the phenomena, that the connexion proved would be between rain and 
an easterly wind, the wind to which, in mere frequency of coincidence, 
it is least allied. 

Here, then, are two examples : in one, the greatest possible fre- 
quency of coincidence, with no instance whatever to the contrary, does 
not prove that there is any law ; in the other, a much less frequency 
of coincidence, even when non-coincidence is still more frequent, does 
prove that there is a law. In both cases the principle is the same. In 
both we consider the positive frequency of the phenomena themselves, 
and how great frequency of coincidence that must of itself bring about, 
without supposing any connexion between them, provided there be no 
repugnance ; provided neither be connected with any cause tending 
to frustrate the other. If we find a greater frequency of coincidence 
than this, we conclude that there is some connexion ; if a less fre- 
quency, that there is some repugnance. In the former case, we con- 
clude that one of the phenomena can under some circumstances cause 
the other, or that there exists something capable of causing them both; 



316 INDUCTION. 

in the latter, that one of them, or some catise which produces oris o 
them, is capable of counteracting the production of the other. We 
have thus to deduct from the observed frequency of coincidence, as 
much as may be the effect of chance, that is, of the mere frequency of 
the phenomena themselves ; and if anything remains, what does re- 
main is the residual fact which proves the existence of a law. 

The frequency of the phenomena can only be ascertained within 
definite limits of space and time ; depending as it does on the quantity 
and distribution of the primeval natural agents, of which we can know 
nothing beyond the boundaries of human observation, since no law, no 
regularity, can be 'traced in it, enabling us to infer the unknown from 
the known. But for the present purpose this is no disadvantage, the 
question being confined within the same limits as the data. The coin- 
cidences occurred in certain places and times, and within those we can 
estimate the frequency with which such coincidences would be pro- 
duced by chance. If, then, we find from observation that A exists in 
one case out of every two, and B in one case out of every three ; then 
if there be neither connexion nor repugnance between them, or be- 
tween any of their causes, the instances in which A and B will both 
exist, that is to say will coexist, will be one case in every six. For A 
exists in three cases out of six ; and B, existing in one case out of 
every three without regard to the presence or absence of A, will exist 
in one case out of those three. There will therefore be, of the whole 
number of cases, two in which A exists without B ; one case of B 
without A ; two in which neither B nor A exists, and one case out of 
six in which they both exist. If then, in point of fact, they are found 
to coexist oftener than in one case out of six ; and, consequently A 
does not exist without B so often as twice in three times, nor B with- 
out A so often as once in every twice ; there is some cause in exist- 
ence, which tends to produce a conjunction between A and B. 

Generalizing the result, we may say, that if A occurs in a larger 
proportion of the cases where B is, than of the cases where B is not ; 
then will B also occur in a larger proportion of the cases where A is, 
than of the cases where A is not ; and there is some connexion, through 
causation, between A and B. If we could ascend to the causes of the 
two phenomena, we should find, at some stage, either proximate or 
remote, some cause or causes common to both ; and if we could ascer- 
tain what these are, we could frame a generalization which would be 
true without restriction of place or time : but until we can do so, the 
fact of a connexion between the two phenomena remains an em- 
pirical law. 

§ 3. Having considered in what manner it may be determined 
whether any given conjunction of phenomena is casual or the result of 
some law ; to complete the theory of chance, it is necessary that we 
should now consider those effects which are partly the result of chance 
and partly of law : or in other words, in which the effects of casual 
conjunctions of causes are habitually blended in one result with the 
effects of a constant cause. 

This is a case of Composition of Causes; and the peculiarity of it 
is, that instead of two or more causes intermixing their effects in a 
regular manner with those of one another, we have now one constant 
cause, producing an effect which is successively modified by a series 



CHANCE, AND ITS RT.IMIN ATTON. 317 

of variable causes. Thus, as summer advances, the approach of the 
sun to a vertical position tends to produce a constant increase of tem- 
perature ; but with this effect of a constant cause, there are blended 
the effects of many variable causes, winds, clouds, evaporation, elec- 
tric agencies, and the like, so that the temperature on any given day 
depends in part upon these fleeting causes, and only in part upon the 
constant cause. If the effect of the constant cause is always accom- 
panied and disguised by effects of variable causes, it is impossible to 
ascertain the law of the constant cause in the ordinary manner, by 
separating it from all other causes and observing it apart. Hence 
arises the necessity of an additional rule of experimental inquiry. 

When the action of a cause A is liable to be interfered with, not 
steadily by the same cause or causes, but by different causes at differ- 
ent times, and when these are so frequent, or so indeterminate, that 
we cannot possibly exclude all of them from any experiment, although 
we may vary them ; our resource is, to endeavor to ascertain what i^ 
the effect of all the variable causes taken together. In order to do 
this, we make as many trials as possible, preserving A invariable. The 
results of these different trials will naturally be different, since the 
indeterminate modifying causes are different in each : if, then, we do 
not find these results to be progressive, but on the contrary to oscillate 
about a certain point, one experiment giving a result a little greater, 
another a little less, one a result tending a little more in one direction, 
another a little more in the contrary direction ; while the average, or 
middle point, does not vary, but different sets of experiments (taken 
under as great a variety of circumstances as possible) yield the same 
mean, provided only they be sufficiently numerous ; then that mean, 
or average result, is the part, in each experiment, which is due to the 
cause A, and is the effect which would have been obtained if A could 
have acted alone : the variable remainder is the effect of chance, that 
is, of causes the coexistence of which with the cause A was merely 
casual. The test of the sufficiency of the induction in this case is, 
when any increase of the number of trials from which the average is 
struck, does not materially alter the average. 

This kind of elimination, in which we do not eliminate any one 
assignable cause, but the multitude of floating unassignable ones, may 
be termed the Elimination of Chance. We afford an example of it 
when we repeat an experiment, in order, by taking the mean of differ- 
ent results, to get rid of the effects of the unavoidable errors of each 
individual experiment. When there is no permanent cause such as 
would produce a tendency to error peculiarly in one direction, we are 
warranted by experience in assuming that the errors on one side will, 
in a certain number of experiments, about balance the errors on the 
contrary side. We have, therefore, to repeat the experiment, until 
any change which is produced in the average of the whole by further 
repetition, falls within limits of error consistent with the degree of 
accuracy required by the purpose we have in view. 

§ 4. In the supposition hitherto made, the effect of the constant cause 
A has been assumed to form so gi^eat and conspicuous a part of the 
general result, that its existence never could be a matter of uncer- 
tainty, and the object of the eliminating process was only to ascertain 
how much is attributable to that cause ; what is its exact law. Cases, 



318 INDUCTION. 

Iiowever, occur in which the effect of a constant cause is so small, 
compared with that of some of the changeable causes with which it is 
liable to be casually conjoined, that of itself it escapes notice, and the 
very existence of any effect arising from a constant cause is first learnt, 
by the process which in general serves only for ascertaining the quantity 
of that effect. This case of induction may be characterized as follows. 
A given effect is known to be chiefly, and not known not to be wholly, 
determined by changeable causes. If it be wholly so produced, then 
if the aggregate be taken of a sufficient number of instances, the 
effects of these different causes will cancel one another. If, therefore, 
we do not find this to be the case, but, on the contrary, after such a 
number of trials has been made that no further increase alters the 
average result, we find that average to be, not zero, but some other 
quantity, around which, though small in comparison with the total 
effect, the effect nevertheless oscillates, and which is the middle point 
in its oscillation ; we may conclude this to be the effect of some con- 
stant cause : which cause, by some of the methods already treated of, 
we may hope to detect. This may be called the discovery of a residual 
phenomenon hy eliminating the effect of chaiice. 

It is in this manner, for example, that loaded dice may be discovered. 
Of course no dice are so clumsily loaded that they must always throw 
certain numbers ; otherwise the fraud would be instantly detected. 
The loading, a constant cause, mingles with the changeable causes 
which determine what cast will be thrown in each individual instance. 
If the dice were not loaded, and the throw were left to depend entirely 
upon the changeable causes, these in a sufficient number of instances 
would balance one another, and there would be no preponderant 
number of throws of any one kind. If, therefore, after such a number 
of trials that no further increase of their number has any material 
effect upon the average, we find a preponderance in favor of a partic- 
'Ular throw; we may conclude with assurance that there is some constant 
cause acting in favor of that throw, or in other words, that the dice 
are not fair ; and moreover the exact amount of the unfairness. In a 
similar manner, what is called the diurnal variation of the barometer, 
which is very small compared with the vaiiations arising from the 
irregular changes in the state of the atmosphere, was discovered by 
comparing the average height of the barometer at different hours of 
the day. When this comparison was made, it was found that there 
was a small difference, which on the average was constant, however 
the absolute quantities might vary, and which difference, therefore, 
must be the effect of a constant cause. This cause was afterwards 
ascertained, deductively, to be the rarefaction of the air, occasioned 
by the increase of temperature as the day advances. . 

§ 5. After these general remarks on the nature of chance, we are 
prepared to consider in what manner assurance may be obtained that 
a conjunction between two phenomena, which has been observed a 
certain number of times, is not casual, but a result of causation, and 
to be received therefore as one of the uniformities in nature, although 
(until accounted for a priori) only as an empirical law. 

We will suppose the strongest case, namely, that the phenomenon B 
has never been observed except in conjunction with A. Even then, 
the probability that they are connected is not measured by the total 



CALCULATION OF CHANCES. 319 

number of instances in which they have been found together, but by 
the excess of that number above the number clue to the absolute fre- 
quency of A. If, for example, A exists always, and therefore coexists 
with everything, no number of instances of its coexistence v/ith B 
would prove a connexion ; as in our example of the fixed stars. If A 
be a fact of such common occurrence that it may be presumed to be 
present in half of all the cases that occur, and therefore in half the 
cases in which B occurs, it is only the proportional excess above half, 
that are to be reckoned as evidence towards proving a connexion 
between A and B. 

In addition to the question, What is the number of coincidences 
which, on an average of a great multitude of trials, may be expected 
to arise from chance alone 1 there is also another question, namely, Of 
what extent of deviation from that average is the occun^ence credible, 
from chance alone, in some number of instances smaller than that 
which constitutes a fair average ? It is not only to be considered what 
is the general result of the chances in the longf run, but also what are 
the -extreme limits of variation from that general result, which may 
occasionally be expected as the result of some smaller number of 
instances. 

The consideration of the latter question, and any consideration of 
the former beyond that already given to it, belong to what mathema- 
ticians term the doctrine of chances, or, in a phrase of greater preten- 
sion, the Theory of Probabilities. An attempt at a philosophical appre- 
• ciation of that doctrine is, therefore, a necessary portion of our task. 



CHAPTER XVIII. 

OF THE CALCULATION OF CHANCES. 

§ 1. ''Probability," says Laplace,* "has reference partly to our 
ignorance, partly to our knowledge. We know that among three of 
more events, one, and only one, must happen ; but there, is nothins 
leading us to believe that any one of them will happen rather than the 
others. In this state of indecision, it is impossible for us to pronounce 
with certainty on their occurrence. ^ It is, however, probable that any 
one of these events, selected at pleasure, will not take place ; because 
we perceive several cases, all equally possible, which exclude its oc- 
cun-ence, and only one which favors it." 

Such is this great mathematician's statement of the logical founda- 
tion upon which rests, according to him, the theory of chances : and if 
his unrivaled command over the means which mathematics supply for 
calculating the results of given data, necessarily implied an equally 
sure judgment of what the data ought to be, I should hardly dare give 
utterance to my conviction, that in this opinion he is entirely wrong ; 
that his foundation is altogether insufficient for the superstructure 
erected upon it; and that there is implied, in all rational calculation 
of the probabilities of events, an essential condition, which is either 

* Essai Philosophique sur Us Prohabilites, fifth Palis edition, p. 7. 



320 INDUCTION. 

overlooked in Laplace's statement, or so vaguely indicated as neither 
to be suggested to the reader, nor kept in view by the writer himself. 
To a calculation of chances, according to Laplace, two things are 
necessary : we must know that of several events some one will cer- 
tainly happen, and no more than one ; and we must not know, nor 
have any reason to expect, that it will be one of these events 
rather than another. I contend that these .are not the only requis- 
ites, and that another supposition is necessary. This supposition it 
might be imagined that Laplace intended to indicate, by saying 
that all the events must be equally possible (egalement possibles). 
But his next sentence shows that, by this expression, he did not 
mean to add anything to the two conditions which he had already 
suggested. " The theory of chances consists in reducing all events 
of the same kind to a certain number of cases equally possible, 
that is, such that we are equally undecided as to their existence ; and 
to determine the number of these cases which are favorable to the 
event of which the probability is sought." By " events equally possi- 
ble," then, he only means events " such that we are equally undecided 
as to their existence ;" that we have no reason to expect one rather 
than another ; which is not a third condition, but the second of the 
two previously specified. I, therefore, feel warranted in affirming 
that Laplace has overlooked, in this general theoretical statement, 
a necessary part of the foundation of the doctrine of chances. 

§ 2. To be able to pronounce two events equally probable, it is not 
enough that we should know that one or the other must happen, and 
should have no ground for conjecturing which. Experience must 
have shown that the two events are of equally frequent occurrence. 
Why, in tossing up a halfpenny, do we reckon it equally probable 
that we shall throw cross or pile ] Because experience has shovni 
that in any gi'eat number of throws, cross and pile are thrown about 
equally often ; and that the more throws we make, the more nearly 
the equality is perfect. We call the chances even, because if we 
stake equal sums, and play a certain large number of times, experi- 
ence proves that our gains and losses will about balance one another ; 

' and will continue to do so, however long afterwards we continue play- 
ing : while on the contrary, if we give the slightest odds, and play a 
great number of times, we are sure to lose ; and the longer we con- 
tinue playing, the greater losers we shall be. If experience did not 
prove this, we should proceed as much at haphazard in staking equal 

"^Bums as in laying odds ; we should have no more reason for expecting 
not to be losers by the one wager than by the other. 

It would indeed require strong evidence to persuade any rational 
person that by a system of operations upon numbers, our ignorance 
can be coined into science ; and it is doubtless this sti^ange pretension 
which has driven a profound thinker, M. Comte, into the contrary 
extreme of rejecting altogether a doctrine which, however imperfectly 
its principles may sometimes have been conceived, receives daily veri- 
fication from the practice of insurance, and firOm a great mass of other 
positive experience. The doctrine itself is, I conceive, sound, but the 
manner in which its foundations have been laid by its gi'eat teachers is 
most seriously objectionable. Conclusions respecting the probability 
of a fact rest not upon a different, but upon the very same basis, as 



CALCULATION OF CHANCES. 321 

conclusions respecting its certainty ; namely, not our ignorance, but 
our knowledge : knowledge obtained by experience, of the proportion 
Ibetween the cases in which the fact occurs, and those in which it does 
not occur. Every calculation of chances is grounded on an induction : 
and to render the calculation legitimate, the induction must be a valid 
one. It is not less an induction, though it does not prove that the 
'eyent occurs in all cases of a. given description, but only that out of a 
"given number of such cases, it occurs in about so many. The fraction 
which mathematicians use to designate the probability of an event, 
is the ratio of these two numbers ; the ascertained proportion between 
the number of cases in which the event occurs, and the sum of all the 
cases, tliose in which it occurs and in which it does not occur taken 
together. In playing at cross and pile, the description of cases con- 
cerned are throws, and the probability of cross is one half, because it 
is found that if we throw often enough, cross is thrown about once in 
every two throws ; and because this induction is made under circum- 
stances justifying the belief that the proportion will be the same in 
other cases as in the cases examined. In the cast of a die, the proba- 
bihty of ace is one-sixth ; not, as Laplace would say, because there 
are six possible throws, of which ace is one,' and because we do not 
know any reason why one should turn up rather than another; but 
because we do know that in a hundred, or a million of throws, ace will 
be thrown about one-sixth of that number, or once in six times. 

Not only is this third condition indispensable, but if we have that, 
we do not want Laplace's two. It is not necessary that we should 
know bow many possibilities there are, or that we should have no 
tnore reason for expecting one of them than another. If a north wind 
blows one day in every ten, the probability of a north wind on any 
given day will be one-tenth, even though of. the remaining possibilities 
a west wind should be gi'eatly the most probable. If we know that 
half the trees in a particular forest are oaks, though we may be quite 
ignorant hpw many other kinds of trees it contains, the chance that a 
tree indiscriminately selected will be an oak is an even chance, or, in 
mathematical language, one-half. So that the condition which Laplace 
omitted is not merely one of the requisites for the possibility, of ia cal- 
culation of chances ; it is the only requisite. 

In saying that he has omitted this condition, I am far from meaning 
to assert, that he does not frequently take it into consideration in par- 
ticular instances : nor indeed could he fail to do so, since whenever 
any experience bearing upon the case really exists, he would naturally 
consult that experience to assure himself of the fulfilment of his second 
condition, that there be no reason for expecting one event rather than 
another. When experience is to be had, he takes that experience as 
the measure- of the probabiUty : his eiTor is only in imagining that 
there can be a measurement of probability where thei^ is no expe- 
rience. The consequence of this eiTor has been his adoption of con- 
clusions not indeed contrary to, but unsupported by, experience. • He 
has been led to push the theoiy and its applications beyond the bounds 
which confine all legitimate inferences of the human mind ; by extend- 
ing them to subjects on which the absence of any gi'ound for deter- 
mining between two suppositions, does not arise from our having equal 
gi-ounds for presuming both, but from our having an equal absence of 
gi;ounds for piesuming either. 

Ss * • ^ 



323 " INDUCTION. 

According to his views, indeed, tlie (Mlculation of chances sliOiild*be 
much more universally applicable to things of which we are com- 
pletely ignorant, than to things of which we have partial knowledge. 
Where we have some experience of the occurrence of each of the con- 
flicting possibilities, it may often be difficult, according to the prescrip- 
tions of the theory, to reduce those possibilities to a definite number of 
cases, all equally probable ; but when the case is out of the reach of 
all experience, so that we have no difficulty in being "equally unde- 
cided" respecting the possibilities, there is nothing to make us halt or 
waver in applying the theory. If the question be whether the inhabit- 
ants of Saturn have red hair, we need only know the number of the 
prismatic colors, and of th-eir more marked compounds, and we can at 
once assign the fraction corresponding to the probability! It is evi- 
dent that probability, in any sense in which it can operate upon our 
belief or conduct, has nothing to do with such chimerical evaluations, 
and that entire suspension of judgment, where we have no evidence, is 
the only course befitting a rational being. To entitle us to affirm any- 

, thing positive about uncertain facts, whether it be that orie supposition 
is more probable than another, or only that it Is equally probable, we 
mu^t have the testimony of experience, that, taking the whole of some 

* class of cases, the one guess will be oftener right, or as often right as 
the other. The estimation, in short, of chances, like that of certain- 
ties, is only rational when grounded upon a complete induction by 
observation or experiment.* '• 

§ 3. From these principles.it is easy to deduce the demonstration of 
that theorem of the doctrine of probabilities, which is the foundation 
of its principal application to judicial or other inquiries for ascertain- 
ing the occuiTence of a given event, or the reality of an individual 
fact. . .The signs or evidences by which a fact is usually proved, are 

■* Confusion IS sometime's ifltfodueed.in:to this- subject' bt 'not adverting to the* distinction 
between the chances that a' given erent will happen, and the chances that a guess, not yet 
, made, respecting its occurrence, will be right. Supposing that I have no more reason to 
expect one event than another, it is (from experience of "human actions) an equal chance 
whether I guess A or B ; but it is not, thel-efore, aji, equal' chance, whether A or B takes 
place. , : * ' , 

The fallacy has been stated thns. Suppose that either A or B must happen: and let 
the chance that A will happen be x: as certainty is represented by 1, the chance that B 
will happen is 1 — x. Now, the chance that the event I, guess will come to pass, is made 
np of two chances: the" chance that I shall guess A and that A will happen, p/ws the 
chance that I shall guess B and that B will' happen. The chance that 1 shall guess A 
being ^ ; the chance that I shall guess A and that A will happen, is compounded of ^ and a; ; 
it is therefore ^;r. The chance that I shall guess B being also 4, the chance that I shall 
guess B and that B will happen, is|- (1 — x). But the sum of these two io \ : therefore the 
chance that the event I guess will come to pass, is always an even chance. But since it 
is an even chance that my guess will be right, it is an even chance which of the two events 
will occur, whatever m.ay be their comparative frequency in nature. 

The whole of this reasoning is sound up to the last step, but that step is a nG?i spqvUw. 
Before I have guessed, or until I have made my guess known, it is an even chance that I 
^guess right ; but when I have guessed, and guessed A, it is no longer an even chance that 
'l have guessed right: otherwise there vv'.ould be an even chance in favor of the most im- 
probable event. Let the question be, Is Queen Victoria at this moment alive: and let me 
be r^uired to guess aye or no, .without knowing about what, in order that I may be equally 
likely to guess the one and the other.. No on€ will say it is an even chance which is trua; 
but it really is an even chance whether my guess will be right. The chance of my gufiss- 
ing in the negative and being right, is ^ of a very small chance, nay, perhaps y-g-^'jy^.jj^, but 
the chance of my guessing in the affirmative, and being right, is J of the remaining --Ll.^l-^; 
so that the two together are ?,. When, however, I have' guessed, and told my gyess, the 
even chance wluch of the two I should guess is converted into a certainty. If IJlave 
guessed aye, the chance that I am right is i^f-21^ • ^ "0» it is only yoWCVI^' ' • " " 



CALCULATION OF CHANCES. 323 

some of its consequences : and tlio inquiry hinges upon determining 
what cause is most likely to have produced a given effect. The theo- 
rem applicable to such investigations is the Sixth Principle in Laplace's 
Essai Pkilosophique sivr les ProhabiliUs, which is described by him as 
*' the fundamental principle of that branch of the Analysis of Chances, 
which consists in ascending from events to their causes."* 

Given an effect to be accounted for, and there being several causes 
which might have produced it, but of the presence of which, in the 
particular case, nothing is known ; the probability that the effect was 
produced by any one of these causes is as the antecedent probability 
of the cause, multiplied by the probability that the cause, if it existed, 
would have produced the given effect. 

Let M be the effect, and A, B, two causes, by either which it might 
have been produced. To find the probability that it was produced 
by the one and not by the other, ascertain which of the two is most 
likely to have existed, and which of them, if it did exist, was most 
likely to produce the effect M : the probability sought is a compound 
of these two probabilities. 

Case I. Let the causes be both alike in the second respect; either 
A or B, when it exists, being supposed equally likely (or equally 
certain) to produce M ; but let A be in itself twice as likely as B to 
exist, that is, twice as frequent a phenomenon. Then it is twice as 
likely to have existed in this case, and to have been the cause which 
produced M. 

For, since A exists in nature twice as often as B; in any 300 cases 
in which one or other existed, A has existed 200 times and B 100. 
But either A or B must have existed wherever M is produced : there- 
fore m 300 times that M is produced, A was the producing cause 200 
times, B only 100, that is, in the ratio of 2 to 1. Thus, then, if the 
causes are alike in their capacity of producing the effect, the proba- 
bility as to which actually produced it, is in the ratio of their antecedent 
probabilities. 

Case IT. Reversing the last hypothesis, let us suppose that the 
causes are equally frequent, equally -likely to have existed, but not 
equally likely, if they did exist, to produce M : that in three times that 
A occurs, it produces that effect twice, while B, in three times, pro- 
duces it only once. Since the two causes are equally frequent in their 
occurrence ; in every six times that either one or the other exists, A 
exists three times and B three iimes. A, of its three times, produces 
M in two ; B, of its three times, produces M in one. Thus, in the 
whole six times, M is only produced thrice ; but of that thrice it is 
produced twice by A, once only by B. Consequently, when the an-' 
tecedent probabilities of the causes are equal, the chances that the 
effect was produced by them are in the ratio of the probabilities that 
if they did exist they would produce the effect. 

Case IIL The third case, that in which the causes are? unlike i^L 
hoth respects, is solved by what has preceded. For, when a quantity' 
depends upon two other quantities, in such a manner that while either 
of them remains constant it is proportional to- the other,'it must neces- 
sarily, be prtiportionsil to the product of the two quantities, the product 

* Pp. 18, 19. The theorem is not slated by Laplace in the exact ternis in which I have 
stated it ; but the identity of import of the two modes of expression is easily demonstrable. 



324 . . INDUCTION. 

beino- the only function of the two which obeys that particular law of 
variation. Therefore, the probability that M was produced by either 
cause, is as the antecedent probability of the cause, multiplied by the 
probability that if it existed it would produce M. Which was to be 
demonstrated. 

Or we may prove the third case as we proved the first and second. 
Let A be twice as jfrequent as B ; and let them also be unequally likely^ 
when they exist, to produce M : let A produce it twice in four times, 
B thrice in four times. The antecedent probability of A is to that of 
B as 2 to 1 ; the probabilities of their producing M are as 2 to 3 ; the 
product of these ratios is the ratio of 4 to 3, which, therefore, if the 
theorem be true, will be the ratio of the probabilities that A or B was 
the producing cause in the given instance. And such will that ratio 
really be. For since A is twi€e as frequent as B, out of twelve cases in 
which one or other exists, A exists in 8 and B in 4, But of its eight 
cases, A, by the supposition, produces M in only 4, while B of its four 
cases produces M in 3. M, therefore, is only produced at all in 
seven of the twelve cases ; but in four of these it is produced by A, in 
three by B ; hence, the probabilities of its being produced by A and 
by B are as 4 to 3, and are expressed by the fractions ^ and |. Which 
was to be demonstrated. 

It is here necessary to point out another serious oversight in La- 
place's theory. When he first introduces the foregoing theorem, he 
characterizes it correctly, as the principle for determining to which of 
several causes we are to attribute a known fact. But after having con- 
ceived the principle thus accurately, when he comes to its applications 
he no longer restricts it to the ascertainment of causes alone, but, with- 
out any previous notice substitutes for the idea of causes that of hypo- 
theses ^or suppositions of any kind. In this extended sense, I do not 
conceive the proposition to be tenable. The hypotheses must be either 
causes, or at least signs showing the existence of causes. If we could 
be permitted to substitute mere suppositions affording no ground for 
concluding that the effect would be produced, in the room of causes 
capable of producing it, the theorem thus extended would stand as 
follows. A fact, M, having happened, the probability of the truth of 
any arbitrary supposition altogether unconnected with M,'is as the^ 
antecedent probability of the suppoBiiion, multiplied by the probability 
that if the supposition was true M would happen ; that is, multiplied 
by the antecedent probability of M, since M is neither more nor less 
probable on account of a supposition which has nothing to do with the 
causes of it. Now the proposition as thus stated, is an absurdity. The 
probability that when M happened A had previously happened, is not 
the antecedent probability of M multiplied by that of A, but the ante- 
cedent probability of A only. The antecedent probability of M cannot 
be an element of a question into which the occun-ence of M enters not 
as a contingency but as a certainty. What the product of the antece-- 
dent probabilities of A and M does give, is, not the probability of the. 
the one when the other is a known past event, but the antecedent prob: 
ability of the two together, considered as future events. 

This error of Laplace has not been harmless. We shall see here- 
after, in treating of the Grounds of Disbelief, that he has been led by 
it into serious practical mistakes when attempting to pronounce iLpon 
the circumstances which render any statement incredible. 



CALCULATION OF CHANCES. 325 

§ 4. From the preceding view of the foundation of the doctrine of 
chances, its general principles may be seen to be applicable in a rough 
way to many subjects which are by no means amenable to its precise 
calculations. To render these applicable, there must be numerical 
data, derived from the observation of a very large number of instances. 
The probabilities of life at different ages, or in different climates ; the 
probabilities of recovery from a particular disease ; the chances of the 
birth of male or female offspring ; the chances of the loss of a vessel 
in a particular voyage ; all these admit of estimation sufficiently pre- 
cise to render the numerical appreciation of their amount a thing of 
practical value • because there are bills of mortality, returns from 
hospitals, registers of births, of shipwrecks, &c., founded on cases 
sufficiently numerous to afford average proportions which do not 
materially vaiy from yOar.to year, or from ten years to ten years. But 
where observation and experiment have not afforded a set of instances 
sufficiently numerous to eliminate chance, and sufficiently various to 
eliminate all non-essential specialities of circumstance, to attempt to 
calculate chances is to convert mere ignorance into dangerous en-or 
by clothing it in the garb of knowledge. 

It remains to examine the bearing of the doctrine of chances upon 
the peculiar problem for the sake of which we have on this occasion 
adverted to it, namely, how to distinguish coincidences which are 
casual from those which are the result of law ; from those in which the 
facts which accompany^ or follow one another are somehow connected 
through causation. 

§ 5. The doctrine of chances affords means by which, if we knew 
the average 'numbeT of coincidences to be looked for between two 
phenomena connected only casually, we could determine how often 
any given deviation from that average will occur by chance. If the 

probability of any casual coincidence, considered in itself, be — , the 
probability that the same coincidence will be repeated n times in suc- 
cession is — ^. For example, in one throw of a die the probability of 

ace being —; the probability of throwing ace twice in succession will 

. . 1 

be 1 divided by the square of 6, or — . For ace is thrown at the first 

throw once in six, or six in thirty-six times ; and of those six, the die 
being cast again, ace will be thrown but once; being altogether once 
in thirty-six times. The chance of the same cast three times succes- 
sively is, by a similar reasoning, — or -r^ : that is, the event will hap- 
pen, on a large average, only once in two hundred and sixteen 
throws. 

We have thus a rule by which to estimate the probability that any 
given series of coincidences arises from chance ; pro-vdded we can 
measure coiTectly the probability of a single coincidence. If we could 
obtain an equally precise expression for the probability that the same 
series of coincidences arises from causation, we should only have to 
compare the numbers. This, however, can rarely be done. Let us 



326 ^ INDUCTION. 

see what degree of approximation can practically be made to the 
necessary precision. 

The question falls within Laplace's sixth principle, of which a short 
distance back, we gave the demonstration. The given fact, that is to 
say, the series of coincidences, may have originated either in a causal 
conjunction of causes or in a law of nature. The probabilities, there- 
fore, that the fact originated in these two modes, are as their ante- 
cedent probabilities, multiplied by the probabilities that if they existed 
they would produce the effect. But the particular combination of 
chances if it occurred, or the law of nature if real, would certainly 
produce the series of coincidences. The probabilities, therefore, 
that the coincidences are 'produced by the two causes in question, 
are as the antecedent probabilities of the causes. One of these, the 
antecedent probability of the combination of mere chances which 
would produce the given result, is an appreciable quantity. The 
antecedent probability of the other supposition may be susceptible 
of a more or less exact estimation, according to the nature of the 
case. ^ . 

Jn some cases, ^ the coincidence, supposing it to.be the 'result of 
causation at all, must be the result of a knowTi cause ; as the sue- ' 
cession of aces, if not accidental, must arise from the loading of the 
die. In such cases we may be able to form a conjecture as to the 
antecedent probability of such a circumstance, from the characters 
of the parties concerned, or other such evidence ; but it would clearly 
be impossible to estimate that probability vdth anythiug like numerical 
precision. The counter-probability, however, that of the accidental 
origin of the coincidence, dwindhng so rapidly as it does at each new 
trial ,' the stage is soon reached at which the chance of unfairness in 
the die, however small in itself, must be gi'eater than that of a causal 
coincidence : and on this ground, a practical decision can generally be 
come to without much hesitation, if there be the power of repeating the 
experiment. 

When, however, tbe coincidence is one which cannot be accounted 
for by any known cause, and the connexion between the two phenom- 
ena, if produced by causation, must be the result of some law of nature 
hitherto unknown ; which is the case we had in yiew in the last chap- 
ter; then, although the probability of a casual coincidence may be 
capable of appreciation, that of the. counter-supposition, the existence 
of an undiscovered law of nature, is clearly unsusceptible of even an 
approximate evaluation. In order to have the data which such a case 
would require, it would be necessary to know what proportion of all 
the individual sequences or coexistence^ occurring in nature are the 
result of law, and what proportion are the result of chance. It being 
evident that we cannot form any plausible conjecture as to this propor- 
tion, much less appreciate it numerically, we cannot attempt any pre- 
cise estimation of the comparative probabilities. But of this we are 
sure, that the detection of an unknown law of nature — of some previ- 
ously unrecognized constancy of conjunction among phenomena — is- 
no uncommon event. If, therefore, the number of instances in which- 
a coincidence is observed, over and above that which would arise on 
the average from the mere concurrence of chances, be such that sio 
great an amount of coincidences from accident alone would be art 
extremely uncommon event ; we have reason to conoljad^ that the com- 



EXTENSION OF LAWS TO ADJACENT CASES. 327 

cldence is. the effect of causation, and may be received (subject to 
correction from further experience) as an empirical law. Further 
than this, in point of precision, we. cannot go; nor, in most cases, is 
greater precision req[uired for the solution oi' any practical doubt. 



CHAPTER XIX. 

OF THE EXTENSION OF DERIVATIVE LAWS TO ADJACENT CASES. 

^ § 1. We have had frequent occasion to notice the inferior generality 
of derivative laws, compared with the ultimate laws from which they 
are derived. This inferiority, which affects not only the extent of the 
propositions themselves, but their degiee of certainty wdthin that ex- 
tent, is most conspicuous in the uniformities of coexistence and sequence 
obtaining between effects which depend ultimately upon different 
primeval , -causes. Such uniformities will only obtain where there 
exists the same collocation of those primeval causes. If the collo- 
cation varies, though the laws themselves remain the same, a totally 
different set of derivative uniformities may, and generally will, be the 
result. 

Even where the derivative unifomiity is between different effects of 
the same cause, it will by no means obtain as universally as the law of 
the cause itself. If a and h accompany or succeed one another as 
effects of the cause A, it by no means follows that A is the only cause 
which can produce them, or that if there be another cause, as B, 
capable of producing a, it must produce h likewise. The conjunction, 
therefore, of <2 and h, perhaps does not hold universally, but only in the 
instances in which a arises from A. When it is produced by a cause 
other than A, a and h may be dissevered. Day (for example) is always 
in our experience followed by night ; but day is not the cause of night; 
both are successive effects of a common cause, the periodical passage 
of the spectator into and out of the earth's shadow, consequent on the 
earth's rotation, and on the illuminating property of the sun. If, there- 
fore, day is ev«r produced by a different cause or set of causes fi'oni 
this, day will not, or at least may not, be followed by night. On the 
sun's ovvoi surface, for instance, this may be the case. 

Finally, even when the derivative uniformity is itself a law of causa- 
tion (resulting from the combination of several causes), it is not alto- 
gether independent of collocations. If a cause supervenes, capable of 
wholly or partially counteracting the effect of any one of the conjoined 
causes, the effect will no longer conform to the derivative law. \\Tiile, 
therefore, each ultimate law is only liable to ft'usti'ation from one set of 
counteracting causes, the derivative law is liable to it from several. 
Now, the possibility of the occurrence of counteracting causes which 
do not arise from any of the conditions involved in the law itself, 
depends on the original collocations. 

It is true that (as we formerly remarked) laws of causation, whether 
ultimate or derivative, are, in most cases, fulfilled even when counter- 
acted ; the cause produces its effect, though that effect is destroyed by 
soiiiething else. That the effect may be frustrated, is, therefore, no 



•328 , INDUCTION. 

objection to the universality of the law of causation. But it is an ob- 
jection to the universality of the sequences or coexistences of effects, 
which compose the greater part of the derivative laws flowing from 
laws of causation. When, from the law of a certain combination of 
causes, there results a certain order in the effects ; as from the combi- 
nation of a single sun with the rotation of an opaque body round its 
axis, theref results, on the whole surface of that opaque body, an alter- 
nation of day and night; then if we suppose one of the combined 
causes ' counteracted, the rotation stopped, the sun extinguished, or a 
second sun superadded, the truth of that particular law of causation is 
in no way affected ; it is still true that one sun shining upon an opaque 
revolving body will alternately produce day and night ; but since the 
sun no longer does shine upon such a body, the derivative uniformity, 
the succession of day and night on the given planet, is no longer true. 
Those derivative uniformities, therefore, which are not laws of causa- 
tion, are (except in the rare case of their depending upon one cause 
alone, not upon a combination of causes), always more or less contin- 
gent upon collocations; and are hence subject to the characteristic 
infirmity of empirical laws, that of being admissible only where the 
collocations are known by experience to be such as are requisite for 
the truth of the law, that is, only within the conditions of time and 
,J)lace confirmed by actual observation. 

§ 2. This principle, when stated in general terms, seems clear and 
indisputable ; yet many of the ordinary judgments of mankind, the 
propriety of which is not questioned, have at least the semblance of 
being inconsistent with it: On what grounds, it may be asked, do we 
expect that the sun will rise to-morrow "? Is to-morrow within the 
limits of time comprehended in our observations 1 They have extended 
over some thousands of years past, but do they include the future 1 
Yet we infer with confidence that the sun will rise to-morrow ; and 
nobody doubts that we are entitled to do so. Let us consider what is 
the warrant for this confidence. 

In the example in question, we know the causes upon which the 
derivative uniformity depends. They are, the sun giving out light, 
the earth in a state of rotation and intercepting light. The induction 
which shows these to be the real causes, and not merely prior effects 
of a common cause, being complete and irrefragable ; the only circum- 
stances which could defeat the derivative law ar;e such as would de- 
stroy or counteract one or other of the combined causes. While the 
causes exist, and are not counteracted, the effect will continue. If 
they exist and are not counteracted to-morrow, the sun will rise to- 
Tnorro\^. 

Since the causes, namely, the sun and the earth, the one in the state 
of giving out light, the other in a state of rotation, will exist until some- 
thing destroys them ; all depends upon the probabilities of their destruc- 
tion, and upon, those of their counteraction. We know by observation 
(omitting the inferential proofs of an existence for, thousands of ages 
anterior), that these phenomena have continued for five thousand years. 
Within that time there has existed no cause sufficient to diminish them 
appreciably ; nor which has counteracted their effect in any appreciable 
degree. The chance, therefore, that the sun may not rise to-morrow, 
amounts to the chance that some cause, which has not manifested itself 



EXTENSION OF LAWS TO ADJACENT CASES. 329 

in the smallest degree during five tliousand years, will exist to-morrow 
in such intensity as to destroy the sun or the earth, the sun's light or 
the earth's rotation, or to produce an immense disturbance in the effect 
resulting from those causes. 

Now, if such a cause will exist to-morrow, or at any future time, 
some cause, proximate or remote, of that cause must exist now; and 
must have existed during the whole of the five thousand years. If, 
therefore, the sun do not rise to-morrow, it will be because some caiuse 
has existed, the effects of which, though during five thousand years they 
have not amounted to a perceptible quantity, will in one day become 
overwhelming. Since this cause has not been recognized during such 
an interval of time, by observers stationed on our earth, it must, if it 
.^xist, be either some agent whose effects develop themselves gradually 
,sftid very slowly, or one which existed in regions beyond our observq.- 
tion, and is now on the point of arriving in our part of the universe. 
Now all causes which we have experience of, act according to laws 
incompatible with the supposition that their effects, after accumulating 
so slowly as to be imperceptible for five thousand years, should start 
into immensity in a single day. No mathematical law of proportion 
between an effect and the quantity or relations of its cause, could pro- 
duce such contradictory results. The sudden development of an effect, 
of which there was no previous trace, always arises from the coming 
together of several distinct causes, not previously conjoined; but if 
such sudden conjunction is destined to take place, the causes, or their 
causes, must have existed during the entire five thousand years, and 
their not having once come together during that period, shows how 
rare that particular combination is. We have, therefore, the warrant 
of a rigid induction for considering it probable, in a degree undistin- 
guishable from certainty, that the known conditions requisite for the' 
sun's rising will exist to-morrow. 

§ 3. But this extension of derivative laws, not causative, beyond the 
limits of observation, can only be to adjacent cases. If instead of to- 
morrow we had said this day twenty thousand years, the inductions 
would have been anything but conclusive. That a cause which, in 
opposition to very powerful causes,' produced no perceptible effect 
during five thousand years, should produce a very considerable one by 
the end of twenty thousand, has nothing in it which is not in conformity 
with our experience of causes. We know, many agents, the effect of 
which in a short period does not amount to a perceptible quantity, but 
by accumulating for a much longer period becomes considerable. 
Besides, looking at the immense multitude of the heavenly bodies, their 
vast distances, and the rapidity of the motion of such of them as are 
known to .move, itis a supposition not at all contradictory to experi- 
ence that some body may be in motion towards us, or we towards it, 
\\dthin the limits of whose influence we have not come during five thou- 
sand years, but which in twenty thousand more may be 2:)roducing 
effects upon us of the most extraordinary kind. Or the fact w^hich is 
capable of preventing «unrise may be, not the cumulative effect of one 
cause, but some new combination of causes; and the chances favorable 
to that combination, though they have not produced it once in five 
thousand years, may produce it once in twenty thousand. So that the 
inductions which authorize us to expect future events, gi'ow weaker 
Tx 



330 INDUCTION. 

and weaker the further we look into the future, and at length beconje 
inappreciable. 

We have considered the probabilities of the sun's rising to-mor- 
row, as derived from the real laws, that is, from the laws of the causes 
on which that uniformity is dependent. Let us now consider how the 
matter would have stood if the uniformity had been known only as an 
empirical law ; if we had not been aware that the sun's light, and the 
earth's rotation (or the sun's motion), were the causes on which the 
periodical occurrence of sunrise depends. We could have extended 
this empirical law to cases adjacent in time, though not to so great a 
distance of time as we can now. Having evidence that the effects had 
remained unaltered and been punctually conjoined for five thousand 
years, we could infer that the unknown causes on which the conjunc- 
tion is dependent had existed undiminished and un counteracted during 
the same period. 'The same conclusions, therefore, would follow as in 
the preceding case ; except that we should only know that during five 
thousand years nothing had occurred to defeat perceptibly this particu- 
lar effect ; while, when we know the causes, we have the additional 
assurance, that during that interval no such change has been noticeable 
in the causes themselves, as by any degree of multiplication or length 
of continuance could defeat the effect. 

To this must be added, that when we know the causes, we may be 
able to judge whether there exists any k^iown cause capable of coun- 
teracting them : while as long as they are unknown we cannot be sure 
but that if we did know them, we could predict their destruction from 
causes actually in existence, A bedridden savage, who had never 
seen the cataract of Niagara, but who lived within hearing of it, might, 
imagine that the sound he heard would endure for ever ; but if he 
knoAV it to be the effect of a rush of waters over a barrier of rock 
which is progi'essively wearing away, he would know that within a 
number of ages which may be calculated, it will be heard no more. 
In proportion, therefore, to our ignorance of the causes on which the 
empirical law depends, we can be less assu^^ed that it will continue to 
hold good; and the further, we look into futurity, the less improbable 
is it that some one of the causes, whose coexistence gives rise to the 
derivative uniformity, may be destroyed or counteracted. With every 
prolongation of time the chances multiply of such an event, that is to 
say, its non-occarrence hitherto becomes a less guarantee of its not 
occumng within the given time. If, then, it is only to cases which in 
point of time are adjacent (or nearly adjacent) to those which we have 
actually observed, that any derivative law, not of causation, can be ex- 
tended with an assurance equivalent to certainty, much more is this 
true of a merely empirical law. Happily, for the purposes of life it is 
to such cases alone that we can almost ever have occasion to extend 
. them. 

In respect of place, it might seem that a merely empirical law could 
not be extended even to adjacent cases ; that we could have no assu- 
rance, of its being true in any place where it has not been specially 
obsetved. The past duration of a cause is a guarantee for its future 
existence, unless something occurs to destroy it ; but the existence of 
a cause in one or any number of places, is no guarantee for its exist- 
ence in any other place, since there is no uniformity in the collocations 
of primeval causes. When, therefore, an empirical law is extended 



EXTENSION OF LAWS TO ADJACENT CASES. 331 

beyond the local limits within which it has been found true by obser- 
vation, the cases to which it is thus extended must be such as are pre- 
sumably within the influence of the same individual agents. If we 
discovered a new planet within the known bounds of the solar system 
(or even beyond those bounds, but indicating its connexion with the 
system by revolving round the sun), we might conclude, with great prob- 
ability, that it revolves upon its axis. For all the known planets do so ; 
and this uniformity points to some common cause, antecedent to the 
first records of astronomical observation : and although the nature of 
this cause can only be matter of conjecture, yet if it be, as is not 
unlikely (and as Laplace's theory suggests,) one and the same indi- 
vidual impulse given to all the bodies at once, that cause, acting at 
the extreme points of the space occupied by the sun and planets, 
must, unless defeated by some counteracting cause, have acted at 
every intermediate point, and probably somewhat beyond : and there- 
fore acted, in all probability, upon the supposed newly-discovered 
planet. 

When, therefore, effects which are always found conjoined, can be 
traced with any probability to ati identical (and not merely a similar) 
origin, we may with great probability extend the empirical law of their 
conjunction to all places within the extreme local boundaries within 
which the fact has been observed ; subject to the possibility of coun- 
teracting causes in some portion of the field. Still more confidently 
may we do so when the law is not merely empirical ; when the phe- 
nomena which we find conjoined are effects of ascertained causes, 
from the laws of which the conjunction of their effects is deducible. 
In that case, we may both extend the derivative uniformity over a 
larger space, and with less deduction for the chance of counteracting 
causes. The first, because instead of the local boundaries of our ob- 
servation of the fact itself^ we may include the extreme boundaries of 
the ascertained influence of its causes. Thus the succession of day and 
night, we know, holds true of all the bodies of the solar system except 
the sun himself; but we know this only because we are acquainted 
with the causes: if we were not, we could not extend the proposition 
beyond the orbits of the earth and moon, at both extremities of which 
we have the evidence of obsei'vation for its truth. With respect to the 
probability of counteracting causes, it has been seen that this calls for 
a greater abatement of confidence, in proportion to our ignorance of 
the causes on which the phenomena depend. On both accounts, there- 
fore, a derivative law which we know how to resolve, is susceptible of 
a greater extension to cases adjacent in place, than a merely, em- 
pirical law. 



332 INDUCTION. 



CHAPTER XX. 

OF ANALOGY. 



§ 1. The word Analogy, as the name of a mode of reasoning, is gen- 
erally taken for some kind of argument supposed to be of an inductive 
nature, but not amounting to a complete induction. There is no 
word, however, which is used more loosely, or in a greater variety of 
, senses than Analogy. It sometimes stands for arguments which may 
be examples of the most rigid Induction. Archbishop Whately, for 
instance, following Ferguson and other writers, defines Analogy con- 
formably to its primitive acceptation, that which was given to it by 
mathematicians. Resemblance of Relations. In this sense, when a 
country which has sent out colonies is termed the mother countiy, the 
expression is analogical, signifying that the colonies of a country stand 
in the same relation to her in which children stand to their parents. 
And if any inference be drawn from this resemblance of relations, as, 
for instance, that the same obedience or affection is due from colonies 
to the mother country which is due from children to a parent, this is 
called reasoning by analogy. Or if it be argued that a nation is most 
beneficially governed by an assembly elected by the people, from the 
admitted fact that other associations for a common purpose, such as 
joint stock companies, are best managed by a committee chosen by the 
parties interested ; this is an argument from analogy in Archbishop 
Whately's sense, because its foundation is not, that a nation is like a 
joint stock company, or Parliament like a board of directors, but that 
Parliament stands in the same relation to the nation in which a board 
of directors stands to a joint stock company. Now, in an argument of 
this nature, there is no inherent inferiority of conclusiveness. Like' 
other arguments from resemblance, it may amount to nothing, or it 
may be a perfect and conclusive induction. The circumstance in which 
the two cases resemble, may be capable of being shown to be tl^e 
material circumstance ; to be that on which all the consequences, 
necessary to be taken into account in the particular discussion, depend. 
In the case in question, the resemblance is one of relation ; xhejunda- 
mentum relationis being the management, by a few persons, of affairs 
in which a much greater number are interested along with them. 
Now, some may contend that this circumstance which is common to 
the two cases, and the various consequences which follow from it, have 
the chief share in determining all those effects which make up what we 
term good or bad administration. If they can establish this, their 
argument has the force of a rigid induction : if they cannot, they are 
said to have failed in proviiig the analogy between the two cases ; a 
mode of speech which implies that when the analogy can be proved, 
the argument founded upon it cannot be resisted. 

§ 2. It is on the whole more usual, however, to extend the name of 
analogical evidence to arguments from any sort of resemblance, pro- 
vided they do not amount to a complete induction ; without peculiarly 
distinguishing resemblance of relations. Analogical, reasoning, in this 
sense, may be reduced to the following formula : Two things resemble 



ANALOGY. 333 

each, other in one or more, respects ; a certain proposition is true of the 
one ; therefore it is true of the other. But we have here nothing by 
which to discriminate analogy from induction, since this type will sei-ve 
for all reasoning from experience. In the most rigid induction, equally 
with the faintest analogy, we conclude because A resembles B in one 
or more propterties, that it does so in a certain other property. The 
difference is, that in the case of a real induction it has been previously 
showTi, by due comparison of instances, that there is an invariable 
conjunction between the former property or properties and the latter 
property : but in what is called analogical reasoning, no such conjunc- 
tion has been made out. There have been no opportunities of putting 
in practice the Method of Difference, or even the Method of Agree- 
ment ; but we conclude (and that is all which the argument of analogy 
gjnounts to) that a fact m, known to be true of A, is more likely to be 
true of B if B agrees with A in some of its properties . (even though 
no connexion is known to exist between m and those properties), than 
if no resemblance at all could be traced between B and any other thing 
known to possess the attribute m. 

To this argument it is of course requisite, that the properties com- 
mon to A with B shall be merely not known to be connected vnth m; 
they must not be properties known to be unconnected with it. If, 
either by processes of elimination, or by deduction from previous 
knowledge of the laws of the properties in question, it can be con- 
cluded that they have nothing to do with m, the argument of analogy 
is put out of court. The supposition must be, that m is an effect, 
really dependent upon some property of A, but v/e know not upon 
which. We cannot point out any qf the properties of A, which is the 
cause of m, or united with it by any law. After rejecting all which 
we know to have nothing to do with it, there remain several between 
which we are unable to decide : of which remaining properties, B 
possesses one or more. This, accordingly, we consider as affording 
grounds, of more or less weight, for concluding by analogy that B 
possesses the attribute in. 

There can be no doubt that every such resemblance which can be 
pointed out between B and A, affords some degree of probability, 
beyond what, would otherwise exist, in favor of the conclusion drawn 
from iti If B resembled A in all its ultimate properties, its possessing 
the attribute- m would be a certainty, not a probability : and every re- 
semblance which can be shown to exist between them, places it by so 
much the nearer to that point. If the resemblance be in an ultimate 
property, there will be resemblance in all the derivative properties 
dependent on that ultimate property, and of these m may be one. If 
the resemblance be in a derivative property, there is reason to expect 
resemblance in the ultimate property on which it depends, and in the 
Qther derivative properties dependent upon the same ultimate property. 
Every resemblance which can be shown to exist, affords gi'ound for 
expecting an indefinite number of other resemblances ; the particular 
resemblance sought will, therefore, be oftener found among things 
thus known to resemble, than among things between which we know 
of no resemblance.* 

* There was no greater foundation than this for Newton's celebrated conjecture that the 
diamond was combustible. He grounded his guess upon the very high refractnig power of 
the diamond, comparatively to its density ; a peculiarity which had been observed to exist 



S34 INDUCTION. 

For example, I might infer that there are probably inhabitants in 
the moon, because there are inhabitants on the earth, in the sea, and in 
the air; and this is the evidence of analogy. The circmnstance of 
having inhabitants is here assumed not to be an ultimate property, but 
(as it is reasonable to suppose) a consequence of other properties ; 
and depending, therefore, in the case of our earth, upon some of its 
properties as a portion of the universe, but upon vs^hich of those prop- 
erties we know not Now, the moon resembles the earth in being a 
solid, opaque, nearly spherical substance ; containing active volcanoes; 
receiving heat and light from the sun, in about the same quantity as 
our earth ; revolving on its axis ; whose materials gravitate, and which 
obey all the various laws resulting from that property. And I think 
no one will deny that if this were all that was known of the moon, the 
existence of inhabitants in that luminary would derive from these 
various resemblances to the earth, a greater degree of probability 
than it would otherwise have : although the amount of the augmenta- 
tion it would be ridiculous to attempt to estimate. 

If, however, every resemblance proved between B and A, in any 
point not known to be immaterial with respect to 7n, forms some addi- 
tional reason for presuming that B has the attribute m ; it is clear e con- 
tra, that every dissimilarity which can be proved between them,, fur- 
nishes a counter-probability of the same nature on the other pide. It is 
not indeed impossible that different ultimate properties may, in some- 
particular instances, produce the same derivative property; but on the 
whole it is certain that things which differ in their ultimate properties, 
will differ at least as much in the aggregate of their derivative proper* 
ties, and that the differences which are tmknown will on the average 
of cases bear some proportion to those which are knovni. There will, 
therefore, be a competition between the known points of agreement 
and the known points of difference in A and B ; and according as the 
one or the other are deemed to preponderate, the probability derived 
from analogy will be for or against B's having the property m. The 
moon, for instance, agrees with the earth in the circumstances already 
"mentioned; but differs in being smaller, in having its surface more 
unequal, and apparently volcanic throughout, in having no atmosphere 

, sufficient to refract light, no clouds, and therefore (it is inferentially 
concluded) no water. These differences, considered merely as such, 

'niight perhaps balance the resemblances, so that analogy would afford 
no presumption either way. But considering that some of the circum- 
stances which are wanting on the moon are among those which, on our 
earth, are found to be indispensable conditions of animal life, we may 
conclude that if that phenomenon does exist in the moon, it must be as 
the effect of causes totally different from those on which it depends 
here ; as a consequence, therefore, of the moon's differences fi-ora the 
earth, not of their points of agreement. Viewed in this light, all the 
resemblances which exist become presumptions against, not in favor of, 

in combustible substances ; and on similar grounds be conjectured that water, though not 
combustible, contained a combustible ingredient. Experiment having subsequently shown 
that in both instances he guessed right, the prophecy is considered to have done great 
honor to his scientific sagacity ; but it is to this day uncertain whether the praise was 
merited ; whetlier the guess was, in truth, what there are so many examples of in the 
history of science, a far-sighted anticipation of a law afterwards to be discovered. The 
progress of science has not hitherto shown ground for believing that there is any real con- 
nexion between combustibility and a high refracting power. 



ANALOGY. 335 

her being inhabited. Since life cannot exist there in the manner in 
which it exists here, the greater the resemblance of the lunar world to 
the terrestrial in all other respects, the less reason we have to believe 
that it can contain life. - . 

There are, however, other bodies in our system, between which and 
the earth there is a much closer resemblance ; which possess an atmos- 
phere, clouds, consequently water (or some fluid analogous to it), and 
even give strong indications of snow in their polar regions; while the 
cold, or heat, though differing greatly on the average from ours, is, in 
some parts at least of those planets, possibly not more extreme than in 
some regions of our own which are habitable. To balance these agree- 
ments, the ascertained differences are chiefly in the average light and 
heat, velocity of rotation, intensity of gravity, and similar circumstances 
of a secondary kind. With regard to these planets, therefore, the argu- 
ment of analogy gives a decided preponderance in favor of their resem- 
bling the earth in any of its derivative properties, such as that of having 
inhabitants : though, when we consider how immeasurably multitudi- 
nous are those of their properties which we are entirely ignorant of, 
compared with the few which we know, we cannot attach more than 
a very trifling weight toi any ^considerations of resemblance in which 
the known elements bear so inconsiderable a proportion to the un- 
known. 

Besides the competition between analogy and diversity, there may 
be a competition of conflicting analogies. The new case may be sim- 
ilar in some of its circumstances to cases in which the fact m exists, 
but in. others to, cases in which it is known not to exist. Amber has 
some properties in common with vegetable, others with mineral pro- 
ducts, A painting, of unknown origin, may resemble, in certain of its 
characters, known works of a particular master, but in others it may 
as strikingly resemble productions known not to be his. A vase may 
hear some analogy to works of Grecian, and some to those of Etruscan 
or Egyptian art. We are of course supposing that it does not possess 
any quality which has been ascertained, by a sufficient induction, to be 
a conclusive mark either of the one or of the other. 

§ 3. Since the value of an- analogical argument inferring one resem- 
blance from other resemblances without any antecedent evidence of a 
connexion between* them, depends upon the extent of a,scertained 
resemblance, compared first with the amount of ascertained difference, 
and next v^ith the extent of the unexplored region of unascertained 
properties; it follows that where the resemblance is very great, the 
ascertained difference very small, and our knowledge of the subject- 
matter tolerably extensive, the argument from analogy may approach 
in strength very near to a valid induction. If, after much observation 
of B, we find that it agrees with A in nine out of ten of its known 
properties, we may conclude with a probability of nine to one-, that it 
will possess any given derivative property of A. If we discover, for. 
example, an unknown animal or plant, resembling closely some known 
one in the greater number of the properties we observe in it, but dif-"' 
fering in, some few, we may reasonably expect to find in the unob- 
served remainder of its properties, a general agreement with those of 
the former ; but also a difference, corresponding proportionally to the 
amount of obseiTed diversity. 



336 INDUCTION. 

It thus appears that the conclusions derived from analogy are only 
of any considerable value, when the case to v^^hich ,we reason is an ad- 
jacent case; adjacent, not as before, in place or time, but in circum- 
stances. In the case of effects of v^hich the causes are imperfectly or 
not at all known, when consequently the observed order of their oc- 
currence amounts only to an empirical law, it often happens that the 
conditions which have coexisted whenever the effect was observed, have 
been very numerous. Now if a new case presents itself, in which all 
these conditions" do not exist, but the far greater part of them do, some 
one or a few only being wanting; the inference that the effect will 
occur notwithstanding this deficiency of complete resemblance to the 
cases in which it has been observed, may, although of the nature of 
analogy, possess a high degree of probability. It is hardly necessary 
to add that, however considerable this probability may be, no com- 
petent inquirer into nature will rest satisfied with it when it is possible 
to obtain a complete induction ; but will consider the analogy as a 
mere guide-post, pointing out the direction in which more rigorous 
investigations should be prosecuted. 

It is in this last respect that considerations of analogy have the high* 
est philosophical value. The cases in which analogical evidence 
affords in itself any very high degree of probability, are, as we have 
just obsei-ved, only those in which the resemblance is very close and 
extensive; but there is no analogy, however faint, which may not be 
of the utmost value in suggesting experiments or observations that 
may lead to more positive conclusions. When the agents and their . 
effects are out of the reach of further observation and experiment, as 
in the speculations^ already alluded to respecting the moon and planets, 
such slight probabilities are no more than an interesting theme for the 
pleasant exercise of imagination ; but any suspicion, however slight, 
that sets an ingenious person at work to contrive an experiment, or 
that affords a reason for trying one experiment rather than another, 
may be of eminent service to philosophy. 

On this gi'ound, notwithstanding the unfavorable judgment which I 
have concurred with M. Comte in passing upon those scientific hypo- 
theses (when considered as positive doctrines) which are unsusceptible 
of being ultimately brought to the test of actual induction, such for in- 
stance as the two theories of light, the emission theory of the last cen- 
tury, and the undulatory theory which predominates in the present ; I 
am yet unable to agree with M. Comte in considering those hypo- 
theses to be worthy of entire disregard. . As is well said by Hartley 
(and concurred in by a philosopher in general so diametrically opposed 
to Hartley's views as Dugald Stewart), " any hypothesis that has so 
much plausibility as to explain a considerable number of facts, helps 
us to digest these facts in proper order, to bring new ones to light, 
and make experimenta crucis for the sake of future inquirers."* If an 
hypothesis not only explains known facts, but has led to the prediction 
of others previously unknown, and since verified by experience, the 
laws of the phenomenon which is the subject of inquiry must bear at 
least a great similarity to those of the class of phenomena to which the 
hypothesis assimilates it; and since the analogy which extends so far 

* Hartley's Observations on Man, vol. i., p. 16. The passage is not in Priestley's cur- 
tailed edition. 



EVIDENCE OF UNIVERSAL CAUSATION. 337 

may probably extend further, nothing is more likely to suggest experi- 
ments tending to throw light upon the real properties of the phenom- 
enon, than the following out such an hypothesis. But to this end it is 
by no means necessary that the hypothesis be mistaken for a scientific 
truth. On the contrary, that illusion is in this respect, as in every 
other, an impediment to the progress of real knowledge, by leading 
men to restrict themselves arbitrarily to the particular hypothesis 
which is most accredited at the time, instead of looking out for every 
class of phenomena between the laws of which and* those of the given 
phenomenon any analogy exists, and trying all such experiments as 
may tend to the discovery of ulterior analogies pointing in the same 
direction. 



CHAPTER XXI. 

OF THE EVIDENCE OF THE LAW OF UNIVERSAL CAUSATION. 

§ 1. We have now completed our review of the logical processes by 
which the laws, or uniformities, of the sequences of phenomena, and 
those uniformities in iheir coexistence which depend upon the laws of 
their sequence, are ascertained. As we recognized in the commence- 
ment, and have been enabled to see more clearly in the progress of 
the investigation, the basis of all these logical operations is the uni- 
versality of the law of causation. The validity of all the Inductive 
Methods depends upon the assumption that every event, or the begin- 
ning of every phenomenon, must have some cause ; some antecedent, 
upon the existence of which it is invariably and unconditionally conse- 
quent. ,, In the Method of Agreement, this is obvious ; that Method 
avowedly proceeding on the supposition, that we have found the true 
cause so soon as we have negatived every other. The assertion is 
equally true of the Method of Difference. That Method authorizes us 
to infer a general law from two instances ; one, in which A exists to- 
gether with a multitude of other circumstances, and B follows ; 
another, in which, A being removed, and all other circumstances 
remaining the same, B is prevented. What, however, does this prove"? 
It proves that A, in the particular instance, cannot have had any other 
cause than B ; but to conclude from this that A was the cause, or that 
A will on other occasions be followed by B, is only allowable on the 
assumption that B must have some cause ; that among its antecedents 
in any single instance in which it occurs, there must be one which has 
the capacity of producing it at other times. This being admitted, it is 
seen that in the case in question that antecedent can be no other than 
A ; but, that if it be no other than A it must be A, is not proved, by 
these instances at least, but taken for gi^anted. There is no need to 
spend time in proving that the same thing is true of the other Induc- 
tive Methods. The universality of the law of causation is assumed in 
them all. 

But is this assumption Warranted] Doubtless (it may be said) most 
phenomena are connected as effects with some antecedent or cause, 
that is, are never produced unless some assignable fact has preceded 
Uu 



338 INDUGTION. 

them; but the very circumstance that complicated processes of induc- 
tion are sometimes necessary, shows that cases exist in which this 
regular order of succession is not apparent to our first and simplest 
apprehension. If, then, the processes which bring these cases within 
the same category with the rest, require that we should assume the 
universality of the very law which they do not at first sight appear to 
exemplify, is not this a ve^ petitio pfincipiil Can we prove a propo- 
sition, by an argument which takes it for granted 1 And if not so 
proved, on what evidence does it rest '? 

For this difficulty, which I have purposely stated in the strongest 
terms it would admit of, the school of metaphysicians who have long 
predominated in this country find a ready salvo. They affirm, that the 
universality of causation is a truth which wd cannot help believing ; 
that the belief in it is an instinct, one of the laws of our believing 
faculty. As the proof of this, they say, and they have nothing else to 
say, that everybody does believe it ; and they number it among the 
propositions, rather numerous in their catalogue, which may be logi- 
cally argued against, and perhaps cannot be logically proved, but which 
are of higher authority than logic, and which even he who denies in 
speculation, shows by his habitual practice that his arguments make 
no impression upon himself. 

I have no intention of entering into the merits of this question, as a 
problem of transcendental metaphysics. But I must renew my protest 
against adducing as evidence of the truth of a fact in external nature, 
any necessity which the human mind may be conceived to be under of 
believing it. It is the business of the human intellect to adapt itself to 
the realities of things, and not to measure those realities by its own capa- 
cities of comprehension. The same quality which fits mankind for the 
offices and purposes of their own little life, the tendency of their belief 
to follow their experience, incapacitates them for judging of what lies 
^beyond. Not only what man can know, but what he can conceive, 
depends upon what he has experienced. Whatever forms a part of all 
his experience, forms a part also of all his conceptions, and appears to 
him ymiversal arid necessary, though really, for aught he knows, having 
no existence beyond certain, nan-ow limits. The habit, however, of 
philosophical analysis, of which it is the surest effect to enable the 
mind to command, instead of being commanded by, the laws of the 
merely passive part of its own nature, and which, by showing to us 
that things are not necessarily connected in fact because their ideas 
are connected in our minds, is able to loosen innumerable associations 
which reign despotically over the undisciplined mind ; this habit is not 
without power even over those associations which the philosophical 
school of which I have been speaking, regard as connate and instinc- 
tive. I am convinced that any one accustomed to abstraction and 
analysis, who will fairly exert his faculties for the purpose, will, when 
his imagination has once learnt to entertain the notion, find no difficulty 
in conceiving that in some one for instance of the many firmaments 
into which sidereal astronomy now divides the universe, events may 
succeed one another at random, without any fixed law; nor can any- 
thing in our experience, or in our mental nature, constitute a sufficient, 
or indeed any, reason for believing that this is nowhere the case. The 
grounds, therefore, which warrant us in rejecting such a supposition 
with respect to any of the phenomena of which we have experience, 



EVIDENCE OF UNIVERSAL CAUSATION. 339 

must be sought elsewhere than in any supposed necessity of our intel- 
lectual faculties. 

As was observed in a former place,* the belief we entertain in the 
universality, throughout nature, of the law of cause and effect, is itself 
an instance of induction ; and by no means one of the earliest which 
any of us, or which mankind in general, can have made. We arrive 
^t this universal law, by generalization from many laws of inferior 
generality. The generahzing propensity, which, instinctive or not, is 
one of the most powerful principles of our nature, does not indeed 
wait for the period w^hen such a generalization becomes strictly legiti- 
mate. The mere unreasoning propensity to expect what has been 
often experienced, doubtless led men to believe that everything had a 
cause, before they could have conclusive evidence of that truth. But 
even this cannot be supposed to have happened until many cases of 
causation, or, in other words, many partial uniformities of sequence, 
had become familiar. The more obvious of the particular uniformi- 
ties suggest and prove the general uniformity, and that general uni- 
formity, once established, enables us to prove the remainder of the 
particular uniformities of which it is made up. As, however, all rigor- 
ous processes of induction presuppose the general uniformity, our 
knowledge of the particular uniformities from which it was first in- 
ferred was not, of course, derived from rigid induction, but from the 
loose and uncertain mode of induction jper enumerationem simplicem ; 
and the- law of universal causation, being collected from results so ob- 
tained, cannot itself rest upon any better foundation. 

§ 2. This opens to us a consideration of very great importance; 
namely, that induction by simple enumeration, or, in other words, gen- 
eralization of an observed fact from the mere absence of any known 
instances to the contrary, is by no means the illicit logical process in 
all cases which it is in most. It is delusive and insufficient exactly in 
proportion as the subject-matter of the observation is special and lim- 
ited in extent.^ As the sphere widens, this unscientific method becomes 
less and less liable to mislead ; and the most universal class of truths, 
the law of causation for instance, and the principles of number and of 
geometry, are duly and satisfactorily proved by that method alone, 
nor are they susceptible of any other proof. 

With respect to all the class of generalizations of which we have 
recently treated, the uniformities which depend upon causation, the 
ti'uth of the remark just made follows by obvious inference from the 
principles laid down in the preceding chapters. When a fact has 
been observed a certain number of times to be true, and is not in any 
instance known to be false ; if we at once affirm that fact as an uni- 
versal truth or law of nature, without testing it by any of the four 
methods of induction, nor deducing it by reasoning from other known 
laws, %ve shall in general err grossly : but we are jjerfectly justified in 
affirming it as an empirical law, true within certain limits of time, 
place, and circumstance, provided the number of coincidences is greater 
than can with any probability be ascribed to chance. The reason for 
not extending it beyond those limits is, that the fact of its holding true 
within them may be a consequence of collocations, which cannot be 
concluded to exist in one place because they exist in another ; or may 

* Supra, pp. 184-5. 



340 INDUCTION. 

be dependent upon the accidental absence of counteracting agencies, 
which any variation of time, or the smallest change of circumstances, 
may possibly bring into play. If we suppose, then, the subject matter 
of any generalization to be so widely diffused that there is no time, no 
place, and no combination of circumstances, but must afford an exam- 
ple either of its truth or of its falsity, and if it be never found otherwise 
than true, its truth cannot depend upon any collocation unless such as 
exist at all times and places ; nor can it be frustrated by any counter- 
acting agencies, unless by such as never actually occur. It is, therefore, 
an empirical law coextensive with all human experience ; at which point 
the distinction between empirical laws and lav/s of nature vanishes, and 
the proposition takes its place in the highest order of truths accessible 
to science. Such a character strictly belongs to the law of universal 
causation, and to the ultimate principles of mathematics. The induc- 
tion by which they are established is of that kind which can establish 
nothing but empirical laws ; an empirical law, however, of which the 
truth is exemplified at every moment of time and in every variety of 
place or circumstance, has an evidence which surpasses that of the 
most rigid induction, even if the foundation of scientific induction were 
not itself laid (as. we have seen that it is) in a generalization of tliis. 
very description. - 

§ 3. With respect to the general law of causation, it does appear 
that there must have been a time when the universal prevalence of 
that law throughout nature could not have been affirmed in the same 
confident and unqualified manner as at present. There was a time 
when many of the phenomena of nature must have appeared altogether 
capricious and irregular, not governed by any laws, nor steadily con- 
sequent upon any causes. Such phenomena, indeed, were commonly, 
in that early stage of human knowledge, ascribed to the direct inter- 
vention of the will of some supernatural being, and therefore still to 
a cause. This shows the strong tendency of the human mind to 
ascribe every phenomenon to some cause or other ; but it shows also 
that experience had not, at that time, pointed out any regular order in 
the occurrence of those particular phenomena, nor proved them to be, 
as we now know that they are, dependent upon prior phenomena as 
their proximate causes. There have been sects of philosophers who 
have admitted what they termed Chance as one of the agents in the 
order of nature, by which certain classes of events were entirely regu- 
lated ; which could only mean that those events did not occur in any 
fixed, order, or depend upon uniform laws of causation. Finally, there 
is one class of phenomena which, even in our own day, at least one- 
half of th^ speculative world do not admit to be governed by causes ; 
I mean human volitions. These are believed, by the metaphysicians 
who espouse the free-will doctrine, to be self-determining, self-causing; 
that is, not caused by anything external to themselves, not determined 
by any prior fact. It is true that the real opinion of these philosophers 
docs not go quite so far as their words seem to imply ; they do not in 
reality claim for this class of phenomena much more than the absence 
of that mystical tie which the word necessity seems to involve, and the 
existence of which, even in the case of inorganic matter, is but an 
illusion produced by language. But their system of philosophy does 
not the less prove that the existence of phenomena which are not 



EVIDENCE OF UNIVERSAL CAUSATION. 341 

rigorously consequent upon any antecedents, does not necessarily, 
even in the present state of our experience, appear an inadmissible 
paradox. 

The truth is, as M. Comte has well pointed out, that (although the 
generalizing propensity must have prompted mankind from almost the 
beginning of their experience to ascribe all events to some cause more 
ov less mysterious) the conviction that phenomena have invariable laws, 
and follow with regularity certain antecedent phenomena, was only 
acquired gradually; and extended itself, as knowledge advanced, from 
one order of phenomena to another, beginning with those whose laws 
were most accessible to observation. This progi-ess has not yet 
attained its ultimate point; there being still, as before observed, one 
class of phenomena, the subjection of which to invariable laws is not 
yet universally recognized. So long as any doubt hung over this 
fundamental principle, the various Methods of Induction which took 
that principle for granted could only afford results which were admissi- 
ble conditionally ; as showing what law the phenomenon under inves- 
tigation must follow if it followed any fixed law at all. As, however, 
when the rules of correct induction had been conformed to, the result 
obtained never failed to be verified by all subsequent experience; 
every such inductive operation had the effect of extending the acknowl- 
edged dominion of general laws, and bringing an additional portion 
of the experience of mankind to strengthen the evidence of the uni- 
versality of the law of causation : until now at length we are fully 
warranted in considering that law, as applied to all phenomena within 
the range of human observation, to stand on an equal footing in respect 
to evidence with the axioms of geometry itself. 

§ 4. I apprehend that the considerations which give, at the present 
day, to the proof of the law of uniformity of succession as true of all 
phenomena without exception, this character of completeness and 
conclusiveness, are the following : — -First ; that we now know it directly 
to be true of far the greatest number of phenomena ; that there are 
none of which we know it not to be true, the utmost that can be said 
being that of some we cannot positively from direct evidence affirm its 
truth ; while phenomenon after phenomenon, as they become better 
known to us, are constantly passing from the latter class into the 
former ; and in all cases in which that transition has not yet taken 
place, the absence of direct proof is accounted for by the rarity or the 
obscurity of the phenomena, our deficient means of observing them, 
or the logical difficulties arising from the complication of the circum- 
stances in which they occur ; insomuch that, notwithstanding as rigid 
a dependence upon given conditions as exists in the case of any other 
phenomenon, it was not likely that w^ should be better acquainted 
with those conditions than we are. Besides this first class of con- 
siderations there is a second, which still further corroborates the 
conclusion, and from the recognition of which the complete establish- 
ment of the universal law may reasonably be dated. Although there 
are phenomena, the production and changes of which elude all our 
attempts to reduce them universally to any ascertained law; j^et in 
every such case, the phenomenon, or the objects concerned in it, are 
found in some instances to obey the known laws of nature. The wind, 
for example, is the type of uncertainty and caprice, yet we find it in 



342 INDUCTION. 

some cases obeying with as much constancy as any phenomena in 
nature the law of the tendency of fluids to distribute themselves so as 
to equalize the pressure on every side of each of their particles ; as 
in the case of the trade winds, and the monsoons. Lightning might 
once have been supposed to obey no laws ; but since it has been ascer- 
tained to be identical with electricity, we know that the very same 
phenomenon in some of its manifestations is implicitly obedient to the 
action of fixed causes. I do not believe that there is now one object 
or event in all our experience of nature, within the bounds of. the solar 
system at least, which has not either been ascertained by direct 
observation to follow laws of its own, or been proved to he exactly 
similar to objects and events which, in more familiar manifestations, or 
on a more limited scale, follow strict laws : our inability: to trace the 
same laws on the larger scale and in the more recondite instances 
being accounted for by the number and complication of the modifying 
causes, or by their inaccessibility to observation. , 

The progress of experience, therefore, has dissipated the doubt 
which must have rested upon the universality of the law of causation 
while there were phenomena which seemed to he sui generis, not sub- 
ject to the same laws with any other class of phenomena, and not as 
yet ascertained to have peculiar laws of their own. This great gener- 
alization, however, might reasonably have been, as it in fact was by 
all great thinkers, acted upon as a probability of the highest order, be- 
fore there were sufficient grounds for receiving it as a certainty. For, 
whatever has been found true in innumerable instances, and never 
found to be false after due examination in any, we are safe in acting 
upon as universal provisionally, until an undoubted exception appears f 
provided the nature of the case be such that a real exception could 
scarcely have escaped our notice. When every phenomenon that we 
ever knew sufficiently well to be able to answer the question, had a 
cause on which it was invariably consequent, it was more rational to 
suppose that our inability to assign the causes of other phenomena 
arose from our ignorance, than that there were phenomena which were 
uncaused, and which happened accidentally to be exactly those which 
we had hitherto had no sufficient opportunity of studying. 

§ 5. It must, at the same time, be remarked, that the reasons for this 
reliance do not hold in circumstances unknown to us, and beyond the 
possible range of our experience. In distant parts of the stellar 
regions, where the phenomena may be entirely unlike those with 
which we are acquainted, it would be folly to affirm confidently that 
this general law prevails, any more than those special ones which we 
have found to hold universally on our own planet. The uniformity in 
the succession of events, otherwise called the law of causation, must be 
received not as a law of the universe, but of that portion of it only 
which is within the range of our means of sure observation, with a 
reasonable degree of extension to adjacent cases. To extend it 
further is to make a supposition without evidence, and to which in 
the absence of any ground from experience for estimating its degree 
of probability, it would be ridiculous to affect to assign any. 

But, on the other hand, within the bounds of human experience, this 
fundamental law, though itself obtained by induction from particular 
laws of causation cannot be deemed less certain, but on the contrary 



COEXISTENCES INDEPENDENT OF CAUSATION. 343 

more so, than any of those from which it was drawn. It adds to them 
as much proof as it receives from them. For there is probably no one 
even of the best estabUshed laws of causation which is not sometimes 
counteracted, and to which, therefore, apparent exceptions do not 
present themselves, which would have necessarily and justly shaken 
the confidence of mankind in the universality of those laws, if inductive 
processes founded on the universal law had not enabled us to refer those 
exceptions to the agency of counteracting causes, and thereby reconcile 
them with the law with which they apparently conflict. Errors, more- 
over, may have slipped into the statement of any one of the special 
laws, through inattention to some material circumstance ; and instead 
of the true proposition, another may have been enunciated, false as an 
universal law, though leading, in all cases hitherto observed, to the 
same result. But the general law of causation would remain un- 
affected by any such error. The law of cause and effect is therefore, 
not without reason, placed, in point of certainty, at the head of all our 
inductions; on a level with the first principles of mathematics, which 
rest, as we shall see presently, upon much the same species of induc- 
tion as itself. 



CHAPTER XXII. 

OP UNIFORMITIES OF COEXISTENCE NOT DEPENDENT UPON CAUSATION. 

§ 1. The order of the occurrence of phenomena in time, is either 
successive or simultaneous; the uniformities, therefore, which obtain 
in their occurrence, are either uniformities of succession or of coex- 
istence. Uniformities of succession are all comprehended under the 
law of causation and its consequences. Every phenomenon has a 
cause, which it invariably follows ; and from this are derived other 
invariable sequences among the successive stages of the same effect, 
as well as between the effects resulting from causes which invariably 
succeed one another. 

In the same manner with these derivative uniformities of succession, 
a great variety of uniformities of coexistence also take their rise. Co- 
ordinate effects of the same cause naturally coexist with one another. 
High water at any point on the earth's surface, and high water at^the 
point diametrically opposite to it, are effects uniformly simultaneous, 
resulting from the direction in which the combined attraction of the 
sun and moon act upon the waters of the ocean. An eclipse of the sun 
to us, and an eclipse of the earth to a spectator situated in the moon, 
are in like manner phenomena invariably coexistent; and their coex- 
istence can equally be deduced from the laws of their production. 

It is an obvious question, therefore, whether all the uniformities of 
coexistence among phenomena may not be accounted for in this man- 
ner. And it cannot be doubted that between phenomena which are 
themselves effects, the coexistences must necessarily depend upon the 
causes of those phenomena. If they are effects immediately or remote- 
ly of the same cause, they cannot coexist except by virtue of some laws 
or properties of that cause : if they are effects of different causes, they 



344 INDUCTION. 

cannot coexist unless it be because their causes coexist ; and the uni- 
formity of coexistence, if such there be, between the effects, proves 
that in the original collocation those particular causes, within the limits 
of our observation, have uniformly been coexistent. 

§ 2. But these same considerations compel us to recognize that there 
must be one class of coexistences which cannot depend upon causation; 
the coexistences between the ultimate properties of things : between 
those properties which are the causes of all phenomena, but are not 
themselves caused by any phenomenon, and to find a cause for which, 
we must ascend to the origin of all things. Yet among these ultimate 
properties there are not only coexistences, but uniformities of coex- 
istence. General propositions may be, and are formed, which assert 
that whenever certain properties are found, certain others are found 
along vsdth them. We perceive an object; say, for instance, water. 
We recognize it to be water, of course, by certain of its properties. 
Having recognized it, we are able to affirai of it innumerable other 
properties ; which we could not do unless it were a general truth, a 
law or uniformity in nature, that the set of properties by which we 
identified the substance as water, always have those other properties 
conjoined with them. 

In a chapter of a former book, it has been explained in some detail 
what is meant by the Kinds of objects,* those classes which differ from 
one another not by a limited and definite, but by an indefinite and un- 
known, number of distinctions. To this we have now to add, that 
every proposition by which anything is asserted of a Kind, affirms an 
uniformity of coexistence. Since we know nothing of Kinds but their 
properties, the Kind, to us, is the set of properties by which it is 
identified, and which must of course be sufficient to distinguish it from 
every other Kind.f In affirming anything, therefore, of a Kind, we are 
affirming something to be unifomily coexistent with the properties by 
which the Kind is recognized ; and that is the sole meaning of the 
assertion. 

Among the uniformities of coexistence which exist in nature, may 
hence be numbered all the properties of Kinds. The whole of these, 
however, are not independent of causation, but only a portion of them. 
Some are ultimate properties, others derivative ; of some, no cause 
can be assigned, but others are manifestly dependent upon causes. 
Thus, atmospheric air is a Kind, and one of its most unequivocal 
properties is its gaseous form : this property, however, has for its 
cause the presence of a certain quantity of latent heat; and if that heat 
could be taken away (as has been done from so many gases in Mr. 
Faraday's experiments), the gaseous form would doubtless disappear, 
together with numerous other properties which depend upon, or are 
caused by, that property. 

* Supra, book i., chap. vii. 

t In some cases, a Kind is sufficiently identified by some one remarkable property ; but 
most commonly several are required; each property, considered singly, being a joint 
property of that and of other Kini^s. The mere color and brightness of the diamond are 
common to it with the paste from which false diamonds are made ; the double refraction is 
common to it witli Iceland spar, and many other stones ; but the color and brightness 
and the double refraction together, identify its Kind ; that is, are a mark to us that it is 
combustible ; that When bunit it produces carbonic acid ; that it cannot be cut with any 
known substance ; together with many other ascertained properties, and the laci that 
there exist an indefinite number still unascertained. 



COEXISTENCES INDEPENDENT OF CAUSATION. 345 

In regard to all substances which are chemical compounds, and 
which therefore may be regarded as products of the juxtaposition of 
substances different in. Kind from themselves, there is considerable 
reason to presume that the specific properties of the compound are 
consequent, as etlects, upon some of the properties of the elements, 
although but little progress has yet been made in tracing any invariable 
relation between the latter and the former. Still more strongly will a 
similar presumption exist, when the object itself, as in the case of 
organized beings, is no primeval agent, but an effect, which depends 
upon a cause or causes for its very existence. The Kinds therefore 
which are called in chemistry simple substances, or elementary natural 
agents, are the only ones, any of whose properties can with certainty 
be considered ultimate ; and of these the ultimate properties are 
probably much more numerous than we at present recognize, since 
every successful instance of the resolution of the properties of their 
compounds into simpler laws, generally leads to the recognition of 
properties in the elements distinct from any previously known. The 
resolution of the laws of the heavenly motions, established the pre- 
viously unknown ultimate property of a mutual attraction between all 
bodies : the resolution, so far as it has yet proceeded, of the laws of 
crystalization, of chemical composition, electricity, magnetism, &c., 
points to various polarities, ultimately inherent in the particles of which 
bodies are composed ; the comparative atomic weights of different 
kinds of bodies were ascertained by resolving, into more general laws, 
the uniformities observed in the proportions in which substances com- 
bined with one another; and so forth. Thus although every resolution 
of a complex uniformity into simpler and more elementary laws has 
an apparent tendency to diminish the number of the ultimate properties, 
and really does remove many properties from the list ; yet (since the 
result of this simplifying process is to trace up an ever gi'eater variety 
of different effects to the same agents,) the further we advance in this 
direction, the greater number of distinct properties we are forced to 
recognize in one and the same object: the coexistences of which prop- 
erties must accordingly be ranked among the ultimate generalities of 
nature. 

§ 3. There are, therefore, only two kinds of propositions which assert 
an uniformity of coexistence between properties. Either the properties 
depend on causes, or they do not. If they do, the proposition which 
affirms them to be coexistent is a derivative law of coexistei^ip between 
effects, and until resolved into the laws of causation upon which it 
depends, is an empirical law, and to be tried by the principles of 
induction to which such laws are amenable. If, on the other hand, 
the properties do not depend upon causes, but are ultimate properties; 
then if it be true that they invariably coexist, they must both be ulti- 
mate properties of one and the same Kind ; and it is of these only that 
the coexistences can be classed as a peculiar sort of laws of nature. 

Wlien we affinn that all crOws ^re black, or that all negroes have 
woolly hair, we assert an uniformity of coexistence. We assert that 
the property of blackness, or of having woolly hair, invariably coexists 
with the properties which, in common language, or in the scientific 
classification that we adopt, are taken to constitute the class crow, or 
the class negro. Now, supposing blackness to be an ultimate property 
X X 



346 INDUCTION. 

of black objects, or woolly hair an ultimate property of the animals 
which possess it; supposing that these properties are not results of 
causation, are not connected with antecedent phenomena by any law; 
then if all crows are black, and all negroes have woolly hair, those 
must be ultimate properties of the Kind crow, or negro, or of some 
Kind which includes them. If, on the contrary, blackness or woolly 
hair be an effect depending on causes, these general propositions are 
manifestly empirical laws; and all that has already beensaid respect- 
ing that class of generalizations may be applied without modification 
to these. 

Now, we have seen that in the case of all compounds — of all things, 
in short, except the elementary substances and primary powers of 
nature — the presumption is, that the properties do really depend upon 
causes ; and it is impossible in any case whatever to be certain that 
they do not. We therefore should not be safe in claiming for any 
generalization respecting the coexistence of properties, a degree of 
certainty to which, if the properties should happen to be tbe result of 
causes, it would have no claim. A generalization respecting coexist- 
ence, or in other words respecting the properties of Kinds, may be an 
ultimate truth, but it may, also, be merely a derivative one ; and since, 
if so, it is one of those derivative laws which are neither laws of 
causation, nor have been resolved into the laws of causation upon 
which they depend, it can possess no higher degree of evidence than 
belongs to an empirical law. 

§ 4. This, conclusion will be confirmed by the consideration of one 
great deficiency, which precludes the application to the ultimate uni- 
formities of coexistence, of a system of rigorous and scientific induc- 
tion, such as the 'Uniformities in the succession of phenomena have 
been found to be susceptible of. The basis of such a system is want- 
ing : there is no general axiom, standing in the same relation to the 
uniformities of coexistence as the law of causation does to those of suc- 
cession. The Methods of Induction applicable to the ascertainment of 
causes and effects, are grounded upon the principle that everything 
which has a beginning must have some cause or other ; that among 
the circumstances which actually existed at the time of its commence- 
ment, there is certainly some one or more, upon which the eff'ect in 
question is unconditionally consequent, and on the repetition of which 
it would certainly again recur. But in !an inquiry whether some kind 
(as croi^;) ^iversally possesses a certain property (as blackness), there 
is no room for any assumption analogous to this. We have no pre- 
vious certainty that the property must have something which constant- 
ly coexists with it ; must have an invariable coexistent, in the same 
manner as an event must have an invariable antecedent. When we 
feel pain, we must be in some circumstances under which if exactly 
repeated we should always feel j)ain. But when we are conscious of 
blackness, it does not follow that there is something present of which 
blackness is a constant accompaniment. There is, therefore, no room 
for elimination ; no Method of Agreement or Difference, or of Con- 
comitant Variations (which is but a modification either of the Method 
of Agreement or of the Method of Difference). We cannot conclude 
that the blackness we see in crows must be an invariable property of 
crows, merely because there is nothing else present of which it can be 



COEXISTENCES INDEPENDENT OF CAUSATION. 347 

an invariable property. We therefore inquire into the truth of a 
proposition like " All crows are black," under the same disadvantage 
as if, in our inquiries into causation, we were compelled to let in, as 
one of the possibilities, that the effect may in that particular instance 
have arisen without any cause at all. 

' To overlook this grand distinction was, as it seems to me, the capital 
error in Bacon's view of inductive philosophy. The principle of elim- 
ination, that great logical instrument which he had the immense merit 
of first bringing into general use, he deemed applicable in the same 
sense and in as unqualified a manner,, to the investigation of the coex- 
istences, as to that of the successions of phenomena. He seems to 
have thought that as every event has.ii cause, or invariable antecedent, 
so every property of an object has an invariable coexistent, which he 
called its Form : and the examples he chiefly selected for the applica- 
tion and illustration of his method, were inquiries into such Forms; 
attempts to determine in what else all those, objects resembled, which 
agreed in some one general property, as hardness or softness, dryness 
or moistness, heat or coldness. Such inquiries could lead to no result. 
The objects seldom have any such circumstance in common. They 
usually agree in the one point inquired into, and in nothing else. A 
great proportion of the properties which, so far as we can conjecture, 
are the likeliest to be really ultimate, would seem to be inherently 
properties of many different Kinds of things, not allied in any other 
respect. And as for the properties which, being effects of causes, we 
are able to give some account of, they have generally nothing to do 
with the ultimate resemblances or diversities in the objects themselves, ' 
but depend upon some outward circumstances, under the influence of 
which any objects whatever are capable of manifesting those proper- 
ties : as is emphatically the case with those favorite subjects of Bacon's 
scientific inquiries, hotness and coldness ; as well as with hardness 
and softness, solidity and fluidity, and many other very conspicuous 
qualities. 

In the absence, then, of any universal law of coexistence, similar 
to the universal law of causation which regulates sequence, we are 
thrown back upon the unscientific induction of the ancients, jper enu- 
merationem 'simplice?n, ubi non reperitui' instantia contradictoria. The 
reason we have for believing that all crows are black, is simply that we 
have se^n and heard of many black crows, and never of one of any 
other color. It reraains to be considered how far this evidence can 
reach, and how we are to measure its strength in any givQJi case. 

§ 5. It sometimes happens that a mere change in the mode of ver- 
bally enunciating a question, although nothing is really added to the . 
meaning expressed, is of itself a considerable step towards its solution. 
This, I think, happens in the present instance. The degree of cer- 
tainty of any generalization which rests upon no other evidence than 
the agi-eement, so far as it goes, of all past observation, is but another 
phrase for the degree of improbability that an exception, if it existed, 
could have hitherto remained unobserved. The reason for believing 
that all crows are black, is measured by the improbability that crows 
of any other color should have existed to the present time without our 
being aware of it. Let us state the question in this last mode, and 
consider what is" implied in the supposition that there may be crows 



348 INDUCTION. .- ,. • • • 

which are not black, and under what conditions we can be justified in 
regarding this as incredible. 

If there really exist crows which are not black, one of two things 
must be the fact. Either the circumstance of blackness, in all crows 
hitherto observed, must be, as it were, an accident, not connected with 
any distinction of Kind ; or if it be a property of Kind, the crows 
which are not black must be a new Kind, a Kind hitherto overlooked, 
though coming under the same general description by, which crows 
have hitherto been characterized. The first supposition would be, 
proved true if we were to discover casually a white crow among black 
ones, or if it were found that black crows sometimes turn white. The 
second would be shown to be the fact if in Australia or Central Africa 
a species or a race of white or gray crows- were found to prevail. 

§ 6. The former of these suppositions necessarily implies, that the 
color is an effect of causation. If blackness, in the crows in which it 
has been observed, be not a property of Kind, but can be present or ab- 
sent without any difference, generally, in the properties of the object ; 
then it is not an ultimate fact in the individuals themselves, but is cer- 
tainly dependent upon a cause. There are, no doubt, many properties 
which vary from individual to individual of the same Kind, even the 
s.ame infima species, or lowest Kind. A flower may be either white 
ox red, without differing in any other respect. But these properties 
are not ultimate ; they depend on causes. So far as the properties of 
a ^ing belong to its own nature, and do not arise from some cause 
extrinsic to it, they are always the same in the same Kind.* Take, 
for instance, all simple substances and elementary powers ; the only 
things of which, we are certain tliat some at least of the properties are 
really ultimate. Color is generally esteemed the most variable of all 
properties: yet we do not find that sulphur is sometimes yellow and 
sometimes white, or that it varies in color at all, except so far as color 
is the effect of some extrinsic cause, as of the sort of light thrown upon 
it, the mechanical arrangement of the particles, &c. (as after fusion). 
W-e do not find that iron is sometimes fluid and sometimes solid at the 
same temperature ; gold sometimes malleable and sometimes brittle ; 
that hydrogen will sometimes combine with oxygen and sometimes 
not ; or the like. If from simple substances we pass to any of their 
definite compounds, as water, lime, or sulphuric acid, there is the same 
constancy in their properties. When properties vary from individual 
to individual, it is either in the case of miscellaneous aggregations, 
such as atmospheric air or rock, composed of heterogeneous substances, 
and not constituting or belonging to any real Kind, or it is in the case 
of organic beings. In them, indeed, there is variability in a high 
degree. Animals of the same species and race, human beings of the 
same age, sex, and country, will be most different, for example, in face 
and figure. But Organized beings (from the extreme complication of 
the laws by which they are regulated) being more eminently modifi- 
able, that is, liable to be influenced by a greater number and variety 
of causes, than any other phenomena whatever; having, moreover, 
themselves had a beginning, and therefore a cause ; there is reason to 

* I do not here include among properties the accidents of quantity and local position. 
Every one is aware that no distinctions of Kind can be grounded upon these ; and that they 
are incident equally to things of diflerent Kinds and to things of the sam,e. 



COEXISTENCES INDEPENDENT OF CAUSATION. 349 

believe that none of their properties are ultimate, but all of thera deriv- 
ative, and produced by causation. And the presumption is confirmed 
by the fact that the properties which vary from one individual to 
another, also generally vary more or less at different times in the same 
individual ; vi^hich variation, like any other event, supposes a cause, 
and implies, consequently, that the properties are not independent of 
causation. 

If, therefore, blackness be merely accidental in crows, and capable 
of varying while the Kind remains the same, its presence or absence 
is doubtless no ultimate fact, but the effect of some unknown cause; 
and in that case the universality of the experience that all crows are 
black is sufficient proof of a common cause, and establishes the gener- 
alization as an empirical law. Since there are innumerable instances 
in the affirmative, and hitherto none at all in the negative, the causes 
on which the property depends must exist everywhere in the limits of 
the observations which have been made ; and the proposition may be 
received as universal within those limits, and with the allowable degree 
of extension to adjacent cases. 

§ 7. If, in the second place, the property, in the instances in which 
it has been observed, is not an effect of causation, it is a property of 
Kind ; and in that case the generalization can only be set aside by the 
discovery of a new Kind of crow. That, however, a peculiar Kind, 
not hitherto discovered, should exist in nature, is a supposition so often 
realized, that it cannot be considered at all improbable. We have 
nothing to authorize us in attempting to limit the Kinds of things which 
exist in nature. The only unlikelihood would be that a new Kind 
should be discovered in localities which there was previously reason to 
believe had been thoroughly explored ; and even this improbability 
depends upon the degree of conspicuousness of the difference between 
the newly discovered Kind and all others, since new Kinds of minerals, 
plants, and even animals, previously overlooked or confounded with 
known species, are still continually detected in the niost frequented 
situations. On this second ground, therefore, as well as on the first, 
the observed uniformity of coexistence can only hold good as an empir- 
ical law, within the limits not only of actual observation, but of an 
observation as accurate as the nature of the case required. And hence 
it is that (as remarked in an early chapter of the present Book) we so 
often give up generalizations of this class at the first summons. If any 
credible witness stated that he had seen a white crow, under circum- 
stances which made it not incredible that it should have escaped notice 
previously, we should give full credence to the statement. 

It appears, then, that the uniformities which obtain in the coex- 
istence of phenomena — those which we have reason to consider as 
ultimate, no less than those which arise from the laws of causes yet 
undetected — are entitled to reception only as empirical laws ; are not 
to be presumed true except in the limits of time, place, and circum- 
stance, in which the observations were made, or except in cases strictly 
adjacent. 

§ 8. We have seen in the last chapter that there is a point of gener- 
ality at which empirical laws become as certain as laws of nature, or 
~ rather, at which there is no longer any distinction between empirical 



350 INDUCTION. 

laws and laws of nature. As empirical Jaws approach this point, in 
other words, as they rise in their degree of generality, they become 
more certain ; their universality may be more strongly relied upon. 
For, in the first place, if they are results of causation (which, even 
in the class of uniformities treated of in the present chapter, we never 
can be certain that they are not) the more general they are, the greater 
is proved to be the space over which the necessary collocations pre- 
vail, and within which no causes exist capable of counteracting the, 
.unknown causes upon which the empirical law depends. To say that 
anything is an invariable property of some very limited class of objects, 
is to say that it invariably accompanies some very numerous and com- 
plex group of distinguishing properties; which, if causation be at all 
concerned in the matter, argues a combination of many causes, and 
therefore a very great hability to counteraction; while the compara- 
tively narrow range of the observations renders it impossible to pre- 
dict to what extent unknown counteracting causes may be distributed 
throughout nature. But when a. generalization has been found to hold 
good of a very large proportion of all things whatever, it is already 
proved that nearly all the causes which exist in nature have no power 
over it ; that very few changes in the combination of causes can affect 
it; since the greater number of possible combinations must have 
already existed in some one or other of the instances in which it has 
been found true. If, therefore, any empirical law is a result of causa- 
tion, the more general it is, the more it may be depended upon. And 
even if it be no result of causation, but an ultimate coexistence, the 
more general it is, the greater amount of experience it is derived from, 
and the greater therefore is the probability that if exceptions had 
existed, some would already have presented themselves. . 

■ For these reasons, it requires much more evidence to. establish an 
exception to one of the more general empirical laws than to the more 
special ones. We should not have any difficulty in believing that there 
might be a new Kind of crow ; or a kind of bird resembling a crow in 
the properties hitherto considered distinctive of that Kind. But it 
would require stronger proof to convince us of the existence of a kind 
of crow having properties at variance with any generally recognized 
universal property of birds; and a still higher degree if the properties- 
conflict with any recognized universal property of animals. And this 
is conformable to the mode of judgment recommended by the common 
sense and general practice of mankind, who are more incredulous as to 
any novelties in nature, according to the degree of generality of the 
experience which these novelties seem to contradict. 

§ 9: Still, however, even these greater generalizations, which em- 
brace comprehensive Kinds, containing under them a great number 
and variety of infimoi species, are only empirical l^ws, resting upon 
induction by simple enumeration merely, and not upon any process of 
elimination, a process wholly inapplicable to the kind of case. Such 
generalizations, therefore, ought tO be grounded upon an examination^ 
of all the infimai species comprehended in them, and not of a portion 
only. We cannot conclude, merely because a proposition is true of a 
number of things resembling one another only in being animals, that 
it is therefore true of. all animals. If, indeed, anything be true of 
species which differ more from one another than either differs frorri a 



APPROXIMATE GENERALIZATIONS. 351 

third, (especially if that third species occupies in most of its known 
properties a position between the two forn;ier,) there is some proba- 
bility that the same thing will also be true of that intermediate species; 
for it is often, though by no means universally, found, that there is a 
sort of parallelism in the properties of different kinds, and that their 
degree of unlikeness in one respect, bears some proportion to their 
unlikeness in others. We see this parallelism in the properties of the 
diiferent metals; in those of sulphur, phosphorus, and carbon; of 
oxygen, chlorine, iodine, and brome ; in the natural orders of plants 
and animals, &c. But there are innumerable anomalies and excep- 
tions to this sort of Conformity, or rather the conformity itself is but an 
anomaly and an exception in nature. , 

Universal propositions, therefore, respecting the properties of su- 
perior Kinds, unless "grounded on proved or presumed connexion by 
causation, ought not to be hazarded except after separately examining 
every known sub-kind included in the larger Kind. And even then 
such generalizations must be held in readiness to be given up on the 
occuiTonce of some new anomaly, which, when the uniformity is not 
derived from causation, can never, even in the case of the most general 
of these empirical laws, be considered very improbable. Thus all the 
universal propositions which it has been attempted to lay down 
respecting simple substances, or concerning any of the classes which 
have been formed among simple substances (and the attempt has been 
often made) have, with the progress of experience, either faded into 
inanity, or been proved to be erroneous ; and each Kind of simple 
substance remains with its own collection of properties apart from the 
rest, saving a certain parallelism with a few other Kinds, the most 
similar to itself In organized beings, indeed, there are abundance of 
propositions ascertained to be universally true of superior genera, to 
many of which the discovery hereafter of any exceptions must be 
regarded as supremely improbable. But these, as already observed, 
are, we have every reason to believe, truths dependent upon causation. 

Uniformities of coexistence, then, not only when they are conse- 
quences of laws of succession, but also when they are ultimate truths, 
must be ranked, for the purposes of logic, among empirical laws ; and 
are amenable in every respect to the same rules wdth those unresolved 
uniformities which are known to be dependent upon causation. 



CHAPTER XXIII. 

OP APPROXIMATE GENERALIZATIONS, AND PROBABLE EVIDENCE. 

§ 1. In our inquiries into the nature of the inductive process, we 
have hitherto confined our notice to such generalizations from experi- 
ence as profess to be universally true. We indeed recognized a 
distinction between generalizations which are certain and thxDse which 
are only probable : but the propositions themselves, though they 
differed in being more or less doubtful in the one case, and not at all 
doubtful in the other, were always of the form^ Every A i s B ; they 
claimed nothing less than universality, whatever might be the com- 



352 ' INDUCTION. 

pleteness or the incompleteness of our "Assurance of their truth. There 
remain, however, a class of propositions avowedly not universal; in 
which it is not pretended that the predicate is always true of the 
subject ; but the value of which, as generalizations, is nevertheless 
extremely great. An important portion of the field of inductive 
knowledge does not consist of universal truths, but of approximations 
to such truths; and when a conclusion is said to rest upon probable 
evidence, the prpmisses it is dravni from are usually generalizations of 
this sort. / > 

As every certain inference respecting a particular case, implies that 
there is ground for a general proposition, of the form, Every A is B; 
so does every probable inference suppose that there is ground for a 
proposition of the form. Most A are B : and the degree of probability 
of the inference in an average case, will depend upon the proportion 
between the number of instances existing in nature which accord with 
the generalization, and the number of those w^hich conflict with it. 

§ 2. Propositions in the form, Most A are B, are of a v6ry different 
degree of importance in science, and in the practice of life. To the 
scientific inquirer they are valuable chiefly as materials for, and steps 
towards, universal truths. The discovery of these is the proper end 
of science : its work is not done if it stops at the proposition that a 
majority of A are B, without circumscribing that majority by some 
common character, fitted to distinguish them from the minority. Inde- 
pendently of the inferior precision of such imperfect generalizations, 
and the inferior assurance with which they can be applied to individual 
cases, it is plain that, compared with exact generalizations, they are 
almost useless as means of discovering ulterior truths by way of 
deduction. We may, it is true, by combining the proposition. Most A 
are B, with an universal proposition, Every B is C, arrive at the con- 
clusion that most A are C. But when a second proposition of the 
approximate kind is introduced — or even when there is but one, if 
that one be the major premiss — nothing can be positively concluded. 
"When the major is Most B are D, then, even if the minor be Every A 
is B, we cannot infer that most A are D, or with any certainty that 
even some A are J). Though the majority of the class B have the 
attribute signified by D, the whole of the sub-^dass A may belong to 
the minority. 

Though so little use can be made, in science, of approximate gen- 
eralizations, except as a sta^e on the road to something better, for 
practical guidance they are often all we have to rely upon. Even 
when science has really determined the universal laws of any phe- 
nomenon, not only. are those laws generally too much encumbered 
with conditions to be adapted for every-day use, but the cases which 
present themselves in life are too complicated, and our decisions 
require to be taken too rapidly, to admit of waiting' till the existence 
of a phenomenon can be proved by what have been scientifically 
ascertained to be Universal marks of it. To be indecisive and 
reluctant to act, because we have not evidence of a perfectly con- 
clusive character to act upon, is a.defect sometimes incident to scientific 
minds, but which, wherever it exists, renders them unfit for practical 
emergencies. If we would succeed in action, we must judge by indi- 
cations which, although they do not generally mislead us, sometjimes 



APPROXIMATE GENERALIZATIONS. 353 

do; and must make up as far as possible for the incomplete conclusive- 
ness of any one indication, by obtaining others to corroborate it. The 
principles of induction applicable to approximate generalization are 
therefore a not less important subject of inquiry, than the rules for the 
investigation of universal truths ; and might reasonably be expected 
to detain us almost as long, were it not that these principles are mere 
corollaries from those which have been already treated of. 

§ 3. There are two sorts of cases in which we are forced to guide 
ourselves by generalizations of the imperfect form, Most A are B. 
The first is, when we have no others ; when we have not been able to 
carry our investigation of the laws of the phenomena any further; 
as in the following propositions: Most dark-eyed persons have dark 
hair ; Most springs contain mineral substances ; Most stratified forma- 
tions contain fossils. The importance of this class of generalizations is 
not very great ; for, though it frequently happens that we see no rea- 
son why that which is true of most individuals of a class is not true of 
the remainder, nor are able to bring the former under any general 
description which can distinguish them from the latter, yet if we are 
willing to be satisfied with propositions of a less degi'ee of generality, 
and to break down the class A into sub-classes, we may generally 
obtain a collection of propositions exactly true. We do not know why 
most wood is lighter than water, nor can we point out any general 
property which discriminates wood that is lighter than water from that 
which is heavier. But we know exactly what species are the one and 
what the other. And if we meet with a specimen not conformable to 
any known species (the only case in which our previous knowledge 
affords no other guidance than the approximate generalization), we 
can generally make a specific experiment, which is always a safer 
resource. 

It oftener happens, however, that the proposition, Most A are B, is 
not the ultimatum of our scientific progress, though the knowledge we 
possess beyond it cannot conveniently be brought to bear upon the 
particular instance. In such a case, we know well enough what cir- 
cumstances really distinguish the portion of A which have the attribute 
B from the portion which have it not, but have no means, or no time, 
to examine whether those characteristic circumstances exist or not in 
the individual case. This is generally the. situation we are in when 
the inquiry is of the kind called moral, that is, of the kind which have 
in view to predict human actions. To enable us to affirm anything 
universally concerning the actions of classes of men, the classification 
must be grounded upon the circumstances of their mental cultm'e and 
habits, which in an individual case are seldom exactly known; and 
classes grounded on these distinctions would never precisely accord 
with those into which mankind are necessarily divided for social 
purposes. All propositions which can be framed respecting the actions 
of men as ordinarily classified, or as classified according to any kind of 
outward indications, are merely approximate. We can only say. Most 
men of a particular age, profession, country, or rank in society, have 
such and such qualities, or. Most persons when placed in certain cir- 
cumstances act in such and such a way. Not that we do not in general 
know well enough upon what causes the qualities depend, or what sort 
of persons they are who act in that particular way ; but we have sel- 
Yy 



354 - INDUCTION. 

dom the means of knowing whether any individual person has been 
under the influence of those causes, or is a person of that particular 
sort. We could replace the approximate generalizations by proposi- 
tions universally true; but these would hardly ever be capable of 
being applied to practice. We should be -sure of our majors, but we 
should not be able to ' get minors corresponding to them : we are 
forced therefore, to draw our conclusions from, coarser and more fallible 
indications. 

§ 4. Proceeding now to consider, what is to be regarded as suf- 
ficient evidence of an approximate generalization ; we can have no 
difficulty in at once recognizing that when admissible at all, it is ad- 
missible only as an empirical law. Propositions of the form, Every 
A is B, are not necessarily laws of causation, or ultimate uniformities 
of coexistence ; propositions like Most A are ^, cannot be so. Propo- 
sitions hitherto found true in every observed instance, may yet be no 
necessary consequence of laws of causation or' of ultimate uniformities, 
and unless they are so, may, for aught we know, "be false beyond the 
limits of actual observation ; still more evidently must this be the case 
with propositions which are only true in a mere majority of the ob- 
served instances. 

There is some difference, however, in the degree of certainty of the 
proposition, Most A are B, according as that approximate generaliza- 
tion composes the whole of our knowledge of the subject, or not. 
Suppose, first, that the former is the case. We know only that most 
A are B, not why they are. so, nor in v?^hat respect those which .are, 
differ from those which are not. How then did we learn 'that most A 
arp B % Precisely in the manner in which we should have learnt, had 
such happened to be the factj that allA are B. We collected a num-, 
berof instances sufficient to eliminate chance, and having done* so, 
compared the number of instances in the affirmative with the number in 
the negative. The result, like other unresolved derivative laws, can be 
relied on solely within the limits not only of place and time, but also of 
circumstance, under which its truth has been actually observed; fdr 
as we are supposed to be ignorant of the causes which make the 
proposition true, we cannot tell in what manner any new circumstance 
might perhaps affect it.' The proposition, Most judges are inaccessi- 
ble to bribes, would be fbund true of Englishmen, Frenchmen, Ger- 
mans, North Americans, and so forth ; but if on this evidence alone we 
extended the assertion to Orientals, we' should step beyond the limits, 
not only of place but of circumstance, within which the fact had beeti 
observed, and should let in possibilities of the absence of the deter- 
mining caurses, or the presence of counteracting ones^ which might be 
fatal to the approximate generalization. - 

In the case where the approximate proposition is not the ultimatum 
of our scientific knowledge, but only the" most available form of it for 
our practical guidance ; where we know not only that most A have the 
attribute 3,d3ut also the caiis'es of B, or some properties by which the 
portion of A which has that attribute is distinguished from the portion 
which has it not; we are rather more favorably situated' than in the 
preceding case. For we have ♦now. a double mode of ascertaining 
whether it be true that most A are B ; the direct mode, as before, 
and an indirect one, that of examining whether the proposition admits 



APPROXIMATE GENERALIZATIONS. 855 

of being deduced frorji the known cause, or from the known criterion, 
of fi. Let the question, for example, be. Whether most Scotchmen 
can read *? We may not have observed, or received the testimony of 
others respecting, a sufficient number and variety of Scotchmen to 
ascertain this fact ; but when we consider that the cause of being able 
to read is the having been taught it, another mode of determining the 
question presents itself, namely, by inquiring whether most Scotchmen 
have been sent to schools where reading is effectually taught. Of 
these two modes, sometimes one and sometimes the other is the more 
available. In some cases, the frequency of the effect is the more ac- 
cessible to that extensive and varied observation which is indispensable 
to the establishment of an empirical law; at other times, the frequency 
of the causes, or of some collateral indications. It commonly happens 
that neither is susceptible of so satisfactory an induction as could be 
desired, and that the grounds on which the conclusion is received are 
compounded of both. Thus a man may believe that most Scotchmen 
can read, because, so. far as his information extends, most Scotch- 
men have been sent to school, and most Scotch schools teach reading 
effectually; and also because most of the Scotchmen whom he has 
known or heard of, could read ; though neither' of these two sets of 
observations may by itself fulfill the necessary conditiotis of extent ai:^d 
variety. <■ 

Although the approximate generahzation may in .most cases be 
indispensable fo-r our guidance, even when we know the cause, or 
sofne certaiii .mark, of the attribute predicated ; it needs hardly be 
observed that we may always replace the uncertain indication by a 
certg^in one,, in any case in which we can actually recognize the ex- 
istence of the cause or mark. For example, an assertion is made 
by a witness, and the question is, whether to believe it. If we do not 
look to any of the individual circumstances of the case, we have 
nothing to direct us but the approximate generalization, that truth 
is more common than falsehood, . or, in other words, that most per- 
sons, on most occasi^ons, speak truth. But if we consider in what 
circumstances the , cases when truth is spoken differ from those in 
which it is not, we find, for instance, the following ; the witness's being 
an honest man or not; his being an accurate observer or not; his 
having an interest to serve in the matter or, not. JSTow, not only may 
we be able to obtain other approximate generalizations respecting the 
degree, of frequency of these various possibilities, but we may know 
whiqh of them is positively realized in the individual case.- That the 
witness has or has not an interest to serve, we may know directly ; 
and the other two points indirectly, by means of marks ; as, for ex- 
ample, from his conduct on some former occasion ; or fr'om hife rep- 
utation, which, though not a sure mark, affords- an approximate 
generalization (as, for instance, Most persons who are reputed honest 
by those with whom they have had frequent dealings, are really so,) 
which approaches nearer to an universal truth than the approximate 
general proposition with which' we 'set out, viz., Most persons on most 
occasions speak truth. 

As it seems unnecessary to .dwell any further upon the question of 
the evidence of approximate generalizations, we shall proceed to a not 
less important topic, that of the cautions to be observed in arguing 
from these incompletely universal propositions to particular cases 



356 INDUCTION. 

§ 5 So far as regards the direct application of an approximate 
genei alization to an individual instance, this question presents no diffi- 
culty. If the proposition, Most A are B, has been established, by a 
sufficient induction, as an empirical law, we may conclude that any 
particular A is B, with a probability proportioned to the preponder- 
ance of the number of affirmative instances over the number of excep- 
tions. If it has been found practicable to attain numerical precision 
in the data, a corresponding degree of precision may be given to the 
evaluation of the chances of error in the conclusion. If it can be 
established as an empirical law that nine out of every ten A are B, 
there will be one chance, in ten of error in assuming that any A, not 
individually known to us, is a B : but this of course holds only within 
the limits of time, place, and circumstance, embraced in the observa- 
tions, and therefore cannot be counted upon for any sub-class or variety 
of A (or for A in any set of external circumstances) which were not 
included in the average. It must be added, that we can only guide 
ourselves by the proposition. Nine out of every ten A are B, in cases 
of which we know nothing except that they fall within the class A. 
For if we know, of any particular instance i, not only that it falls 
under A, but to what species or variety of A it belongs, we shall 
generally err in applying to i the average struck for the whole genus, 
from which the average corresponding to that species alone would, in 
all probability, materially differ. And so if i, instead of being a par- 
ticular sort of instance, is an instance known to be under the influence 
of a particular set of circumstances. The presumption drawTi from 
the numerical proportions in the M^hole genus would prcbably, in such 
a case, only mislead. A general average should only be applied to a 
case which is neither known; nor can be presumed, to be other than an 
average case. Such averages, therefore, are commonly of little use 
for the practical guidance of any affairs but those which concera large 
numbers. Tables of the chances of hfe are useful to insurance offices, 
but they go a very little way towards informing any one of the chances 
of his own life, or any other life in which he is interested, since almost 
every life is either better or worse than the average. Such averages 
can only be considered as supplying the first term in a series of ap- 
proximations ; the subsequent terms proceeding upon an appreciation 
of the circumstances belonging to the particular case. 

§ 6. From the application of a single approximate generalization to 
individual cases, we proceed to the application of two or more of them 
together to the same case. 

When a judgment applied to an individual instance is gi'ounded 
upon two approximate generalizations taken in conjunction, the prop- 
ositions may cooperate towards the result in two different ways. In 
the one, each proposition is separately applicable to the case in hand, 
and our object in combining them is to give to the conclusion in that 
particular case the double probability arising from the two propositions 
separately. This may be called joining two probabilities by way of 
Addition ; and the result is a probability greater than either. The 
other mode is, when only one of the propositions is directly applicable 
to the case, the second being only applicable to it by virtue of the 
application of the first. This is joining two probabilities by way of 
Deduction ; the result of which is a less probability than either. The 



APPROXIMATE GENERALIZATIONS. 357 

type of the first argument is, Most A are B ; most C are B ; this 
thing is both an A and a C ; therefore it is probably a B. The type 
of the second, is, Most A are B ; most C are A ; this is a C ; therefore 
it is probably an A, therefore it is probably a B. The first is exem- 
plified when we prove a fact by the testimony of two unconnected 
witnesses ; the second, when we adduce only the testimony of one 
witness that he has heard the thing asserted by another. Or again, in 
the first mode it may be argued that the accused committed the crime, 
because he concealed himself, and because his clothes were stained 
with blood ; in the second, that he committed it because he washed or 
burnt his clothes, which is supposed to render it probable that they 
were stained with blood. Instead only of two links, as in these 
instances, we may suppose chains of any length. A chain of the 
former kind was termed by Mr. Bentham* a self-corroborative chain 
of evidence ; the second, a self-infirmative chain. 

When approximate generalizations are joined by way of addition, it 
is easily seen from the theory of probabilities laid down in a former 
chapter, in what manner each of them adds to the probability of a con- 
clusion which has the warrant of them all. If two of every three A are B, 
and three of every four C are B, the probability that something which 
is both an A and a C is a B, will be more than two in three, or than 
three in four. Of every twelve things which are A, all except four 
are B, by the supposition ; and if the whole twelve, and consequently 
those four, have the characters of C likewise, three more will be B on 
that ground. Therefore, out of twelve which are both A and C, eleven 
are B, To state the argument in another way ; a thing which is both 
A and C, but which is not B, is found in only one of three sections 
of the class A, and in only one of four sections of the class C ; but this 
fourth of C being spread over the whole of A indiscriminately, only 
one-third part of it (or one-twelfth of the whole number) belongs to the 
third section of A ; therefore a thing which is not B occurs only once, 
among twelve things which are both A and C. The argument would, 
in the language of the doctrine of chances, be thus expressed : — the 
chance that an A is not B is i, the chance that a C is not B is i, hence 
if the thing be both an A and a C the chance is |- of i = j\. 

This- argument presupposes (as the reader will doubtless have re- 
marked) that the probabilities arising from A and C are independent 
of one another. There must not be any such connexion between A 
and C, that when a thing belongs to the one class it will therefore 
belong to the other, or even have a greater chance of doing so. Else 
the fourth section of C, instead of being equally distributed over the 
three sections of A, might be comprised in greater proportion, or even 
wholly, in the third section ; in which last case the probability arising 
from A and C together would be no greater than that arising from A 
alone. 

When approximate generalizations are joined together in the other 
mode, that of deduction, the degree of probability of the inference, in- 
stead of increasing, diminishes at each step. From two such prem- 
isses as Most A are B, Most B are C, we cannot with certainty conclude 
that even a single A is C ; for the whole of the portion of A which in 
any way falls under B, may, perhaps, be comprised in the exceptional 

* Rationale of Judicial Evidence. Book v. Circumstantial, 



358 INDUCTION. 

part of it. Still, tlie two propositions in question afford an appreciable 
probability that any given A is C, provided the average, on v^hicli the 
second 2:)roposition is grounded, was taken fairly with reference to the 
first ; provided the proposition Most B are C was an-ived at in a man- 
ner leaving no suspicion that the probability arising from it is other- 
wise than fairly distributed over the section of B which belongs to A. 
For although tlie instances which are A tnay be all in the minority, 
they may, also, be all in the majority ; and the one possibility is to be 
set against the other. On liie whole, the prpbability arising from the 
two propositions taken together will be correctly measured by the 
probability arising from the one, abated in the ratio of that arising 
from the 'other. If nine out of ten Swedes have light hair, and eight 
out of nine inhabitants of Stockholm are Swedes, >the probability 
arising from these two propositions, that any given inhabitant of Stock- 
holm is lio-ht-haired, will amount to eis^ht in ten ; althouo;h"it is rig^or- 
ously possible (however improbable) that the whole Swedish p'opula- 
lation of Stockholm may belong to that tenth section of the people of 
Sweden who are an exception to the rest. 

If the premisses are known to be tfue not of a bare majority, but of 
nearly the whole, of their respective subjects, we may go on joining 
one such proposition to another for several steps, before we reach a 
conclusion not presumably true dven of 'a majority. The error of the 
conclusion will amount to the aggregate of the errors of all the prem- 
isses. Let the proposition, Most A are B, be true of nine in ten ; Most 
B are C, of eight in nine : then not only will one A in ten not be C, 
because not B, but even of the nine-tenths which are B, only eigbt- 
ninths wiH be C : that is, the cases of A which "^re C will be only 
I of y^jf, or four-fifths. Let uf? now add Most C are,-D, and suppose 
this to be true of seven, cases, out of eight ; the proportion of A which 
is D will be only |- of | of —-, or y\. Thus the probability progressively 
dwindles. The experience, however, on which our approximate gen- 
eralizations are grounded, has so rarely been subjected to, or admits of, 
accurate numerical estimation, that we cannot in general apply any 
measurement to' the diminution of probability which takes place at 
each illation;- but must be content with rememberings that i4: does 
diminish at every^ step, and that unless the premisses approach very 
nearly indeed to being universal truths, the fconclusion after a very few 
steps is worth nothing. A hearsay of a hearsay, or an argument from 
presumptive evidence depending not upon immediate marks but upon 
marks of marks, is worthless at a very few removes from the first stage. 

§ 7. There-are, however, two cases in w^hich reasonings depending 
upon approximate generalizations maybe carried to any length wo 
please with as much assurance, and are as strictly scientific, as if they 
were composed of universal laws of nature. Both these cases are ex- 
ceptions of the sort which are currently said to prove the rule. The 
approximate generalizations are as suitable, in the cases in question, 
for purposes of ratiocination, as if they were complete generalizations, 
because they are capable bf being transformed into complete general- 
izations exactly equivalent. 

First : If the approximate generalization i« of the class in which our 
reason for stppping at the approximation is not the impossibility, but 
only the inconvenience, of going further ; if we ai'e cognizant of the 



APPROXIMATE GENERALIZATIONS. - 359 

character which distinguishes the cases that, accord with the generali- 
zation from those which are exceptions to it ; we may then substitute, 
for the approximate proposition,. an' universal proposition with a pro- 
viso. The proposition, Most persons who have- uncontrolled power 
employ it ill, is a generalization of this clafes, and may be transformed 
into the following : — All persons vvho have uncontrolled power employ 
it ill, provided they are not persons of unusual strength of judgment 
and will, and confirmed ]i.abits of virtue. The proposition, carrying 
the hypothesis or proviso with it, may then be dealt with no longer as 
an approximate, but as an universal proposition; and to whatever 
number of steps the reasoning may reach, the hypothesis, being carried 
forward to the conclusion, will exactly indicate how far that conclusion 
is from being applicable, universally. If in the course of the argument 
other approximate generalizations are introduced, each of them being 
in like manner expressed as an universal proposition vs^'ith a condition 
annexed, the sum of all the conditions will appear at the end as the 
sum_of all the errors which affect the conclusion. Thus, to the propo- 
sition last cited, let us add the following: — All absolute monarchs have 
uncontrolled power, unless their position is . such that they need the 
active support of their subjects (as was the case with Queen Elizabeth, 
.Frederick of Prussia, and others). Combining these two propositions 
we can deduce from them an universal conclusion, which will be sub- 
ject to- both the hypotheses -in the premisses : All absolute monarchs 
employ their power ill, unless their position makes them need the 
active support of their subjects, or unless they are persons, of unusual 
strength of judgment and will, , and confirmed habits of virtue. It is of 
no consequence ho\^ rapidly the errors in our premisses, accumulate, 
if we are able in this manner to record,each errol-, and keep an account 
of the aggregate as it swells up. 

Secondly: there is a case in which approximate propositions, even 
without our taking, note of the conditions under which they are not 
true of individual cases, are yet, for the purposes of science, universal 
ones ; namely, in the scientific inquiries which relate to the properties 
not of individuals, but of multitudes. The principal of these is the 
science of politics, ox, of.hmiig,n society. This science is principally 
concerned \vith the actions not of solitary individuals, but of masses ; 
with the fortunes not of single pdi'sons, but of communities. For the 
statesman, therefore, it is generally enough to know that 7nost persons 
act or are acted upon in a particular way; since his speculations and 
his practicail arrangements refer almost exclusively to cases in which 
the whole community, or some large portion of it, is acted upon' at 
once, and in which, therefore, what is done or felt by 7nost persons 
determines the result produced by or upon the body at large. He can 
get on well enough with approximate generalizations on human nature, 
since what is true approximately of all individuals is true absolutely of 
all masses.' And even when the operations of individual men have a 
part to play in his deductions, as when he is reasoning of kings, or 
'other single rulers, still as he is providing for indefinite duration, in- 
volving an indefinite succession of such individuals, he must in general 
"both reason and act as if w4iat is true of most persons were true of all. 

The two kinds of considerations above adduced are a sufficient 
refutation of the popular error, that speculations on society and govern- 
ment; as resting upon merely probable evidence, must be inferior in 



i360 INDUCTION. 

certainty and scientific accuracy ta the conclusions of what are called 
the exact sciences, and less to be relied upon in practice. There are 
reasons enough why the moral sciences must remain inferior to at leasl 
the more perfect of the physical; why the laws^of their more compli- 
cated phenomena cannot be so completely deciphered, nor the phe- 
nomena predicted with the same degree of assurance. But though we 
cannot attain to so many truths, there is no reason that those we can 
attain should deserve less reliance, or have less of a scientific character. 
Of this topic, however, we shall treat more systematically in the con- 
cluding Book, to which place any further consideration of it must be 
deferred. 



CHAPT:eR XXIV. 

OF THE REMAINING LAWS OF NATURE. 

§ 1. In the First Book we found that all the assertions which can be 
conveyed by language, express some one or more of five different 
things: Existence; Order in Place; Order in Time; Causation; and 
Resemblance.* Of these, Causation, in our view of the subject, not 
being fundamentally different from Order in Time, the five species of 
possible assertions are reduced to four. The propositions which affirm 
Order in Time, in either of its two modes. Coexistence and Succession^ 
have formed, thus far, the subject of the present Book. And we have 
now concluded the exposition, so far as it falls within the limits 
assigned to this work, of the nature of the evidence on which these 
propositions rest, and the processes of investigation by which they are 
discovered and proved., There remain three classes of facts: Exist- 
ence, Oi'der in Place, and Resemblance ; in regard to which the same 
questions are now to be resolved. 

Regarding the first of these, very little needs be said. Existence in 
genera], is a subject not for our science, but for the higher metaphysics. 
To determine what things can be recognized as really existing, inde- 
pendently of our own sensible or other impressions, and in what mean- 
ing the term is, in that case, predicated of them, belongs to the con- 
sideration of " Things in themselves," from which, throughout this 
work, we have as much as possible kept aloof. Existence, so far as 
Logic is concerned about it, has reference only to phenomena ; to actual, 
or possible, states of external or internal consciousness, in ourselves or 
others. Feelings of sensitive beings, or possibilities of having such 
feelings, are the only things the existence of which can be a subject of 
logical induction, because the only things of which the existence in 
individual cases can be a subject of experience. 

It is true that a thing is said by us to exist, even when it is absent, 
and therefore is not and cannot be perceived. But even then, its exist- 
ence is to us only another word for our conviction that we should iper- 
ceive it on a certain supposition ; if we were placed in the needful 

* Supra, 70. 



REMAINING LAWS OF NATURE. 3G1 

circumstances of time and place, and endowed with the needful perfec- 
tion of organs. My belief that the Emperor of China exists, is simply 
my belief that if I were transported to the imperial palace, or some 
other locality in Pekin, I should see him. My belief that Julius Cae- 
sar existed, is my belief that I should have seen him if I had been pres- 
ent in the iield of Pharsalia, or in the senate-house at Rome. When 
I believe that stars exist beyond the utmost range of my vision, though 
assisted by the most powerful telescopes yet invented, my belief, philo- 
sophically expressed, is, that with still better telescopes, if such existed, 
I could see them, or that they may be perceived by beings less remote 
from them in space, or whose capacities of perception are superior to 
mine. 

The existence, therefore, of a phenomenon, is but another word for 
its being perceived, or for the infeiTed possibility of perceiving it. 
When the phenomenon is within the range of present obseiTation, by 
present observation we assure ourselves of its existence ; when it is 
beyond that range, and is, therefore, said to be absent, we infer its 
existence from marks or evidences. But what can these evidences be 1 
Other phenomena ; ascertained by induction to be connected with the 
given phenomenon, either in the way- of succession or of coexistence. 
The simple existence, therefore, of an individual phenomenon, when 
not directly perceived, is inferred from some inductive law of succes- 
sion or coexistence : and is consequently not amenable to any peculiar 
inductive principles. We prove the existence of a thing, by proving that 
it is connected by succession or coexistence with some known thing. 

With respect to general propositions of this class, that is, which affirm 
the bare fact of existence, they have a peculiai'ity which renders the 
logical treatment of them a very easy matter ; they are generalizations 
which are sufficiently proved by a single instance. That ghosts, or 
unicorns, or sea-serpents exist, would be fully established if it could 
be ascertained positively that such things had been even once seen. 
Whatever has once happened, is capable of happening again ; the only 
question relates to the conditions under which it happens. 

So far, therefore, as relates to simple existence, the Inductive Logic 
has no knots to untie. And we may proceed to the remaining two of 
the great classes into which facts have been divided ; Resemblance, and 
Order in Space. 

§ 2. Resemblance and its opposite, except in the case in which they 
assume the names of Equality and Inequality, are seldom regarded as 
objects of science ; they are supposed to be perceived by simple appre- 
hension ; by merely applying our senses or directing our attention to 
the two objects at once, or in immediate succession. And this simul- 
taneous or virtually simultaneous application of our faculties to the two 
things which are to be compared, does necessarily constitute the ulti- 
mate appeal, wherever such application is practicable. But in most 
cases, it is not practicable : the objects cannot be brought so closely 
together that the feeling of their resemblance (at least a complete feel- 
ing of it) directly arises in the mind. We can only compare each of them 
with some third object capable of being transported from one to the other. 
And besides, even when the objects can be brought into immediate 
juxtaposition, their resemblance or difference is but imperfectly known 
to us unless we have compared them minutely, part by part. Until 
Zz 



362 INDUCTION. 

this has been done, things in reaUty very dissimilar often appear undis- 
guishably ahke. Two lines of very unequal length will appear about 
equal when lying in different directions ; but place them parallel, with 
their further extremities even, and if you look at the nearer extremities, 
their inequality becomes a matter of direct perception. 

•To ascertain whether, and in what, two phenomena resemble or dif- 
fer, is not always, therefore, so easy a thing as it might at first appear. 
When the two cannot be brought into juxtaposition, or not so that the 
observer as able to compare their several parts in detail, he must em- 
ploy the indirect means of reasoning and general propositions. When 
we cannot bring two straight lines together, to determine whether they 
are equal, we do it by the physical aid of a foot rule applied first to 
one and then to the other, and the logical aid of the general proposition 
or formula, " Things which are equal to the same thing are equal to 
one another." The comparison of two things through the intervention 
of a third thing, when their direct comparison is impossible, is the ap- 
propriate scientific process for ascertaining resemblances and dissimi- 
la,rities, and is the sum total of what Logic has to teach on the subject. 

An undue extension of these views induced Locke to consider 
reasoning itself as nothing but the comparison of two ideas through 
the medium of a third, and knowledge as the perception of the agree- 
ment or disagreement of two ideas : <ioctrines which the Condillac 
school blindy adopted, without the qualifications and distinctions with 
which they were, studiously guarded by their illustrious author. 
Where, indeed, the agreement or disagreement (otherwise called re- 
semblance or dissimilarity) of any two things is the very matter to be 
determined, as'is the case particularly in the s(5iences of quantity and 
extension, there the process by wh\,ch a solution, if not attainable by 
direct perception, must be indirectly sought, consists in comparing 
these two things through the medium of a third. But this is far from 
being true of all inquiries. The knowledge that bodies fall to the 
ground is not a perception of agreement or disagreement, but of a 
series of physical occurrences, a succession of sensations. Locke's defi- 
nitions of knowledge and of reasoning required to be limited to our 
knowledge of; and reasoning about. Resemblances. Nor, even wheii 
thus restricted, are the propositions strictly correct ; since the com- 
parison is not made, as he representee, between the ideas of tlie two 
phenomena, but between the phenomena themselves. This mistake 
has been pointed out in an earlier paH of our inquiry,* and we traced 
if to an 'imperfect • conception of what takes place in mathematics, 
where very often the comparison is really made between the ideas, 
withoht any appeabto the outward -senses ; only, however, because in 
miathematics a comparison of the ideas is strictly equivalent to a com- 
parison of the phenomena themselves. Where, as in the case of num- 
bers, lines, and figures, our idea of -an object is a complete picture of 
the object, so far as respects the matter in' hand ; we can of course 
learn from the picture, whatever could be liearnt from the object itself 
by mere contemplation of it as' it" exists at the particular instant when 
the picture is taken. No tnere contemplation of gunpowder would 
ever teach us that a spark vi^ould make it explode, nor, consequently, 
would the contemplation of the idea of gunpowder do so : but the mere 

* Supra, pp. 59, 154. 



REMAINING LAWS OF NATURE. 863 

contemplation of a straight line shows that it cannot inclose a space; 
accordingly the contemplation of the idea of it will show the same. 
What takes place in mathematics is thus no argument that the com- 
parison is between the ideas only. It is always, either indirectly or 
directly, a comparison of the phenomena. ^ 

In cases in which we x^annot brin^ the pheilomeng, to the test of direct 
inspection at all, or npt in a matter sufficiently precise, but must judge 
of their resemblance by inference from other resemblances or dissim- 
ilarities more accessible to observation, we of course require, as in all 
cases of ratiocination, generalizations or formulfe applicabl-e to the 
subject. We must reason fi'om laws of nature ; from the uniformities 
which are observable in the fact of likeness or unlikeness. 

§ 3. Of these laws or uniformities, the most comprehensive are 
tljose supplied by mathematics ; the axioms relating to equality, ine- 
quality, and proportionality, and the various theorems thereon founded. 
And these are the only Laws of Resemblance which require to be, or 
which can be, treated apart. It is true there are ifmumerable other 
theorems which affirm resemblances among phenomena ; as that the 
angle of the reflexion of light is equal to it sangle of incidence (equality 
being merely, exact resemblance' in magnitude). Again, that the 
heavenly bodies describe equal areas in equal times ; and that their 
periods of revolution ^ve proportional (another species af resemblance) 
to tli,e sesq\iiplicate powers of their distances from the centre of force. 
These and similar propositions affirm resemblances, of the same nature 
with those asserted in the theorems of mathematics : but the distinction 
is, that the propositions of mathematics are true of all phenomena 
whatever, or at least without distinction of origin ; while the truths in 
question are affirmed oidy of special phenomena, which originate in a 
certain way ; and the equalities, proportionalities, pr other resemblances, 
which exist between such phenomena, must necessarily be either de- 
rived from, or identical with, the law of their origin— the law of caus- 
ation on which they depend. The equality of the areas described by 
the planets, is derived from the laws of the causes ; and, until its deri- 
vation was shown, it was an empirical law. ' The equality of the angles 
of reflexion and incidence \& identical with the law of the cause ; for 
the cause is the incidence of a ray of light upon a reflecting surface, 
and the equality in question is the very law according to which that 
cause produces its effects. This class, therefore, of the uniformities 
of resemblance ^between phenomena, is inseparable, in fact and in 
thought, from the laws of the production of those phenomena ; and the 
principles of induction applicable to them are no other than those 
of which we have treated in the preceding chapters of this Book. 

It is otherwise with the truths of mathematics. The laws of equality 
and inequality between spaces, or between numbers, have no connexion 
with laws of causation. That the angle of reflexion'- is equal to the 
angle of incidence is a statement of the mode" of action of a pgrticular 
cause ; bat that when two straight lines' intersect each other the oppo- 
site angles are equal, is true of all such lines and angles, by whatever 
cause produced. That the squares of the periodic tiliies of the planets 
are proportional to the cubes of their distances from the sun, is an 
uniformity derived frOm the laws of the causes. which produce the 
planetary motions, namely, the central and the tangential force ; but 



364 INDUCTION. 

that the square of any number is four times the square of half the 
number, is true independently of any cause. The only laws of resem- 
blance, therefore, which we ai'e called upon to consider independently 
of causation belong to the province of mathematics. 

§ 4. The same thing is evident with respect to the only remaining 
one of our five categories, Order in Place. The order in place, of the 
effects of a cause, is (like everything else belonging to the effects) a 
consequence of the laws of that cause. The order in place, or, as we 
have termed it, the collocation, of the primeval causes is (as well as 
their resemblance) in each instance an ultimate fact, in which no laws 
or uniformities are traceable. The only remaining general propo- 
sitions respecting order in place, and the only ones which have nothing 
to do with causation, a^re some of the truths of geometry ; laws through 
which we are able, from the order in place of certain points, lines, or 
spaces, to infer the order in place of others which are connected with 
the former in some known mode ; quite independently of the partic- 
ular nature of those points, lines, or spaces, in any other respect than 
position or magnitude, as well as independently of the physical cause 
from which in any particular case they happen to derive their origin. 

It thus appears that mathematics is the only department of science 
into the methods of which it still remains to inquire. And there is the 
less necessity that this inquiry should occupy us long, as we have already 
in the second Book, made considerable progress in it. We there re- 
marked, that the directly inductive truths of mathematics are few in 
number ; consisting of the axioms, together with certain propositions 
concerning existence, tacitly involved in most of the so-called defi- 
nitions. And we proved, at such length as makes any return to the 
subject altogether superfluous, that these original premisses, from 
which the remaining truths of the science are deduced, are, notwith- 
standing all appearances to the contrary, results of observation and ex- 
perience ; founded, in short, on the evidence of the senses. That 
things equal to the same thing are equal to another, or that two straight 
lines which have once intersected with one another continue to diverge, 
are inductive truths ; resting indeed, like the law of universal causation, 
only upon induction jper enumerationem simplicem ; upon the fact that 
they have been perpetually found true and never once false. But as 
we have seen in a recent chapter that this evidence, in the case of a 
law so completely universal as the lav7 of causation, amounts to the 
fullest proof attainable by the human faculties, so is this even more 
evidently true of the general propositions to which we are now ad- 
verting ; because, as a perception of their truth in any individual case 
whatever, requires only the simple act of looking at the objects in a 
proper position, there never could have been in their case (what, for a 
long period, in the case of the law of causation, there were) instances 
which were apparently, though not really, exceptions to them. Their 
infallible truth was recognized from the very dawn of speculation ; and 
as their extreme familiarity made it impossible for the mind to conceive 
the objects under any other law, they were, and still are, generally con- 
sidered as truths recognized by their own evidence, or by instinct. 

§ 5. There is something which seems to require explanation, in the 
fact that the immense multitude of truths (a multitude still as far from 



REMAINING LAWS OF NATURE. 365 

being exhausted as ever) comprised in the mathematical sciences, can 
be eUcited from so small a number of elementary laws. One sees not, 
at first, how it is that there can be room for such an infinite variety of 
true propositions, on subjects apparently so limited. 

To begin with the science of number. The elementary or ultimate 
truths of this science a.re the common axioms concerning equality, 
namely, " Things which are equal to the same thing are equal to one 
another," and '* Equals added to equals make equal sums," (no other 
axioms arfe necessary,*) together with the definitions of the various 
numbers. Like other so-called definitions, these are composed of two 
things, the explanation of a name and the assertion of a fact : of which 
the latter alone can form a first principle or premiss of a science. The 
fact asserted in the definition of a number is a physical fact. Each of 
the numbers two, three, four, &c., denotes physical phenomena, and 
connotes a physical property of those phenomena. Two, for instance, 
denotes all pairs of things, and twelve all dozens of things, connoting 
what makes them pairs, or dozens ; and that which makes them so is 
something physical ; since it cannot be denied that two apples are 
physically distinguishable from three apples, two horses from one horse, 
and so forth : that they are a different visible and tangible phenomenon. 
I am not undertaking to say what the difference is ; it is enough that 
there is a difference of which the senses can take cognizance. And 
although an hundred and two horses are not so easily distinguished 
from an hundred and three, as two horses are from three — though in 
most positions the senses do not perceive any difference — yet they "tnay 
be so placed that a difference will be perceptible, or else we should 
never have distinguished them, and given them different names. 
Weight is confessedly a physical property of things ; yet small differ- 
ences between great weights are as imperceptible to the senses in most 
situations, as small differences between great numbers ; and are only 
put in evidence by placing the two objects in a peculiar position, 
namely, in the opposite scales of a delicate balance. 

What, then, is that which is connoted by a name of number ] Of 
course some property belonging to the agglomeratiorr of things which 
we call by the name ; and that property is, the characteristic manner 
in which the agglomeration is made up of, and may be separated into, 
parts. We will endeavor to make this more intelligible by a' few 
explanations. 

When we call a collection of objects two^ three, or four, they 
are not two, three, or four in the abstract; they are two, three, or 
four things of some particular kind ; pebbles, horses, inches, pounds 
weight. What the name of number connotes is, the manner in 
which single objects of the given kind must be put together, in order 

* The axiom, " Equals subtracted from equals leave equal differences," may be demon- 
strated from the two axioms in the text. If A = a, and B=6, A — B=a — b. For if not, 
let A — B =a — 6 -f c. Then, since B = 6, adding equals to equals, A. = a-\-c. But 
A= a. Therefore a=^a-{- c, which is absurd. 

This proposition having been demonstrated, we may, by means of it, demonstrate the 
following: "If equals be added to imequals, the sums are unequal." If A=a and B 
not = 6, A -f B is not equal a-\-b. For suppose it to be so. Then, since A = a and A + 
B = a + 6, subtracting equals from equals, B = 6 ; which is contrary to the hypothesis. 

So again, it may be proved that two things, one of which is equal and the other unequal 
to a third thing, are unequal tp one another. U K—a and A not = B, neither is a —B. 
For suppose it to be equal. Then, since A= a and a= B, and since things equal to the 
same thing are equal to one another, A = B j which is contrary to the hypothesis. 



SQQ INDUCTION. '^ 

to produce tliat particular aggregate. If the aggregate be of peb-' 
bles, and we call it tw^^, the . name implies that to ^ compose the 
aggregate, one pebble must be joined to one pebble. If we call it 
three, we mean that one and one and one pebble must be brought to- 
gether to produce it, or else that one pebble must be joined to, an 
aggregate of the kind called two, already existing. The aggregate 
which we call Jvur has a still greater number of characteristic modes 
of formation. One and one and one and one pebble may be brought 
together ; or two aggregates of the kind called two may be united ; or 
one pebble may be added to an aggregate of the kind called tJiree. 
Every succeeding number in the ascending series, may be formed by 
the junction of smaller numbers in a progressively greater variety of 
ways. Even limiting the parts to two, the number may be formed, 
and consequently may be divided,- in as many different ways as there 
are numbers smaller than itself; and, if we admit of threes, fours, &c., 
in a still greater variety. Other modes of arriving at the same aggre- 
gate present themselves, not by the union of smaller, but by the dis- 
memberment of larger aggregates. Thus, tJireje pebbles may be formed 
by taking away one pebble from an aggregate of four ; two ^^e^bbles, by 
an equal division of a similar aggregate ; and so on. 

Every arithmetical proposition,; every statement of the result of an 
arithmetical operation ; is >,a statement of one of the modes of the 
formation of a given ^number. It affirms that a certain aggregat-e 
might have been formed by putting together, certain other aggregates, 

by withdrawing certain portions of some aggregate ; and tlmt, by 
consequence, we might reproduce those aggregates from it, by revers- 
ing the process. . ' 

Thus, when we say that the cube of 12 is 1728, what we affirm is 
this: That if, having a sufficient nutober, of pebbles or of any other 
objects, we put them together in, the particular sari of parcels or 
aggregates called twelve ; and put together these twelves again into 
similar collections ; and, finally, make up twelve of' these largest par- 
cels; the aggregate thus formed will be such a one as we* call 1728; 
namely, that which (to take the i^ost familiar of its modes of formation) 
may be made by joining the parcel called a thousand pebbles, the parcel 
called seven hundred pebbles, the parcel called, twenty pebbles, and the 
parcel called eight pebbles. The converse proposition, that the cube 
root of 1728 is 12, asserts that this large aggregate may again be decom- 
posed into the twelve twelves of twelves of pebbles which it consists of. 

The modes of formation of any number are innumerable; but when 
we know one mode of formation of each, all the -rest may be deter- 
mined deductively. If we know that a is formed froiji b and c, b from 
■d and e, c from d and f, and so forth, until \ye have included all the 
numbers of any scale we choose to select, (taking care that for each 
number the mode of formation is really a distinct, one, not bring- 
ing us round again to the former numbers, but introducing a new 
number,) we have a set of propositions from which we may reason 
to all the other modes of formation df those numbers from one 
another. Having established a chain of inductive truths connecting 
together all the numbers of' the scale, we can ascertain the formation 
of any one of those numbers froni 'an^ other by merely travelling 
from the one to the other along the chain. Suppose that we knew 
only the following modes of formation : 6^4 + 2, 4 =: 7 — 3, 7 = 5 + 2, 



REMAINING LAWS OF NATURE. 307 

5 1=: 9 — 4:. We could determine liow 6 maybe formed from 9. For 
6^4 -l-2=z7 — 3 + 2 =5-1-2 — 3 + 2 = 9 — 4 + 2 — 3 + 2. It may 
therefore be formed by taking away 4 and 3,, and adding 2 and, 2. If 
we know" besides that 2 + 2 == 4, we obtain 6 from 9 in a simpler 
mode, by merely taking, away 3. 

It is sufficient, therefore, to select one of the various modes of forma- 
tion. of each number, as a means of ascertaining all the rest. And 
since things which are uniform, and therefore simple, are most easily 
received and retained by the understanding, there is an obvious ad- 
vantage in selecting a mode of formation which shall be alike for all; 
in fixing the connotation of names of number on one uniform principle. 
The mode in which our existing numerical nomenclature is contrived 
possesses this advantage, with the additional one, that it- happily con*- 
veys to the mind two of the modes of formation of every number. 
Each number is considered as formed by the addition of an unit to the 
number next below it in magnitude, and this mode of formation is con- 
veyed by the place which it occupies in the series, And each is also 
considered as formed' by the addition of a number of units- less than 
ten, and a number of aggregates each equal to one of the successive 
powers of; te-n : and this mode of its formation is expressed by its 
spokpn name, and by its numerical character. 

Wliat renders arithmetic a deductive science, is the fortunate appli- 
cability to it of a law so comprehensive as " The sums of equals are 
equals :'i' or (to express the same principle in less familiar but more 
characteristic language). Whatever is made up of parts is made up of 
the parts of those parts. This truth, obvious to the senses in all cases 
which can be fairly referred to their decision, and so general as to be 
coextensive with nature itself, being true of all sorts of phenomena (for 
all admit of being numbered), must be considered an inductive truth, 
or law of nature, of the highest order. And every arithmetical opera- 
tion is an application of this law, or of other laws capable of being. de- 
duced from it. This is our warrant for all calculations. We believe 
that five and two are equal to seven, on the evidence of this inductive 
law, combined with the definitions of those numbers. We arrive at 
that conclusion (as all know who remember how they first learned it) 
by adding a single unit at a time^ 5 + 1= 6, therefore 5 -f- 1 + 1 = 6 
+ 1 z= 7 : and again 2 = 1 + 1, therefore 5 + 2 = 5 + 1 + 1 = 7. 

§ 6. Innumerable as are the true propositions which can be formed 
concerning particular numbers, no adeqliate conception could be gained, 
from these alone, of the extent of the truths composing the, science of 
number. Such propositions as we have spoken of are the least gen- 
eral of all numerical truths. It is true that even these are coextensive 
"with all natul-e: the properties of the number four are true of all ob- 
jects that are di^-isible into four equal parts, and all objects are either 
actually or ideally so divisible. But the propositions which comjDOse 
the science of algebra are true, not of a particular number, but of all 
numbers; not of all things under the condition of being divided in 
a particular way, but of all things under the condition of being divided 
in an]/ way — of being designated by a number at all. 

Since it is impossible for different numbers to have any of their 
modes of formation completely in common, it looks like a paradox to 
say, that all propositions which can be made concerning numbers relate 



368 INDUCTION. t 

to their modes of formation from other numbers,^ and yet that there 
, are propositions which are true of all numbers. But this very paradox 
leads to the real principle of generalization concerning the properties 
of numbers. Two different numbers cannot be formed in the same 
manner from the same numbers ; but they may be formed in the same 
manner from different numbers ; as nine is formed from three by mul- 
tiplying it into 'itself, and sixteen is formed from four by the same 
process. Thus there arises a classification of modes of formation, or, 
in the language commonly used by mathematicians, a classification of 
Functions. Any number, considered as formed from any other num- 
ber^ is called a function of it; and there are as many kinds of functions 
as there are modes of formation. The simple functions are by no 
means numerous, most functions being formed by the combination of 
several of the operations which form simple functions, or by successive 
repetitions of some one of those operations. The simple functions of 
any number x are all reducible to the following forms : x-{-a, x — «, 

X 



Co X^ . X 



5 "^ 5 a/ 

a \f X 



log. X (to the base a), and the same expressions 



varied by putting x for a and a for x, wherever that substitution would 
alter the value : to which perhaps we ought to add (with M. Comte) 
sin X, and arc (sin =.-x). All other functions of x are formed by 
putting some one or more of the simple functions in the place of x 
or a, and subjecting them to the same elementary operations. 

In order to carry on general reasonings on the subject of Functions, 
we require a nomenclature enabling us to express any two numbers 
by names which, without specifying what particular numbers they are, 
shall show what flmction each is of the other ; or, in other words, shall 
put in evidence their mode of formation from one another. The sys- 
tem of general language called algebraical notation does this. The 
expressions a and «^+3 a denote, the one any number, the other the 
number formed from it in a particular manner. The expressions 
a, h, n, and [a + by, denote any three numbers, and a fourth which is 
formed from them in a certain mode. 

The following may be stated as the general problem of the alge- 
braical calculus : F being a certain function of a given number, to find 
what function F will be of any function of that number. For example, 
a binomial a-\-b is a function of its two parts a and b, and the parts 
are, in their turn, functions o^ a -\-b: now (a + b)" is a certain function 
of the binomial ; what function will this be of a and b, and the two 
parts'? The answer to this question is the binomial theorem. The 

71/ 71.71 1 

formula (a -j- ^)" = «" + ~ «"~"'^ -1 — -7-5- ol'^^b'^ -\-, &c., shows in what 

manner the number which is formed by multiplying a -{-b into itself 
71 times, might be formed without that process, directly from a, b, and n. 
And of this nature are all the theorems of the science of number. 
They assert the identity of the result of different modes of formation. 
They affirm that some mode of formation from x, and some mode of 
formation from a. certain function of x, produce the same number. 

Besides these general theorems or formulae, what remains in the 
algebraical calculus is the resolution of equations. But the resolution 
of an equation is also a theorem. If the equation be x^-{-ax — b, the 
resolution of this equation, viz., x——'\a^^ i a'^ + ^, is a general 



REMAINING I^AWS OF NATURE. 369 

proposition, wkicli „ rnay be regarded as an answer to the question, If h 
is a certain function of x and a (namely x^ -\- ax), what function is 
cc of ^ and «? The resolution of equations is, therefore, a mere 
variety of the general problem as above stated. The problem is — 
Given a function, what function is it of some other function ? And, in 
the resolution of an equation, the question is, to find what function of 
one of its own functions the number itself is. 

Such as above described, is the aim and end of the calculus. As 
for its processes, every one knows that they are simply deductive. In 
demonstrating an algebraical theorem, or in resolving an equation, 
we travel from the datum to the qzicBsitum by pure ratiocination ; in 
which the only premisses introduced, besides the original hypotheses, 
are the fundamental axioms already mentioned — -that things equal to 
the same thing are equal to one another, and that the sums of equal 
things are equal. At each step in the demonstration or in the calcu- 
lation we apply one or other of these truths, or ti-uths deduced from 
them, as, that the differences, products, &c., of equal numbers are 
equal. 

It .would be inconsistent with the scale of this work, and not neces- 
sary to its design, to carry the analysis of the truths and processes of 
algebra any further ; which is moreover the less needful, as the task 
has been recently and thoroughly performed by other writers. Profes- 
sor Peacock's Algebra, and Mr. Whewell's Doctrine of L'wiits, should 
be studied by every one who desires to comprehend the evidence of 
mathematical truths, and the meaning of the obscurer processes of the 
calculus ; while, even after mastering these treatises, the student will 
have much to learn on the subject from M. Comte, of whose admirable 
work one of the most admirable portions is that in which he may 
truly be said to have created the philosophy of the higher mathe- 
matics.* 

§ 7. If the extreme generality and remoteness, not so much from 
sense as frOm the visual and tactual imagination, of the laws of number, 
render it a somewhat difficult effort of abstraction to conceive those 
laws as being in reality physical truths obtained by observation ; the 
same difficulty does not exist with regard to the laws of extension. 
The facts of which those laws are expressions, are of a kind peculiarly 
accessible to the sense, and suggesting eminently distinct images to the 
fancy. That geometry is a strictly physical science w^ould doubtless 
have b6en recognized in all ages, had it not been for the illusions pro- 
duced by two causes. One of these is the characteiistic property, 
already noticed, of the facts of geometry, that they may be collected 
from our ideas or mental pictures of objects as effectually as from the 
objects themselves. The other is, the demonstrative character of 
geometrical truths ; which w^as at one time supposed to constitute a 
radical distinction between them and physical truths, the latter, as 
resting on mex'ely prohable evidence, being deemed essentially uncer- 

* In the concluding pages of his Cours de Philosophie Positive, of which the final volume 
has but recently appeared, M. Comte announces the intention of hereafter producing a 
special and systematic work on the Philosophy of Mathematics. All competent judges 
who are acquainted with what M. Comte has already accomplished in that great depart- 
ment of the philosophy of the sciences, will look, with the highest expectations to this 
promised treatise. 

3 A '^ ."^ ', . • ., '( 



370 INDUCTION. . * '-^ '■ 

tain and unprecise. The advance of knowledge has, however, made 
it manifest that physical science, in its better understood branches, is 
quite as demonstrative as geometry : the task of deducing its details 
from a few comparatively simple principles being found to be anything, 
but the impossibility it was once supposed to be\; and the notion of 
the superior certainty of geometry being an illusion arising from the 
ancient prejudice which in that science mistakes the ideal data from 
which we reason, for a peculiar class of realities while the correspond- 
ing ideal data of any deductive physical science are recognized as 
what they really are, mere hypotheses; ' . 

Every theorem in geometry is a law of external nature, and might 
have been ascertained by generalizing from observation and experi- 
ment, which in this case resolve themselves into comparison and . 
measurement. But it was found practicable, and being practicable, 
was desirable, to deduce these truths by ratiocination from a small 
number of general laws of nature, the certainty and universality of 
which was obvious to the most careless observer, and which compose 
the first principles and ultimate premisses of the science. Among 
these general laws must be included the same two which we have 
noticed as ultimate principles of the Science of Number also, and 
which are applicable to every description of quantity : viz,, the sums 
of equals are equal, and things which are equal to the same thing are 
equal to one another; the latter of which may be expressed in a manner 
more suggestive of the inexhaustible multitude of its consequences by 
the following terms : Whatever is equal to any one of a number of 
equal magnitudes, is equal to any other of them. To these two must 
be added, in geometry, a third law of equality, namely, that lines, 
surfaces, or solid spaces, which can be so applied to one another as to 
coincide, are equal. Some writers have asserted that this law of nature 
is a -mere verbal definition : that the expression "equal magnitudes" 
Tneans nothing but magnitudes which can be so applied to one another 
as to coincide. But in this opinion I cannot agree. The equality of 
two geometrical magnitudes cannot differ fundamentally in its nature 
from the equality of two weights, two degrees of heat, or two portions 
of duration, to none of which would this pretended definition of equal- 
ity be suitable. None of these things can be so apphed to. one another 
as to coincide, yet we perfectly understand what we mean when we 
call them equal. Things are equal in magnitude, as things are equal 
in weight, when they are felt to be exactly similar in respect of the 
attribute in which we compare them : and the application of the ob- 
jects to each other in the one case, like the balancing them with a pair 
of scales in the other, is but a mode of bringing them into a position 
in which our senses can recognize deficiencies of exact resemblance 
that would otherwise escape our notice. 

Along with these three general principles or axioms, the remainder 
of the premisses of geometry consist of the so-called definitions, that is 
to say, propositions asserting the real existence of the various objects 
therein designated, together with some one pi-opOrty of each. In some 
cases more than one property is commonly assumed, but in no case is 
more than one necessary. It is assumed that there are such things in 
nature as straight lines, and that any two of them setting out from the 
same point, diverge more and more without limit. This assumption, 
(which includes and goes' beyond Euclid's axiom that two straight 



REMAINING LAWS OF NATURE. 371 

lines cannot inclose a space,) is as indispensable in geometry, and as 
evident, resting upon as simple, familiar, and universal observation, as 
any of the other axioms. It is also assumed that straight lines diverge 
from one another in different degrees ; in other words, that there are 
such things as angles, and that they are capable of being equal or un- 
equal. It is assumed that there is such a thing as a circle, and that all 
its radii are equal; such things as ellipses, and that the sums of the 
focal distances are equal for every point in an ellipse ; such things as 
parallel lines, and that those lines are everywhere equally distant.* 

"> § 8. It is a matter of something more than curiosity to consider to 
what peculiarity of the physical truths which are the subject of geom- 
etry, it is owing that they can all be deduced from so small a number of 
original premisses : why it is that we can set out from only one charac- 
teristic property of each kind of phenomenon, and with that and two 
or three general truths relating to equality, can travel from mark to 
mark until we obtain a vast body of derivative truths, to all appear- 
ance extremely unlike those elementary ones. 

The explanation of this remarkable fact seems to lie in the following 
circumstances. In the first place, all questions of position and figure 
may be resolved into questions of magnitude. The position and figure 
of any object is determined, by determining the position of a sufficient 
number of points in it ; and the position of any point may be deter- 
mined by the magnitude of three rectangular coordinates, that is, of 
•the perpendiculars drawn from the point to three axes at right angles 
,to one another, arbitrarily selected. By this transformation of all ques- 
tions of quality into questions only of quantity, geometry is reduced to 
the single problem of the measurement of magnitudes, that is, the 
ascertainment of the equalities which exist between them. Now when 
we consider that by one of the general axioms, any equality, when 
ascertained, is proof of as many other equalities as there are other 
things equal to either of the two equals; and that by another of those 
ax,ioms, any ascertained equality is proof of the equality of as many 
pairs of magnitudes as can be formed by the numerous operations which 
resolve themselves into the addition of the equals to themselves or to 
other equals: we cease to wonder that in proportion as a science is 
conversant about equality, it should afford a more copious supply of 
marks ; and that the sciences of number and extension, which are con- 
versant with little elsp than, equality, should be. the most deductive of 
all the sciences. .^ ' ... ., \ • ., ', - .n..^. •> •.••'.• , t 

* Geometers have usually preferred to define parallel lines by the property of being in 
the same plane and never meeting. This, however, has rendered it necessary for them to 
assume, as an additional axiom, some other property of parallel lines; and the unsatisfac- 
tory manner in which properties for that purpose have been selected by Euclid and others 
has always been deemed the opprobrmm of elementary geometry. Even as a verbal defini- 
tion, equi-distance is a fitter property to characterize parallels by, since it is the attribute 
really involved in the signification of the name. If to be in the same plane and never to 
meet were all that is meant by being parallel, we should feel no incongruity in speaking of 
a curve as parallel to its asymptote. The meaning of parallel lines is, lines which pursue 
exactly the same direction, and which, therefore, neither approach nearer nor go further 
from one another; a conception suggested at once by the contemplation of nature. That 
the lines will never meet is of course implied in the more comprehensive proposition that 
they are everywhere equally distant. And that any straight Imes which are in the same 
plane and not equi-distant will certainly meet, may be demonstrated in the most rigid 
manner from the fundamental property of straight lines assumed in the text, viz., that if 
they set out from the same point they diverge more and more without limit. 



372 INDUCTION. 

There are, moreover, two or thia^e of the principal laws of space or 
extension which are unusually fitted for rendering one position or 
magnitude a mark of another, and thereby contributing to render the 
science largely deductive. First; the magnitudes of inclosed spaces, 
whether superficial or solid, are completely determined by the magni- 
tudes of the lines and angles which bound them. Secondly, the length 
of any line, whether straight or curve, is measured (certain other things 
being given,) by the angle which it subtends, and vice versd. Lastly, 
the angle which any two straight lines make with each other at an inac- 
cessible point, is measured by the angles they severally make with any 
third line we choose to select. By means of these general laws, the 
measurement of all lines, angles, and spaces whatsoever might be 
accomplished (to borrow an obseiTation from M. Comte), by measuring 
a single straight line and a sufficient number of angles ; which is, indeed, 
the plan actually pursued in the trigonometrical survey of a country ; 
and fortunate it is that this is practicable, the exact measurement of 
straight lines being difficult, but that of angles very easy. Three such 
generalizations as the foregoing afford such facilities for the indirect 
measurement of magnitudes, (by supplying us with known lines or 
angles which are marks of the magnitude of unknown ones, and thereby 
of the spaces which they inclose) that it is easily conceivable how from 
a few data we can go on to ascertain the magnitude of an indefinite 
multitude of lines, angles, and spaces, which we could not easily, or 
could not at all, measure by any more direct process. 

§ 9. Such are the few remarks which it seemed necessary to make 
in this place, respecting the laws of nature which are the peculiar sub- 
ject of the sciences of number and extension. The immense part which 
those laws take in giving a deductive character to the other depart- 
ments of physical science, is well known; and is not surprising, whe-ii 
we consider that all causes operate according to mathematical laws. 
The effect is always dependent upon, or, in mathematical language, is 
a function of, the quantity of the agent ; and generally of its position 
also. We cannot, therefore, reason respecting causation, without intro- 
ducing considerations of quantity and extension at every step; and 'if 
the nature of the phenomena admits of our obtaining numerical data 6f 
sufficient accuracy, the laws of quantity become the grand instruments 
for calculating forward to an effect, or backward to a cause. That in 
all other sciences, as well as in geometry, questions of quality are 
scarcely ever independent of questions of quantity, may be seen from 
the most familiar phenomena. Even when several colors are mixed on 
a painter's pallet, the comparative quantity of each entirely deter- 
mines the color of the mixture. 

With this mere suggestion of the general causes which render math- 
ematical principles and processes so predominant in those deductive 
sciences which afford precise numerical data, I must, on the present 
occasion, content myself; referring the reader who desires a thorough 
acquaintance with this great subject, to the first two volumes of M. 
Comte's systematic work. 

, In the same work, and more particularly in the third volume, are 
also fully discussed the necessary limits of the applicability of mathe- 
matical principles to the improvement of other sciences. Such prin- 
ciples are manifestly inapplicable, where the causes on which any class 



REMAINING LAWS OF NATURE. 373 

of phenomena depend are so imperfectly accessible to our observation, 
that we cannot ascertain, by a proper induction, their numerical laws ; 
or where the causes are so numerous, and intermixed in so complex a 
manner with one another, that even supposing their laws known, the 
cornputation of the aggregate effect transcends the powers of the cal- 
culus as it is. Or as it is ever likely to be ; or lastly, where the causes 
themselves are in a state of perpetual fluctuation, as in physiology, 
and still more, if possible, in the social science. As M. Comte* well 
observes, the mathematical solutions of physical questions become 
progressively more difficult and more imperfect, in proportion as the 
questions divest themselves of their abstract and hypothetical character, 
and approach nearer to the degree of complication actually existing in 
nature ; insomuch that beyond the limits of astronomical phenomena, 
and of those most nearly analogous to them, mathematical accuracy is 
generally obtained " at the expense of the reality of the inquiry :" 
while, even in astronomical questions, " notwithstanding the admirable 
simplicity of their mathematical elements, our feeble intelligence 
becomes incapable of following out effectually the logical combinations 
of the laws on which the phenomena are dependent, as soon as we 
attempt to take into simultaneous consideration more than two or three 
essential influences." Of this, the problem, of the Three Bodies has 
already been cited by us, more than once, as a remarkable instance ; 
the complete solution of so comparatively simple a question having 
vainly tried the skill of the most profound mathematicians. We may 
conceive, then, how chimerical would be the hope that mathematical 
principles could ever be advantageously applied to phenomena depen- 
dent upon the mutual action of the innumerable minute particles of 
bodies, as those of chemistry, and still more, of physiology ; and for 
similar reasons those principles must be for ever inapplicable to the 
still more complex inquiries, the subjects of which are phenomena of 
society and government. 

The value of mathematical instruction as a preparation for those 
more difficult investigations, consists in the applicability not of its 
doctrines, but of its method. Mathematics will ever remain the most 
perfect type of the Deductive Method in general ; and the applications 
of mathematics to the simpler branches of physics, furnish the only 
school in which philosophers can effectually learn the most difficult and 
important portion of their art, the employment of the laws of simpler 
phenomena for explaining and predicting those of the more complex. 
These grounds are quite sufficient for deeming mathematical training 
an indispensable basis of real scientific education, and regarding, with 
Plato, one who is ayew^erpT/ro^, as wanting in one of the most essential 
qualifications for the successful cultivation of the higher branches of 
philosophy. 

* Cours de Philosophie Positive, iii., 4H-416. 



374 INDQGTION. 



CHAPTER XXV. 



§ 1. The method of amving at general truths, or general propo- 
sitions fit to be believed, and the nature of the evidence on which they 
are grounded, have been discussed, as far as space and the v^^riter's 
faculties permitted, in the tw^enty-four preceding chapters. But the 
result of the examination of evidence is not alw^ays belief, nor even 
suspension, of judgment; it is sometimes disbelief The philosophy, 
therefore, of induction and experimental inquiry is incomplete, unless 
the grounds not only of belief, but of disbelief, are treated of; and to 
this topic we shall devote one, and the final chapter. 

By disbelief is not here to be understood the mere absence of belief. 
The ground for abstaining from belief is simply the absence or in- 
sufficiency of proof; and in considering what is sufficient evidence to 
support any given conclusion, we have already, by implication, con- 
sidered what evidence is not sufficient for the same purpose. By dis- 
belief is here meant, not the state of mind in which we are ignorant, 
and form no opinion upon a subject, but that in which we are fully 
persuaded that some opinion is not true; insomuch that if evidence, 
even of great strength, (whether grounded on the testimony of others 
or on our own apparent perceptions,) were produced in favor of the 
opinion, we should believe that the witnesses spoke falsely, or that 
they, or ourselves if we were the direct percipients, were mistaken. 

That there are such cases, no one is likely to dispute. Assertions 
for which there is abundant positive evidence are often disbelieved, on 
account of what is called their improbability, or impossibility. And 
the question for consideration is, what, in the present case, these words 
mean, and how far and under what circumstances the properties which 
they expi'ess are sufficient grounds for disbelief. 

§ 2. It is to be remarked in the first place, that the positive evidence 
produced in support of an assertion which is nevertheless rejected on 
the score of impossibility or improbability, is never such as amounts to 
full proof. It is always grounded upon some approximate generaliza- 
tion. The fact may have been asserted by a hundred witnesses; but 
there are many exceptions to the universality of the generalization 
that what a hundred witnesses affirm is true. We may seem to our- 
selves to have actually seen the fact : bat, that we really see what we 
think we see, is by no means an universal truth; our organs may have 
been in a morbid state, or we may have inferred something, and 
imagined that we perceived it. The evidence, then, in the affirmative, 
being never more than an approximate generalization, all will depend 
upon what the evidence in the negative is. If that also rests upon an 
approximate generalization, it is a case for comparison of probabilities. 
If the approximate generalizations leading to the affirmative are, when 
added together, less strong, or in other words, further removed from 
universality, than the approximate generalizations which support the 
negative side of the question, the proposition is said to be improbable, 
and is to be disbelieved, provisionally. If, however, an alloj2:ed fact 



GROUNDS OF DISBELIEF. 375 

be in contradiction, not to any num|jer of approximate generalizations, 
but to a completed generalization grounded upon a rigorous induction, 
it i^ said to be. impossible, and is to be disbelieved totally. 

' This last principle, simple and evident as it appears, is the doctrine 
which, on the occasion of an attempt to apply it to the question of the 
credibility of miracles, excited so violent a controversy. Hume's cele- 
brated principle, that nothing is credible vi^hich is contradictory to ex- 
perience, or at variance with laws of nature, is merely this very plain 
and harmless proposition, that whatever is contradictory to a complete 
induction is incredible. That such a maxim as this should either be 
accounted a dangerous heresy, or mistaken for a great and recondite 
truth, speaks ill for the state of philosophical speculation on such sub- 
jects. 

But does not (it may be asked) the very statement of the proposition 
imply a contradiction 1 An alleged fact, according to this theory, is 
not to be believed if it contradict a complete induction. But it is 
■essential to the completeness of an induction that it shall not contra- 
dict any known fact. Is it not then a yctitio inincijpii to say, that the 
fact ought to be disbelieved because the induction opposed to it is com- 
plete ] How can we have a right to declare the induction complete, 
while facts, supported by credible evidence, present themselves in op- 
position to it j 

. T answer, we have that right whenever the scientific canons of in- 
duction give it to us ; that is, whenever the induction can be complete. 
We have it, for example, in a case of causation, in which there has 
been an experimentum cruets. If an antecedent A, superadded to a 
set of antecedents in all other respects unaltered, is followed by an 
effect B which did not exist before, A is, in that instance at least, 
the cause of B, or a necessary part of that cause ; and if A be tried 
again with many totally different sets of antecedents and B still fol- 
lows, then it is the whole cause. If these observations or experiments 
have been repeated so often, and by so many persons, as to exclude 
all supposition of error in the observer, a law of nature is established; 
and so long as this law is received as such, the assertion that on any 
particular occasion A took place, and yet B did not follow, without 
any counteracting cause, must be disbelieved. Such an assertion is not 
to be credited upon any less evidence than what would suffice to 
overturn the law. The general truths, that whatever has a beginning 
has a cause, and that when none but the same causes exist, the same 
effects follow, rest upon the strongest inductive evidence possible ; the 
proposition that things aflirmed by even a crowd of respectable wit- 
nesses are true, is but an approximate generalization ; and — even if 
we fancy we actually saw or felt the fact which is in contradiction to . 
the law — ^what a human being can see is no more than a set of appear- 
ances ; from which the real nature of the phenomenon is merely an 
inference, and in this inference approximate generalizations usually 
have a large share. If, therefore, we make our election to hold by 
the law, no quantity of evidence whatever ought to persuade us that 
there has occurred anything in conti-adiction to it. If, indeed, the evi- 
dence produced is such that it is more likely that the set of observa- 
tions and experiments upon which the law rests should have been in- 
accurately performed or incorrectly interpreted, than that the evidence 
in question should be false, we may beheve the evidence : but then we 



376 INDUCTION. 

must abandon the law. And since the law was received on what 
seemed a complete induction, it can only be rejected on evidence 
equivalent ; namely, as being inconsistent not with any flumber of ap- 
proximate generalizations, but with some other and better established 
law of nature. This extreme case, of a conflict between two supposed 
laws of nature, has probably never actually occurred, where, in the 
process of investigating both the laws, the true canons of scientific in- 
duction had been kept in view ; but if it did occur, it must terminate 
in the total rejection of one, of the supposed laws. It would prove 
that there must be a flaw in the logical process by which either one or 
the other was established ; and if there be so, that supposed general 
truth is no truth at all. We cannot admit a proposition as a law of 
nature, and yet believe a fact in real contradiction to it. We must dis- 
believe the alleged fact, or believe that we were mistaken in admitting 
the supposed law. 

But in order that any alleged fact should be contradictory to a law of 
causation, the allegation must be, not simply that the cause existed 
without being followed by the effect, for that would be no uncommon 
occurrence; but that this happened in the absence of any adequate 
counteracting cause. Now in the case of an alleged miracle, the asser- 
tion is the exact opposite of this. It is, that the effect was defeated, 
not in the absence, but in consequence, of a counteracting cause, 
namely, a direct interposition of an act of the will of some being who 
has power over nature ; and in particular of a being, whose will having 
originally endowed all the causes with the powers by which they pro- 
duce their effects, may well be supposed able to counteract them. A 
miracle (as was justly remarked by Brown'*) is no contradiction to the 
law of cause and eflect; it is a new effect, supposed to be produced by 
the introduction of a new cause. Of the adequacy of that cause, if it 
exist, there can be no doubt ; and the only antecedent improbability 
which can be ascribed to the miracle, is the improbability that any such 
cause had existence in the case. 

All, therefore, which Hume has made out, and this he must be con^ 
sidered to have made out, is, that no evidence can be sufficient to prove 
a miracle to any one who did not previously believe the existence of a 
being or beings with supernatural power ; or who believed himself to 
have full proof that the character of the Being whom he recognizes, is 
inconsistent with his having seen fit to interfere on the occasion in 
question. The truth of this (however fatal to a school of theology 
which has recently been revived in this country, and which has the 
weakness to rest all the evidences of religion upon tradition and tes- 
timony) may be, and is, admitted by all defenders of revelation who 
have made much figure as such during the present century. It is now 
acknowledged by nearly all the ablest writers on the subject, that 
natural religion is the necessary basis of revealed; that the proofs of 
Christianity presuppose the being and moral attributes of God ; and 
that it is the conformity of a religion to those attributes which de- 
termines whether credence ought to be given to its external evi- 
dences ; that (as the proposition is sometimes expressed) the doctrine 
must prove the miracles, not the miracles the doctrine. It is hardly 
necessary to point out the complete accordance of these views with 

* See the two very remarkable, ootes (A), and (F), appended to his Inquiry into the JRela- 
tion of Cause and Effect. . '■ ' . - . 



GROUNDS OF DISBELIEF. ' 377 

the opinions wliich (not to mention other testimonies) the New Testa- 
ment itself shows to have been generally prevalent in the apostolic 
age ; when it was believed indeed that miracles were necessary as cre- 
dentials, and that whoever was sent by God must have the power of 
working them ; but no one dreamed that such power sufficed by itself 
as proofof a divine mission, and St. Paul expressly warned the churches, 
if any one came to them working miracles, to observe what he taught, 
and unless he preached " Christ, and him crucified,", not to listen to 
the teaching, TherO is no reason, therefore, that timid Christians 
should shrink from accepting the logical canon of the Grounds of Dis- 
belief. And it is not hazarding much to predict that a school which 
peremptorily rejects all evidences of religion, except such as, when re- 
lied upon exclusively, the canon in question irreversibly condemns ; 
which denies to mankind the right to judge of religious doctrine, and 
bids them depend on miracles as their sole guide ; must, in the present 
state of the human mind, inevitably fail in its attempt to put itself at 
the head of the religious feelings and convictions of this country : by 
whatever learning, argumentative skill, and even, in many respects, 
comprehensive views of human affairs'; its peculiar doctrines may be 
recommended to the acceptance of thinkers. . . „ 

§ 3. It appears from vf'hat has been said, that the assertion that a cause 
has been defeated of an effect which is connected with it by a completely 
ascertained law of causation, is to be disbelieved or not, according to the 
probability or improbability that there existed in the particular instance 
an adequate counteracting cause. To form an estimate of this, is not 
more difficult than of any other probability. With regard to all known 
causes capable of counteracting the given causes, we have generally 
some previous knowledge of the frequency or rarity of their occur- 
rence, from which we may draw an inference as to the antecedent 
improbability of their having been present in any particular case. 
And neither in respect to known nor unknown causes are we required 
to pronounce upon the probability of their existing in nature, but only 
of their having existed at the precise time and place at which the 
transaction is alleged to have happened. We are seldom, therefore, 
without the means (when the. circumstances of the case ' are at all 
known to us) of judging how far it is likely that such a cause should 
have existed at that time and place without manifesting its presence, by 
some other marks, and (in the case of an unknown cause) without 
having hitherto manifested its existence in any other instance. Ac- 
cording as this circumstance or the falsity of the testimony appears 
more improbable, that is, conflicts with an approximate generalization 
of a higher order, We believe the testimony, or disbelieve it ; with a 
stronger or a weaker degree of conviction, according to the prepon- 
derance : at least until we have sifted the matter further. 

So much, then, for the case in which the alleged fact conflicts, or 
appears to conflict, with a real law of causation. But a more common 
case, perhaps, is that of its conflicting with uniformities of mere co- 
existence, not proved to be dependent on causation : in other words, 
with the properties of Kinds. It is with these uniformities princi- 
pally, that the marvelous stories related by travellers are apt to be at 
variance : as of men with tails, or with wings, and (until confirmed by 
experience) of flying fish ; or of ice, in the celebrated anecdote of the 
3B 



37$ * . ' INDUCTION. 

Dutch travellers and the King of Siam. Facts of this description, 
facts previously unheard of, but which could not from any knowTi lav^r 
of causation be pronounced impossible, are what Hume characterizes 
as not contrary to experience, but merely uncomformable to it ; and 
Bentham, in his treatise on Evidence, denominates them facts discon- 
formable in specie, as distinguished from such as are dis conform able 
in toto or in degree. 

In a case of this description, the fact asserted is the existence of a 
new Kind ; which in itself is not in the slightest degree incredible, 
and only to be rejected if the improbability that any variety of object 
existing at the particular place and time should not have been discov- 
ered sooner, be greater than that of error or mendacity in the witnesses. 
Accordingly, such assertions, when made by credible persons, and of 
unexplored places, are not disbelieved, but at most regarded as requiring 
confirmation from subsequent observers ; unless the alleged properties 
of the supposed new Kind are at variance with known properties of 
some larger Kind which includes it ; or, in other words, unless, in the 
new Kind which is asserted to exist, some properties are said to have 
been found disjoined from others which have always been known to 
accompany them ; as in the case of PHny's men, or any other kind ot 
animal of a structure different from that which has always been found 
to coexist with animal life. On the mode of dealing with any such 
case, little needs be added to what has been said on the same topic in 
the twenty-second chapter,* When the uniformities of coexistence 
which the alleged fact w^ould violate, are such as to raise a strong 
presumption of their being the result of causation, the fact which 
conflicts with them is to be disbelieved, at least provisionally, and 
subject to further investigation. When the presumption amounts to a 
virtual certainty, as in the case of the general structure of organized 
beings, the only question requiring consideration is whether, in phenom- 
ena so little known, there may not be liabilities to counteraction from 
causes hitherto unknown ; or whether the phenomena may not be 
capable of originating in some other way, which would produce a 
different set of derivative uniformities. A¥here (as in the case of the 
flying-fish, or the ornithorhynchus) the generalization to which the 
alleged fact would be an exception is very special and of limited range, 
neither of the above suppositions can be deemed very improbable ; and* 
it is generally, in the case of such alleged anomalies, wise to suspend 
our judgment, pending the subsequent inquiries which will not fail to 
confirm the assertion if it be true. But when the generalization is very 
comprehensive, embracing a vast number and variety of observations, 
and covering a considerable province of the kingdom of nature ; then, 
for reasons which have been fully explained, such an empirical law 
comes near to the certainty of an ascertained law of causation: and 
any alleged exception to it cannot be admitted, unless upon the evi- 
dence of some law of causation proved by a still more complete 
induction. 

Such uniformities in the course of nature as do not bear marks of 
being the results of causation, are, as we have already seen, admissible 
as universal truths with a degree of credence pi'oportioned to their 
generality. Those which are true of all things whatever, or at least, 
which are totally independent of the vaiieties of Kinds, namely, the 
* Supra, pp. 349-351. 



GROUNDS OF DISBELIEF. 



3^9 



laws of number and extension, to which we may add the law of causa- 
tion itself, are probably the only ones, an exception to which is abso- 
lutely and for ever incredible. Accordingly, it is to assertions supposed . 
to be contradictory to these Jaws, or to some others coming near to 
them in generality, that the word impossibility (at least absolute impos- 
sibility) seems to be generally confined. Violations of other laws, of 
special laws of causation for instance, are said, by persons studious of 
accuracy in expression, to be impossible in the circumstances of the 
case ; or impossible unless some cause had existed which did not exist 
in the particular case. Of no assertion, not in contradiction to some 
of these, very general laws, will more than improbability be asserted 
by any cautious person ; and improbability not of the very highest 
degree, unless the time and place in which the fact is said to have 
occurred, render it almost certain that the anomaly, if real, could not 
have been overlooked by other observers. Suspension of judgment is 
in all other cases the resource of the judicious inquirer ; provided the 
testimony in favor of the anomaly presents, when well sifted, no sus- 
picioiis circumstances. 

But the testimony is scarcely ever found to stand that test, in cases 
in which the anomaly is not real. In the instances upon record in 
which a great number of witnesses, of good reputation and scientific 
acquirements, have testified to the truth of something which has turned 
out untrue, there have almost always been circumstances which, to a 
keen observer who had taken due pains to sift the matter, would have 
rendered the testimony untrustworthy. There have generally been 
means of accounting for the impression upon the senses or minds of 
the alleged percipients by fallacious appearances ; or some epidemic 
delusion, propagated by the contagious influence of popular feeling, 
has been concerned in the case ; or some strong interest has been 
implicated — religious zeal, party feeling, vanity, or at least the passion 
for the marvelous, in persons strongly susceptible of it. When none 
of these or similar circumstances exist to account for the apparent 
strength of the testimony : and where the assertion is not in contra- 
diction either to those universal laws which know ho counteraction or 
anomaly, or to the generalizations next in comprehensiveness to them, 
but would only amount, if admitted, to the existence of an unknown 
cause or an anomalous Kind, in circumstances not so thoroughly 
explored but that it is credible that things hitherto unknown may still 
come to light; a cautious person will neither admit nor reject the testi- 
mony, but will wait for confirmation at other times and from other 
unconnected sources. Such ought to have been the conduct of the 
King of Siam when the Dutch travellers aflirmed to him the existence 
of ice. But an ignorant person is as obstinate in his contemptuous 
incredulity as he is unreasonably credulous. Anything unlike his own 
narrow experience he disbelieves, if it flatters no propensity; any 
nursery tale is swallowed implicitly by him if it does. 

§ 4, Before concluding this inquiry, we must advert to a very serious 
misapprehension of the principles of the subject, which has been com- 
mitted by some of the writers against Hume's Essay on Miracles, in 
their anxiety to destroy what appeared to them a formidable weapon 
of assault against the Christian religion; and to which, with entirely 
different views on the religious question, Laplace, in his Essay on 



■ 380" INDUCTION. 

Prohahilitics, has been led to give his sanction ; the effect in both cases 
being, entirely to confound the doctrine of the Grounds of Disbelief. 
The mistake consists in overlooking the distinction between (what may 
be called) improbability before the fact, and improbability after it; two 
different properties, the latter of which is always a gi'ound of disbelief; 
the former is so or not, as it may happen. 

Many events are altogether improbable to us, before they have 
happened, or before we are informed of their happening, which are 
not in the least incredible when we are informed of them, because not 
contrary to any, even approximate, induction. In the cast of a per- 
fectly fair die, the chances are five to one against throwing ace, that is,. 
ace will be thrown on an average only once in six throws. But this 
is no reason against believing that ace was thrown on a given occasion, 
if any credible witness asserts it; since although ace is only thrown 
once in six times, so7ne number which is only thrown once in six times . 
must have been thrown if the die was thrown at all. The improba- 
bility, then, or in other words, the unusualness, of any fact, is no reason 
for disbelieving it, if the nature of the case renders it certain that 
either that or something equally improbable, that is, equally unusual, 
did happen. If we disbelieved all facts which had the chances against 
them beforehand, we should believe hardly anything. We are told 
that A. B. died yesterday : the moment before we were so told, the 
chances against his having died on that day may have been ten thou- 
sand to one ; but since he was certain to die at some time or other, 
and when he died must necessarily die on some particular day, while 
the chances are innumerable against every day in particular, experi- 
ence affords no ground whatever for discrediting any testimony which 
may be produced to the event's having taken place on a given day. 

Yet it has been considered, by Dr. Campbell and others, as a com- 
plete answer to Hume's doctrine (that things are incredible which are 
contrary to the unifomi course of experience), that we do not disbe- 
lieve, merely because the chances were against them, things in strict 
conformity to the unifonn course of experience ; that we do not dis- 
believe an alleged fact merely because the combination of causes upon 
which it depends occurs only once in a certain number of times. It is 
evident that whatever is shown by experience to occur in a certain 
proportion (however small) of the whole number of possible cases, is 
not contrary to experience ; (though we are right in disbelieving it, if 
some other supposition respecting the matter in question would be true 
in a greater proportion of the whole number of cases.) What would 
really be contrary to experience, would be the assertion that the event 
had happened more frequently in some large number of times, than 
the same combination had ever been known to occur in that number 
of times; and this alone it is which is improbable, in the sense of in- 
credibility, or, as we have called it, improbability after the fact. 

§ 5, While the defenders of Christianity agahist Hume have thus 
confounded two different meanings of the word improbability, con- 
tending that because improbability of the one kind is not necessarily a . 
ground of disbelief, neither therefore is the other, and that nothing 
supported by credible testimony ought ever to be disbelieved; La- 
place, again, falling into the sarne confusion between the two meanings, 
contends, on the contrary, that because improbability of the one kind 



GROUNDS OF DISBELIEF. 381 

is a sufficient ground for disbelief, the other is so too ; and that what 
is improbable before the fact, is therefore (not indeed in all cases, but 
in a peculiar class of cases which I am about to specify), incredible 
after it. 

If, says Laplace, there are one thousand tickets in a box, and one 
only has been drawn out; then if an eye-witness affirms that the 
number drawn was 79, this, though the chances were 999 in 1000 
against it, is not incredible, because the chances were equally great 
against every other number. But (he continues) if there are in the 
■box 999 black balls and only one white, and the witness affirms that 
the white ball was drawn, this is incredible ; because there was but 
one chance in favor of white, and 999 in favor of some black ball. 

This appears to me entirely fallacious. It is evident, both from 
general reasoning and specific experience, that the white ball will be. 
drawn out exactly as often, in any large number of trials, as the ticket 
No. 79 will ; the two assertions, therefore, are precisely on the same 
level in point of credibility. There is one way of putting the case 
which, I think, must carry conviction to every one. Suppose that the 
thousand balls are numbered, and that the white ball happens to be 
ticketed 79. Then the drawing of the white ball, and the drawing of 
No. 79, are the very same event ; how then can the one be credible, 
the other absolutely incredible 1 A witness sees it drawn, and makes 
his report to us : if he says that No. 79 was drawn, according to 
Laplace, he may be believed; if he says a white ball was drawn, we 
are bound to disbelieve him. Is this rational 1 Is it not clear, on the 
contrary, that the only difference there could be in the credit due to 

,him would arise from moral causes, "namely, from the influence which 
(if the witness knew that there was but one white ball in a thousand) 

_ might be assigned to the greater apparent wonder in the latter case ] 
which to one kind of person would be a temptation to deceive, or to 
take up a hasty impression, while to another, the same thing would be 
a motive for assuring himself more positively of the fact, and would 
therefore actually increase the credit due to his testimony. 

The mathematical reasoning which misled Laplace into this logical 
error, is too long to be here quoted. It is found in the section of his 
Essai PhilosopJdque sur les Probahilites, entitled De la ProhahUite des 
Temoignages, and is founded upon a misapplication, noticed by us in 
^a former place, of his own sixth theorem of the doctrince of chances; a 
theorem which he himself describes as that by which we determine 
the probability that a given effect was produced by one or by another 
of several causes capable of producing it. The substance of his argu- 
ment may be briefly stated as follows : Treating the assertion of the 
witness as the effect, he considers as its two possible causes, the vera- 

. city or mendacity of the witness on the particular occasion, that is, the 
truth or falsity of the fact. According to the theorem, the probability 
that the effect was produced by a particular cause, is as the anteceden'^t 
probability of the cause, multiplied by the probability that the cause, 
if it existed, would produce the given effect. Accordingly (says 
Laplace) in the case of the thousand tickets, the cause mendacity might 
produce any one of 999 untrue statements, while in the case of the 
balls, there being only two statements to make, viz., white or hlaclc, 
and one of these being true, the cause mendacity- could only produce 
one untrue statement : and consequently (the antecedent probability 



^8^ . ,. INDUCTION. 

of mendacity from the character of the witness being supposed the 
same in both cases) mendacity was 999 times less likely to have pro- 
duced the particular assertion made, and is therefore 999 times less 
likely to have existed, in the former case than in the latter. 

The error of this argument seems to be the same which we pointed 
out in a former chapter,* that of applying a theorem, only true of the 
degrees of probability of causes, to the probability of what are neither 
causes nor indications of causes, nor in any other way specially con- 
nected with the effect. The point in question is, the comparative 
probability of two suppositions, that the wdtness lies, and that he speaks 
truth. But these are not two possible causes of the given effect (the 
witness's assertion) ; they are merely two possible qualities of it. The 
truth of the assertion is, indeed, on the supposition of veracity, the 
cause of its being made ; but the falsity of it is not, on any supposition, 
a cause of its being made. It is not incompatible with the dishonesty 
of the witness that he should have spoken the truth : the difference be- 
tween the two suppositions of honesty and dishonesty is, that on the one 
he would certainly speak the truth, while on the other he was just equal- 
ly likely to speak that or anything else. If the falsity of the proposition 
were a real cause for his asserting it, and there were no possible mode 
of accounting for a false assertion but by supposing that it is made pre- 
cisely because of its falsity, I do not see how Laplace's argument could 
be resisted. The case where there are 999 possible false assertions, 
and that in which there is but one, would then present a vast differ- 
ence in the probability that the assertion actually made proceeded from 
falsity ; because in the one case a mendacious witness was sure to as- 
sert the one false fact, in the other there would be an equal chance of 
his asserting any one of the 999. But as it is, the falsity was a mere 
accident of the assertion, not the cause of it ; and even on the suppo- 
sition of dishonesty, the statement is as likely to be true as false, while' 
on the supposition of honesty it is certain to be true. The assertion, " 
therefore, is credible. ^ - ■ 

With these remarks we shall close the discussion of the Grounds of 
Disbelief; and along with it, such exposition as our space admitted, 
and as the writer had it in his power to furnish, of the Logic of Induc- 
tion. . . ,. ' 

; • '• .; " * Supra, p. 324. " ' ' .' * ' 



BOOK IV. 

OF OPERATIONS SUBSIDIARY TO INDUCTION. 



" Clear and distinct ideas are terms which, though familiar and frequent in men's mouths, 
I have reason to think every one who uses does not perl'ectly understand. And possibly it 
is but here and there one who gives himself the trouble to consider them so far as to know 
what he himself or others precisely iriean by them; 1 have, therefore, in most places, 
chose to put determinate or determmed, instead of clear and disiinct, as' more likely to 
direct men's thoughts to my meaning in this matter. "-^Locke's Essay on the Human Un- 
derstanding ; Epistle to the Reader. ' ^ , 

^ " According to this view of the process of the mind, in carrying on general -speculations, 
that Idea which the ancient philosophers considerecl as the essence of an individual, is 
nothing more than the particular quality or qualities in which it resembles other individuals 
of the same class ; and in consequence of which, a generic name is applied to it." — D. 
Stewart, Phil, of the Human Mind, ch. iv., sec. 2. 

" Deux grandes notions philosophiques dominent la theorie fondamentale de la methode 
naturelle proprement dite, savoir, la formation des groupes naturels, et ensuite leur suc- 
cession hierarchique." — Comte, Cours de Philosophic Positive, 42me leqon 



CHAPTER I. ^. ■■'.'••'•'■ 7 



} » ?. -OP OBSERVATION, AND DESCRIPTION. 



■ § 1. The "inquiry which occupied us in the two preceding Booksj 
has conducted us to what appears a satisfactory solution of the principal 
problem of Logic, according to the conception I have formed of the 
science. We have found, that the mental process with which Loo-ic 
is conversant, the operation of investigating truths by means of evidence, 
is always, even when appearances point to a different theory of it, a 
process of induction. And we have particularized the various modes 
of induction, and obtained a clear view of the principles to which it 
must conform, in order to lead to results which can be relied on. 

The consideration of induction, however, does not end with the^ 
direct rules for its performance. Something must be said of those 
other operations of the mind, which are either necessarily presupposed 
in all induction, or are insti'umental to the more difficult and compH- 
cated inductive processes. The present Book will be devoted to the 
consideration of these subsidiary operations : among which our atten- 
tion must first be given to those, which, are indispensable preliminaries 
to all induction whatsoever. 

Induction being merely the extension to a class of cases, of some- 
.thing which has been observed to be true in certain individual instances 
of the class; the first place among the operations subsidiaiy to induc- 
tion, is claimed by Observation. Tliis is not, however, the place to 
lay down rules for making good observers ; nor is it within the com- 
petence of Logic to do so, but of the art of intellectual Education. 
Our business with Obsenation is only in its connexion with the ap- 



384 OPERATIONS SUBSIDIARY TO INDUCTION. 

propriate problem of logic, the estimation of evidence. We have to 
consider, not how or what to observe, but under what conditions ob- 
servation is to be reUed on; what is needful, in order that the fact, 
supposed to be observed, may safely be received as true. 

§ 2. "The answer to this question is very simple, at least in its first 
aspect. The sole condition is, that what is supposed to have been 
observed shall really have been observed ; that it be an observation, 
not an inference. For in almost every act of our perceiving faculties, 
observation and inference are intimately blended. What we are said 
*.o observe is usually a compound result, of which one-tenth maybe 
observation and tihe remaining nine-tenths inference. 

I affirm, for example, that I hear a man's voice. This would pass, 

» in common language, for a direct- perception. All, however, which is 
really perception, is that I hear a sound. That the 'sound is a voice, 

^ and that voice the voice of a man, are not perceptions but inferences. 
.. I affirm, again, that I saw my brother at a certain hour this morning. 
If any proposition concerning a matter of fact would commonly be 
said to be known by the direct testimony of the senses, this surely 
would be so. The truth, however, is far otherwise. I only saw a 
certain colored surface ; or rather 1 had the kind of visual sensations 
which are usually produced by a colored surface ; and from these 

^as marks, known to be such by previous experience, I concluded that I 
. saw my brother. I might have had sensations precisely similar,, when 
my brother was not there. I might have seen some other person 
so nearly resembling him in appearance, as, at the distance, and with 
the degree of attention which I bestowed, to be mistaken for him. I 
might have been asleep and have dreamed that I saw him ; or in a 
sfeate -of' nervous disorder, which brought his image before me in a 
waking hallucination. In all these modes men have been led to be- 
lieve that they saw persons well known to them, who were dead, or 
far distant. If any of these suppositions had been true, the affirmation 
that I saw my brother would have been erroneous ; but whatever was 
matter of direcit perception, namely, the visual sensations, would have 
been real. The inference only would have been ill grounded; I 
should have ascribed those sensations to a wrong cause. 

Innumerable instances might be given, and analyzed in -the same 
mailner, of what are vulgarly called errors of sense. There are none 
of them properly errors of sense ; they are eiToneous inferences from 
sense. When I look at a candle through a multiplying glass, I seem 
to see a dozen candles instead of one : and if the real circumstances of 
the case were skillfully disguised, I might suppose that there were really 
that number; there would be what is called an optical deception. In 
the kaleidoscope there really is that deception : when I look through 
the instrument, instead of what is actually there, namely, a casual ar- 
rangement of colored fragments of glass, I seem to see the same com- 
bination several times repeated in symmetrical arrangement round a 
point. The delusion is of course effected by giving me the same sen- 
sations, which I should have had if such a symmetrical combination had 
really been presented to me. If I cross two. of my fingers, and bring 
any small pbject, a marble for instance, into contact with both, at points 
.not usually touched sinmltanoously by one object, I can hardly, if my 
eyes arc shut, help beheving that there are two marbles instead of one. 



OBSERVATION AND DESCRIPTION. 385 

But it is not my touch in this case, nor my sight in the other, which is 
deceived ; the deception, whether durable or only momentary, is in 
my judgment. From my senses I have only the sensations, and those 
are genuine. Being accustomed to have those or similar sensations 
when, and only when, a certain arrangement of outward objects is 
present to my organs, I have the habit of instantly, when I experience 
the sensations, inferring the existence of that state of outward things. 
This habit has become so powerful, that the inference, performed with 
the speed and certainty of an instinct, is confounded with intuitive 
perceptions. When it is correct, I am unconscious that it ever needed 
proof; even when I know it to be incorrect, I cannot without consid- 
erable effort abstain from making it. In order to be aware that it is 
not made by instinct but by an acquired habit, I am obliged to reflect 
on the slow process by which I learned to judge by the eye of many 
things which I now appear to perceive directly by sight; and on the 
reverse operation performed by persons learning to draw, who with 
difficulty and labor divest themselves of their acquired perceptions, 
and learn afresh to see things as they appear to the eye, instead of see- 
ing them as they really are. 

It would be easy to prolong these illustrations, were there any need 
to expatiate upon a topic so copiously exemplified in various popular 
works. From the examples already given, it is seen sufficiently, that 
the individual facts from which we collect our inductive generalizations 
are scarcely ever obtained by observation alone. Observation extends 
only to the sensations by which we recognize objects ; but the propo- 
sitions "which we make use of, either in science or in common life, 
relate mostly to the objects themselves. In every act of what is called 
observation, there is at least one inference, from the sensations to the 
presence of the object; from the marks or diagnostics to the entire 
phenomenon. And hence, among other consequences, follows the 
seeming paradox, that a general proposition collected from particulars 
is often more certainly true than any one of the particular propositions 
from whicli, by an act of induction, it was inferred. For, each of those 
particular (or rather singular) propositions involved an inference, from 
the impression on the senses to the fact which caused that impression : 
and this inference may have been erroneous in any one of the instances, 
but cannot well have been erroneous in all of them, provided their 
number was sufficient to eliminate chance. The conclusion, therefore, 
that is, the general proposition, may deserve more complete reliance 
than it would be safe to repose in any one of the inductive premisses. 

The logic of observation, then, consists solel}^ in a correct discrimi- 
nation between that, in a result of observation, which has really been 
perceived, and that which is an inference from the perception. What- 
ever portion is inference, is aniena.ble to the rules of induction already 
treated of, and requires no further notice here : the question for us in 
this place is, when all which is inference is taken away, what remains? 
There remain, in the first place, the mind's own feelings or states of 
consciousness, namely, its outward feelings or sensations, and its inward 
feelings — its thoughts, eniotions, and volitions. Whether anything else 
remains, or all else is inference from this ; whether the mind is capable 
of directly perceiving or apprehending anything except states of its 
.own consciousness — is the peculiar problem of the higher or trans- 
cendental metaphysics. But after excluding all questions on which 
3C 



386 OPERATIONS SUBSIDIARY TO INDUCTION. 

metaphysicians differ, it remains true that for most purposes the dis- 
crimination we are called upon practically to exercise is between 
sensations or other feelings, of our own, or of other people; and infer- 
ences drawn from them. And on tlie theory of Observation this is all 
which seems necessary to be said in this place. 

§ 3. If, in the simplest observation, or in what passes for such, there 
is a large part which is not observation but something else ; so in the 
simplest description of an observation, there is, and must always be, 
much more asserted than is contained in the perception itself. We 
cannot describe a fact without implying more than the fact. The per- 
ception is only of one individual thing ; but to describe it is to affirm 
a connexion between it and every other thing which is either denoted 
or connoted by any of the terms used. To begin with an example, 
than which none can be conceived more elementary : I have a sensa- 
tion of sight, and I endeavor to describe it by saying that I see some- 
thing white. In saying this, I do not solely affirm mj sensation ; I 
also class it. I assert a resemblance between the thing I see, and all 
things which I and others are accustomed to call white. I assert that 
it resembles them in the circumstance in which they all resemble one 
another, in that which is the ground of their being called by the name. 
This is not merely one way of describing an observation, but the only 
way. If I would either register my observation for my own future 
use, or make it known for the benefit of others, I must assert a resem- 
blance between the fact which I have observed and something else. 
It is inherent in a description, to be the statement of a resemblance, 
or resemblances. 

These resemblances are not always apprehended directly, by merely 
comparing the object obsei-ved with some other present object, or with 
our recollection of an object which is absent. They are often ascer- 
tained through immediate marks, that is, deductively. In describing 
some new kind of animal, suppose me to say that it measures ten feet in 
length, from the forehead to the extremity of the tail. I did not ascer- 
tain this by the unassisted eye. I had a two-foot rule which I applied 
to the object, and, as we commonly say, measured it; an operation 
which was" not wholly manual, but partly also mathematical, invoh^ng 
the two propositions. Five times two is ten, and Things which are 
equal to the same thing are equal to- one another. Hence, the fact 
that the animal is ten feet long is not an immediate perception, but a 
conclusion from reasoning ; the minor premisses alone being furaished 
by observation of the object. But this does not hinder it from being 
rightly called a description of the animal. 

To pass at once from a very simple to a very complex example : I 
affirm that the earth ia globular. The assertion is not grounded upon 
direct perception ; for the figure of the earth cannot, by us, be directly 
perceived, although the assertion would not be true unless circum- 
stances could be supposed under which its-truth could be so perceived. 
That the form of the earth is globular, is inferred from certain marks, 
as for instance from this, that its shadow thrown upon the moon is cir- 
cular; or this, that on the sea, or any extensive plain, our honzon is 
always a circle ; cither of which marks is incompatible with any other 
than a globular form. I assert further, that the earth is that paiticular 
kind of globe wliich is termed an' oblate spheroid; because it is found 



OBSERVATION. AND DESCRIPTION.- . 387 

by measurement in the direction of the meridian, that the length on the 
surface of the earth which subtends a given angle at its centre, dimin- 
ishes as we recede from the equator and approach the poles. But 
these propositions, that the earth is giohular, and that it is an oblate 
spheroid, assert, each of them, one individual fact ; in its own nature 
capa^ble of being perceived by the senses when the requisite organs 
and the necessary position are supposed, and only not actually per- 
ceived because these organs and that position are wanting. That 
which, if the fact could have been seen, would have been called a de- 
scription of the figure of the earth, may without- impropriety be so 
called when instead of being seen it is inferred. But we could not 
without impropriety call either' of these assertions an induction from . 
facts respecting the earth. They are not general propositions collected 
from particular facts, but particular facts deduced from general prop- 
ositions. They are conclusions obtained deductively, from premisses 
originating in deduction ;. but of these premisses some' were not ob- 
tained by observation of the earth, nor had any peculiar reference to -it. 
If, then, the truth respecting the figure of the earth is not an induc- 
tion, .why should the truth respecting the figure of the earth's orbit be 
so r 'Mr. Whe well contends that it is; although the two cases only 
differ in this, that the form of the orbit was not, like the form of the 
earth itself, deduced by ratiocination from facts which were marks of 
ellipticity, but was got at by boldly guessing that the path was an 
ellipse, and finding afterwards, on examination, that the observations 
were in harmony with the hypothesis. Not only, according to Mr. 
Whewell, is this process of guessing and verifying our guesses induc- 
tion, but it is the whole of induction : no other exposition can be given 
of that logical operation. That he is wrong in the latter assertion, the 
whole of the preceding Book has, I hope, sufiiciently proved ; and that 
even the former of the two contains a large dose of error with but a 
small portion of truth, was attempted to be shown in the second chap- 
ter of the' same Book.* We are now, however, prepared to go more 
into the heart of the question than at that earlier period of our inquiry, 
"and a few words v^ill, I think, suffice to dispel all remaining obscurity. 

§ 4. We observed, in the second chapter, that the proposition "the 
earth moves in an ellipse, "-so far as it only serves for the colligation or 
connecting together of actual observations, (that is, as it only affirms 
that the observed positions of the earth may be correctly represented, 
by as many points in the circumference of an imaginary ellipse,) is not . 
an induction, but a description : it is an induction only when it affirms 
that the intermediate positions, of which there has" been no direct 
observation, would be found to correspond to the remaining points of 
the same elliptic circumference. Now, although this real induction is 
one thing, and the description another, we are in a very difl!e.rent con- 
dition for making the induQtion after we have obtained the description, 
and before it. For inasmuch as the description, like all other descrip- 
tions, contains the assertion of a resemblance between the phenomenon 
described and something else; in' pointing out something which the 
series of observed places of a planet resembles, it points out something 
in which the several places themselves agree.. If tlie series of places 

' . ■ * Supra, pp. 177-183. 



388 OPERATIONS SUBSIDIARY TO INDUCTION. 

corresponds to as many points of an ellipse, the places themselves 
agree in being situated in that ellipse. We have, therefore, by means 
of the description, obtained the requisites for an induction by the 
Method of Agreement. The successive observed places of the earth 
being considered as effects, and its motion as the cause which produces 
them, we find that those effects, that is, those places, agree in the cir- 
cumstance of being in an ellipse. We conclude that the remaining 
effects, the places which have not been observed, agree in the same 
circumstance, and that the law of the motion of the earth is motion in 
an ellipse. 

The Colligation of Facts, therefore, by means of hypotheses, or, as 
Mr. Whewell prefers to say, by means of Conceptions, instead of being, 
as he supposes. Induction itself, takes its proper place among opera- 
tions subsidiary to Induction. All Induction supposes that we have 
previously compared the requisite number of individual instances, and 
ascertained in what circumstances they agree ; the Colligation of Facts 
is no other than this preliminary operation : and the proper office of 
** clear and appropriate ideas," on the necessity of which Mr. Whewell 
has said so much, is to enable us to perform this operation correctly. 
When Kepler, after vainly endeavoring to connect the observed places 
of a planet by various hypotheses of circular motion, at last tried the 
hypothesis of an ellipse and found it answer to the phenomena, what 
he really attempted, first unsuccessfully and at last successfully, was to 
discover the circumstance in which all the observed positions of the 
planet agreed. And when he in like manner connected another set of 
observed facts, the periodic times of the different planets, by the prop- 
osition that the squares of the times are proportional to the cubes of 
the distances, what he did was simply to ascertain the property in 
which the periodic times of all the different planets agreed. 

Since, therefore, all that is true and to the purpose in Mr. Wheweli's 
doctrine of Conceptions might be fully expressed by the more familiar 
term Hypothesis ; and since his Colligation of Facts by means of ap- 
propriate Conceptions j is but the ordinary process of finding by a 
comparison of phenomena, in what consists their agreement or resem- 
blance ; I would willingly have confined myself to those better under- 
stood expressions, and persevered to the end in the same abstinence 
which I have hitherto observed from all ideological discussions ; con- 
sidering the mechanism of our thoughts to be a topic distinct from and 
irrelevant to the principles and rules by which the trustworthiness of 
the results of thinking is to be estimated. Since, however, a work of 
such high pretensions, and, it must also be said, of so much real merit, 
has rested the whole theory of Induction upon such ideological con- 
siderations, it seems necessary for others who follow, to claim for 
themselves and their doctrines whatever position may properly belong 
to them on the same metaphysical ground. And this is the object of 
the succeeding chapter. ... . ^ ., 



ABSTRACTION. 389 

CHAPTER II. 

OF ABSTRACTION, OR THE FORMATION OF CONCEPTIONS. 

§ 1. The metaphysical inquiry into the nature and composition of 
what have been called Abstract Ideas, or in other words, of the notions, 
which answer in the mind to classes and to general names, belongs not 
to Logic, but to a different science, and our purpose does not require 
that we should enter upon it here. We are only concerned ^yith the 
universally acknowledged fact, that such general notions or concep- 
tions do exist. The mind can conceive a multitude of individual things 
as one assemblage or class ; and general names do really suggest to us 
certain ideas or mental representations, otherwise we could not use the 
names with consciousness of a meaning. Whether the idea called up 
by a general name is composed of the various circumstances in which 
all the individuals denoted by the name agree, and of, no others, 
(which is the doctrine of Locke, Brown, and the Conceptualists) ; or 
whether it be the idea of some one of those individuals, clothed in its 
individualizing peculiarities, but with the accompanying knowledge 
that those peculiarities are not properties of the class, (which is the 
doctrine of Berkeley, Dugald Stewart, and the modern Nominalists) ; 
or whether (as held by Mr. Mill), the idea of the class is that of a 
miscellaneous assemblage of individuals belonging to the class ; or 
whether, finally, (what appears to be the truest opinion) it be any one 
or any other of all these, according to the accidental circumstances of 
the case ; certain it is, that some idea or mental conception is suggested 
by a general name, whenever we either hear it or em2:)loy it with con- 
sciousness of a meaning. And this, which we may call if we please a 
general Idea, represents in our minds the whole class of things to which 
the name .is applied. Whenever we think or reason concerning the 
class, we do so by means of this idea. And the voluntary power 
which the mind has, of attending to one part of .what is present to it 
at any •moment, and neglecting another part, enables us to keep our 
reasonings and conclusions respecting the class unaffected by anything 
in the idea or mental image which is not really, or at least which we 
do not really believe to be, common to the whole class. 

We have, then, general conceptions : we can conceive a class as a 
class. But this appears to me to be a fact which Logic, as such, may 
fairly be permitted to take for granted, vdthout any particular exami- 
nation into the manner of it. Logic is concerned with what we can 
know, and with what we can assert, but not with what we can con- 
ceive. We can speak and reason of a number of objects as a class, 
and we can know them to be a class, and know what makes them so ; 
and it is enough for Logic to understand this, and to know that the 
mind has whatever powers this implies, without inquiring what powers 
these are. However, if we are forced to enter upon this foreign 
ground, it cannot but be admitted that there are such things as general 
conceptions, and that when we form a set of phenomena into a class, 
that is, when we compare them with one another to ascertain in what 
they agree, some general conception is implied in this mental opera- 
tion. And inasmuch as such a comparison is a necessary prehminary 



S90 OPERATIONS SUBSIDIARY TO INDUCTION. 

to Induction, it is most true that Induction could, not go on without 
general conceptions. . ' • 

§ 2. But it does not therefore follow that these general conceptions 
must have existed in the mind, previously; to the comparison. It is not 
(as Mr. Whewell seems to suppose,) a law of our intellect, that in- 
comparing thiugs with each other and takirjg note of their agreement 
we merely recognize as realized in -bhe Outward world something that 
we already had in our minds.,.. The conception originally found its 
way to us as the result of such a comparison. It was obtained (in 
metaphysical phrase,) by abstraction from individual things. These, 
things may be things which we perceived or thought of on former 
occasions, but they may also be the things which we are perceiving or 
thinking of on the very occasion. When Kepler compared the observed 
places of the planet Mars, and found that they agreed in being points 
of an elliptic circumference, he applied a general conception which 
was already in his mind, having been derived from his former experi- 
ence. But this is by no means the universal case. When we compare 
several objects and find them to agree in being white, or wKen we 
compare the various species of ruminating animals and find them agree 
in being cloven-footed, we have just as much a general conception in our 
minds as Kepler had in his : we have the conception of " a white thing," 
or the conception of " a cloven-footed animal." But no one supposes 
that we necessarily bring these conceptions with us, and superinduce 
them (to adopt Mr. Whewell's expression*) upon the facts: because in 
these simple cases everybody sees that the very act of comparison which 
ends in our connecting the facts by means of the conception, may be the 
source from which we derive the conception itself If we had never 
seen any white object or had neverseen any cloven-footed animal before, 
we should at the same time and by the same mental act acquire the idea, 
and employ it for the colligation of the observed phenomena. Kepler, 
on the contrary, really had to bring thfe idea with him, and superinduce 
\t upon the facts ; he could not evolve it out of them : if he had not 
already had the idea, he would not have been able to acquire it by a 
comparison of the planet's positions. But this inability was a mere 
accident : the idea of an ellipse could have been acquired ^rom the 
paths of the planets as effectually as from anything else, if the paths 
had not happened to be invisible. If the planot had left a visible 
track,, and we had been so placed that we could see it at the proper 
angle, we might have abstracted our original idea of an ellipse from 
the planetary orbit. - Indeed, every conception which can be made the 
instrument for connecting a set of facts, might have been originally 
evolved from those very facts. The conception is a conception of 
something ; and that which it is a conception of, is really in the facts, 
and might, under some supposable circumstances, or by some suppo- 
sable extension of the faculties which we actually possess, have been 
detected in them. And not only is this always in itself possible, but 
it actually happens, in almost all cases in which the obtaining of the 
right conception is a matter of any considerable difficulty. For if there 
be no new conception required ; if one of those already familiar to 
mankind will serve the purpose, the accident of being the first to 

* Philosophy of the Inductive Sciencea, i., 42. 



ABSTRACTION. ^ 391 

whom the right one occurs, may happen to ahnost anybody ; at least 
in the case of a set of phenomena which the whole scientific world 
are engaged in attempting to connect. The honor, in Kepler's case, 
was that of the accurate, patient, and toilsome calculations hy which 
he compared the resuhs that followed from his different guesses, with 
the observations of Tycho Brahe ; but the. merit was very small of 
guessing an ellipse: the only wonder is that men had not guessed it 
before, nor could they have failed to do" so if there had not existed an 
obstinate a j^riori prejudice that the heavenly bodies 7nust move, if not 
in -a circle, in some combination of circles. 

The, really difficult cases are those in- which the conception, that is 
to create light and order out of darkness and confusion, has to be sought 
for among the very phenomena which it afterwards serves . to arrange. 
Why, according to Mr. Whewell himself, did the ancients fail in dis- 
covering the laws of mechanics^ that is, of equilibrium and of the com- 
munication of motion 1 Because they had not, or at least had not 
clearly, the ideas or conceptions, of pressure and resistance, momen- 
tum, and uniform and accelerating force. And whence could they 
have obtained these ideas, except from the very facts of equilibrium and 
motion? The tardy development of several of the physical sciences, 
for example of optics, electricity, magnetism, and the higher generali- 
zations of chemistry, Mr. Whewell ascribes to the fact that mankind 
had not yet possessed themselves of the Idea of Polarity, that is, the 
idea of opposite properties in Opposite directions. But what was there 
to suggest such an idea, until, by a separate examination of several of 
-these different branches of knowledge, it waS' shown that the facts of 
each of them did present, in some instances at least, the curious phe- 
nomenon of opposite properties in opposite directions ? The thing 
was superficially manifest only in two cases, those of the magnet, and 
of electrified, bodies; and there the conception was encumbered with 
the circumstance of material poles, or fixed points in the body itself, in 
which points this opposition of properties seemed to be inherent. The 
first comparison and abstraction had led only to this conception of poles ; 
and if anything corresponding to that conception had existed in the 
phenomena of chemistry or optics, the difficulty which Mr. Whewell 
justly considers as so great, would have been exti-emely small. The 
obscurity arose from the fact, that the polarities in chemistry and optics 
were distinct species, though of the same genus, with the polarities in 
electricity and magnetism : and that in order to assimilate the phe- 
nomena to one another, it was necessary to compare a polarity without 
poles, such for instance as is exemplified in the polarization of light, 
and the polarity with poles, which we see in the magnet : and to recog- 
nize that these polarities, while different in many other respects, agree 
in the one chai'acter which is expressed by the phrase, opposite prop- 
erties in opposite directions. From the result of such a comparison it 
was that the minds of scientific men formed this new general concep- 
tion ; between which, and the first confused feeling of an analogy 
between some of the phenomena, of light and those of electricity and 
magnetism, there is a long interval, filled up by the labors and more 
or less sagacious suggestions of many superior muids. 

The conceptions, then, wdiich we employ for the colligation and 
methodization of facts, do not develop themselves from within, but are 
impressed upon the mind from without; they are never obtained other- 



392 OPERATIONS SUBSIDARY TO INDUCTION. 

wise than by way of comparison and abstraction, and, in tbe most 
important and the most numerous cases are evolved by abstraction 
from the very phenomena which it is their office to colhgate. I am far 
from wishing to imply that it is not often a very difficult thing to per- 
form this process of abstraction well, or that the success of an indue-- 
tive operation does not, in many cases, principally depend upon the 
skill with which we perform it. Bacon, in his forcible manner, desig- 
nated as one of the principal obstacles to good induction, general con- 
ceptions wrongly formed, " notion es temere a rebus abstractas:" to 
which Mr. Whewell adds, that not only does bad abstraction make bad 
induction, but that in order to perform induction well, we must have 
abstracted well: our general conceptions must be " clear" and " appro- 
priate" to the matter in hand. Nor can it be doubted that, in what 
they thus said, both Bacon and Mr. Whewell, though they expressed 
their meaning vaguely, had a meaning, and a highly important one. 

§ 3. In attempting to show what the difficulty in this matter really 
is, and how it is surmounted, I must beg the reader, once for all, to 
bear this in mind : That although in discussing Mr. Whewell's opin- 
ions I am willing to adopt his language, and to speak, therefore, of 
connecting facts through the instrumentality of a conception, this tech- 
nical phraseology means neither more nor less than what is commonly 
called comparing the facts with one another and determining in what 
they agree. Nor has the technical expression even the advantage of 
being metaphysically correct. The facts are not connected; they 
remain separate facts as they were before. The ideas of the facts may 
become connected, that is, we may be led to think of them together; 
but this consequence is no more than what may be produced by any 
casual association. What really takes place, is, I conceive, more phi- 
losophically expressed by the common word Comparison, than by the 
phrases *'to connect" or "to superinduce." For, as the general con- 
ception is itself obtained by a comparison of particular phenomena, so, 
when obtained, the mode in which we apply it to other phenomena is 
again by comparison^ We compare phenomena with each other to get 
the conception, and we then compare those and other phenomena tvith 
the conception. We get the conception of an animal (for instance) by 
comparing different animals, and when we afterwards see a creature 
resembling an animal, we compare it with our general conception of 
an animal ; and if it agi'ees with that general conception, we include it 
in the class. The conception becomes the type of comparison. 

And we need only consider what comparison is, to see that where 
the objects are more than two, and still more when they are an indefi- 
nite number, a type of some sort is an indispensable condition of the 
comparison. When we have to an-ange and classify a great number of 
objects according to their agreements and differences, we do not make 
a confused attempt to compare all with all. We know that two things 
are as much as the human mind can attend to at a time, and we there- 
fore fix upon one of the objects, either at hazai'd or because it offers in 
a peculiarly striking manner some important character, and, taking this 
as our standard, we compare with it one object after another. If we 
find a second object which presents a remarkable agreement with the 
first, inducing us to class them together, the question instantly arises, 
in what circumstances do they agi'ee ? and to take notice of these cir- 



ABSTRACTION. 393 

cnmstances is already a first stage of abstraction, giving rise to a 
general conception. Having advanced, thus far, when we now take in 
hand a third object, we naturally ask ourselves the question, not merely 
whether this third object agrees with the first, but whether it agrees 
with it in the same circumstances in which the second did 1 in other 
words, whether it agrees with the general conception which has been 
obtained by abstraction from the first and second ] Thus we see the 
tendency of general conceptions, as soon as formed, to substitute them- 
selves as type-s, for whatever individual objects previously answered 
that purpose in our comparisons. We may, perhaps, find that no 
considerable number of other objects agree with this first general con- 
ception; and that we must drop the conception, and beginning again 
with a different individual case, proceed by different comparisons to a 
different general conception. Sometimes, again, we find that the same 
conception will serve, by merely leaving out some of its circumstances ; 
and by this higher effort of abstraction, we obtain a still more general 
conception; as, in the case formerly referred to, we rose from the 
conception of poles to the general conception of opposite properties in 
opposite directions ; or as those South Sea islanders, whose conception 
of a quadruped had been abstracted from hogs (the only animals of that 
description which they had seen), when they afterwards compared that 
conception with other quadrupeds, dropped some of the circumstances, 
and arrived at the more general conception which Europeans associate 
with the term. 

These brief remarks contain, I believe, all that is well-grounded in 
Mr. Whe well's doctrine that the conception by which the mind ar- 
ranges and gives unity to phenomena must be furnished by the mind 
itself, and that we find the right conception by a tentative process, 
trying first one and then another until we hit the mark. It has been 
seen that the conception is not furnished by the mind until it has been 
furnished to the mind ; and that the facts which supply it are some- 
times extraneous facts, but more often the very facts which we are 
attempting to aiTange by it. It is quite true, however, that in endeav- 
oring to arrange the facts, at whatever point we begin, we never ad- 
vance three steps without forming a general conception, more or less 
distinct and precise ; and that this general conception becomes the 
clue which we instantly endeavor to trace through the rest of the facts, 
or rather, becomes the standard with which we thenceforth compare 
them. If we are not satisfied with the agreements which we discover 
among the phenomena by comparing them with this type, or with some 
still more general conception which by an additional stage of abstrac- 
tion we can form from the type : we change our course, and look out 
for other agreements : we recommence the comparison from a different 
starting point, and so generate a different set of general conceptions. 
This is the tentative process which Mr. Whe well speaks of; and this 
it is which suggested the theory that the conception is supplied by the 
mind itself. The diff*erent conceptions which the mind successively 
ti'ies, it either already possessed from its previous experience, or they 
were supplied to it in the very first stage of the corresponding act of 
comparison ; and since, in the subsequent part of the process, the con- 
ception manifested itself as something compared with the phenomena, 
not evolved from them, Mr. Whewell's opinion, though I cannot help 
thinking it erroneous, is not unnatural. 
3D 



394 OPERATIONS SUBSIDIARY TO INDUCTION. 

§ 4. If this be a con'ect account of the instrumentality of general 
conceptions in the comparison which necessarily precedes Induction, 
we shall easily be able to translate into our own language what Mr. 
Whewell means by saying that conceptions, to be subservient to Induc- 
tion, must be " clear" and " appropriate." 

If the conception corresponds to a real agi'eement among the phe- 
nomena ; if the comparison which we have made of a set of objects has 
led us to class .them according to real resemblances and differences ; 
the conception which does this may not indeed be clear, but it cannot 
fail to be appropriate, for some purpose or other. The question of ap- 
propriateness is relative to the particular object we have- in view. As 
soon as, by our comparison, we have ascertained some agreement, somo- 
thing which can be predicated in common of a number of objects; we 
have obtained a basis on which an inductive process is capable of being 
founded. But the agreements, or the ulterior coiisequences to which 
those agreements lead, may be of very different degrees of importance. 

If, for instance, we only compare animals according to their color, 
and class those together which are colored alike, we form the general 
conceptions of a white animal, a black animal, &c., which are concep- 
tions legitimately formed; and if an induction were to be attempted 
concerning the causes of the colors of animals, this comparison would 
be the proper and necessary preparation for such an induction, but 
would not help us towards a knowledge of the laws of any other of the 
; properties of animals: while if, with Cuvier, we compare and class 
them according to the structure of the skeleton, or, with Blainville, 
according to the nature of their outward integuments, the agreements 
and difffirences which are observable in these respects are not only of 
much greater importance in themselves, but are marks of agreements 
and differences in many other most important particulars of the struc- 
ture and mode of life of the animals. If, therefore, the study of their 
structure and habits be our object, the conceptions generated by these 
last comparisons are far morO " appropriate" than those generated by 
the former. Nothing, other than this, can be me'ant by the appropri- 
ateness of a conception. 

When Mr. Whewell says that the ancients, or the schoolmen, or any 
modern philosophers, missed discovering the real law of a phenomenon 
because they applied to it an inappropriate instead of an appropriate 
conception ; he can only mean that in comparing various instances of 
the phenomenon, to ascertain in what those instances agreed, they 
missed the important points of agreement ; and fastened upon such as 
were either imaginary, and no agreements at all, or if real agreements, 
were comparatively ti-ifling, and had no connexion with the phenom- 
enon, the law of which was sought. 

Aristotle^ philosophizing on the subject of motion, remarked that 
certain motions apparently take place spontaneously ; bodies fall to the 
ground, flame ascends, bubbles of air rise in water, &-c. : and these he 
called natural motions ; while others not only never take place without 
external incitement, but even when such incitement is applied, tend 
spontaneously to cease ; Which,, to distinguish them from the former, 
he called violent motions. Now, in comparing the so-called natural 
motions with one another, it appeared to Aristotle that they agreed in 
one circumstance, namely, that the body whic-h moved (or seemed to 
move) spontaneously, was moving tovmrds its oivn /v'/ttce; meaning 



ABSTRACTION. 



395 



tliereby the place from whence it originally came,. or the place where 
a great quantity of matter similar to itself was assembled. In -the other 
class of motions, as when bodies are thrown up in the air, they are, on 
the contrary, moving/rom their own place. Now, this conception of 
a body moving towards its own place may justly be considered inap- 
propriate ; because, though it expresses a chxumstance really found in 
some of the most familiar instances of motion apparently spontaneous, 
yet, first, there are many-other cases of such motion, in which that cir- 
cumstance is absent: the motion, for instance, of the earth and planets. 
Secondly, even when it is present, the motion, on closer examination, 
would often be seen not to be spontaneous: as, when air rises in water, 
it does not rise by its own nature, but is pushed up by the superior 
weight of the water which presses upon it. Finally, there are many 
cases in which the spontaneous motion takes place in the contrary 
direction to what the theory considers as the body's own place ; for 
instance, when a fog rises from a lake, or when water dries up. There 
is, therefore, no agreement, but only a superficial semblance of agree- 
ment, which vanishes on closer inspection : and hence the conception 
is " inappropriate." We may add that, in the case in question, no con- 
ception would be appropriate; there is no agreement which runs 
through all the cases of spontaneous, or apparently spontaneous, mo- 
tion : they cannot be brought under one. law — it is a case of Plurality 
of Causes.* • ' - . • 

§ 5. So much for the first of Mr. Wlie well's conditions, that concep- 
tions must be appropriate. The, second is, that they shall be "clear;" 
and let us consider what this implies. Unless the conception corre- 
sponds to a real agreement, it has a worse defect than that of not being 
clear ; it is not applicable to the case at all. Among the phenomena, 
therefore, which we are attempting to connect by means of the con- 
ception, we must suppose that there really is an agreement, and that 
the conception is a conception o/" that, agreement. In order, then, that 
it should be clear, the only requisite is, that we shall know exactly in 
what the agreement consists; that it shall have been carefully observed, 
and accurately remembered. We are said not to have a clear concep- 
tion of the resemblance among a set of objects, when we have only a 
general feeling that they resemble, without having 'analyzed their 
resemblance, or perceived in what points it consists, and fixed in our 
memory an exact recollection of those points. This want of clearness, 
or, as it may be otherwise called, this vagueness, in the general con- 

* Other examples of inappropriate -conceptions are given by Mr. Whewell {Phil. Lid. Sc. 
ii., 185), as follows: — " Aristotle- and his followers endeavored in vain to account for the 
mechanical relation of forces in. the lever, by applying the inapproprialc geometrical con- 
ceptions of the properties of the circle : they failed in explaining the form of the luminous 
spot made by the sun shining through a hole, because they applied the inappropriate con- 
ception of a circular quality in the sun's light : they speculated to no purpose about the 
elementary composition of bodies, because they assumed the inappropriate conception of 
likeness between the elements and the compound, instead of the genuine notion of elements 
merely determining the qualities of the compound." But in these cases there is more than 
an inappropriate conception ; there is a false conception ; one which has no prototype in 
nature, nothing corresponding to it in facts. This is evident in the last two examples, and 
is equally true in the first; the " properties of the circle" which were referred to, being 
purely fantastical. There' is, therefore, an-error beyond the wrong choice of a principle ol 
generalization ; there is- a false assumption of matters of fact. The attempt is made to re- 
solve certain laws of nature into a more general law, that law being not one which, though 
real, is inappropriate, but one wholly imaginary. 



396 OPERATIONS SUBSIDIARY TO INDUCTION. 

ception, may be owing either to our having no accurate knowledge of 
the objects themselves, or merely to our not having carefully compared 
them. Thus a person may have no clear idea of a ship because he has 
never seen one, or because he remembers but little, and that faintly, 
of what he has seen. Or he may have a perfect knowledge and 
remembrance of many ships of various kinds, frigates among the rest, 
but he may have no clear but only a confused idea of a frigate, because 
he has not compared them sufficiently to have remarked and remem- 
bered in what particular points a frigate differs from some other kind 
of ship. 

It is not, however, necessary, in order to have clear ideas, that we 
should know all the common properties of the things which we class 
together. That would be to have our conceptions of the class com-- 
plete as well as clear. It is sufficient if we never class things together 
without knowing exactly why we do so — without having ascertained 
exactly what agreements we are about to include in our conception ; 
and if, after having thus fixed our conception, we never vary from it, 
never include in the class anything which has not those common 
properties, nor exclude from it anything which has. A clear concep- 
tion means a determinate conception ; one which does not fluctuate, 
which is not ono thing to-day and another to-morrow, but remains fixed 
and invariable, except when, from the progress of our knowledge, or 
the correction of some error, we consciously add to it or alter it. 
A person of clear ideas, is a person who always knows in virtue of 
what properties his classes are constituted ; what attributes are con- 
noted by his general names. 

The principal requisites, therefore, of clear conceptions, are habits 
of attentive observation, an extensive experience, and a memory which 
receives and retains an exact image of what is observed. And in 
proportion as any one has the habit of observing minutely and com- 
paring carefully a particular class of phenomena, and an accurate 
memory for the results of the observation and comparison, so will his 
conceptions of that class of phenomena be clear; provided he has the 
indispensable habit, (naturally, however, resulting from those other 
endowments,) of never using general names without a precise con- 
notation. 

As the clearness of our conceptions chiefly depends upon the care- 
fulness and accuracy of our observing and comparing faculties, so their 
appropriateness, or rather the chance we have of hitting upon the 
appropriate, conception in any case, mainly depends upon the activity 
-of the same faculties. He who by habit, grounded on sufficient natural 
aptitude, has acquired a readiness in accurately observing and com- 
paring phenomena, will perceive so many more agreements and will 
perceive them so much more rapidly than other people, that the chances, 
are much greater of his perceiving, in any instance, the agreement on 
which the important consequences depend. . 

§ 6. We are not, at the same time, to forget, that the agreement 
cannot always be discovered by mere comparison of the very phenom- 
ena in question, without the aid of a conception acquired elsewhere ; 
as in the case, so often referred to, of the planetary orbits. 

The seaich for the agreement of a set of phenomena is in truth 
very similar to the search for a lost or hidden object. At first we place 



NAMING. 397 

ourselves in a sufficiently commanding position, and cast our eyes 
round us, and if we -can see the object, it is well ; if not, we ask our- 
selves mentally what are the places in which it may be hid, in order 
that we may there search for it : and so on, until we imagine the place 
where it really is. And here too we require to have had a previous 
conception, or knowledge, of those different places. As in this fa- 
miliar process, so in the philosophical operation which it illustrates, 
we first endeavor to find the lost object or recognize the common 
attribute, without conjecturally invoking the aid of any pr-eviously 
acquired conception, or in other words, of any hypothesis. Having 
failed in this, we call upon our imagination for some hypothesis of a 
possible place, or a possible point of resemblance, and then look, to 
see whether the facts agree with the conjecture. 

For such cases something more is required than a mind accustomed 
to accurate observation and comparison. It must be a mind stored 
with general conceptions, previously acquired, of the sorts which bear 
affinity to the subject of the particular inquiry. And much will also 
depend upon the natural strength and acquired culture of what has 
been termed the scientific imagination ; upon the faculty possessed of 
mentally arranging known elements into new combinations such as 
have not yet been observed in nature, though not contradictory to any 
known laws. 

But the variety of intellectual habits, the purposes which they serve, 
and the modes in which they may be fostered and cultivated, are con- 
siderations belonging to the Art of Education : a subject far wider 
than Logic, and which the present treatise does not profess to discuss. 
Here, therefore, the present chapter may properly close. It constitutes 
a real digression from the main purpose of this work ; to which no- 
thing would have tempted me but the apparent necessity, in promul- 
gating a view of induction opposed to that which is taught by an 
eminent living writer, of not shrinking from an encounter with him on 
his own ground, but entering sufficiently into the spirit of his views 
to show how much of the difference is apparent and how much real ; 
what is the equivalent expression for his doctrines in my own language ; 
and what are the reasons which lead me, even where the opinions are 
similar, to adopt a different mode of statement. 



CHAPTER III. 

OP NAMING, AS SUBSIDIARY TO INDUCTION. 

§ 1. It does not belong to the present undertaking to dwell on the 
importance of language as a medium of human intercourse, whether 
for pui'poses of sympathy or information. Nor does our design admit 
of more than a passing allusion to that great property of names, upon 
which their functions as an intellectual instrument ai'e, in reality, ulti- 
mately dependent ; their potency as a means of forming, and of rivet- 
ing, associations among our other ideas : a subject on which an able 
thinker has thus written : — 

*' Names are impressions of sense, and as such take the strongest 



398 OPERATIONS SUBSIDIARY TO INDUCTION. 

hold on the mind, and of all other impressions can be most easily Re- 
called and retained in view. They therefore serve to give a point of 
attachment to all the more volatile objects of thought and feeling. 
Impressions, that when past might be dissipated for ever, are, by their 
connexion with language, always within reach. Thoughts, of them- 
selves, are perpetually slipping out of the field of iminediate mental 
vision; but the name abides with us, and the utterance of it restores 
them in a moment. Words are the custodiers of every product of 
mind less impressive than themselves. All extensions- of human knowl- 
edge, all new generalizations, are fixed and spread, even uninten- 
tionally, by the use of words. The child growing up learns, along 
with the vocables of his mother-tongue,, that things which he would 
have believed to be different, are, in important points, the same. 
Without any formal instruction, the language in which we grow up 
teaches us all the common philosophy of the age. It directs us to ob- 
serve and know things. which we should have overlooked ; it supplies 
us with classifications ready made, by which things are arranged (as 
far as the light of by-gone generations admits) with the -objects to 
which they bear the greatest total resemblance. The number of 
general names in a language, and the degree of generality of those 
names, afford a test of the knowledge of the era, and of the intellectual 
insight which is the birth-right of any one born into it."' 

It is not,.however, of the functions of Names, considered generally, 
that we have here to treat, but only of the manner and degree in which 
they are directly instrumental to the investigation of truth -, in other 
words, to the process of induction. 

§ 2. Observation and Abstraction, the operations which formed the 
subject of the two foregoing chapters, are conditions indispensable to 
induction : there can be no induction where they are not. It has been 
imagined that Naming is also a condition equally indispensable. There 
are philosophers who have held that language is not solely, according 
to a phrase generally current, u?i instrument of thought, but the instni- 
ment : that names, or somothing equivalent to them, some species of 
artificial .signs, are necessary to reasoning ; that there could be no in- 
ference, and consequently no induction, without them. But if the 
nature of reasoning was correctly explained in the earlier part of the 
present work, this opinion must be held to' be an exaggeration, though 
of an important truth. If reasoning be from particulars to particulars, 
and if it consist in recognizing one fact as a mark of another, or a 
mark of a mark of another, nothing is required to render reasoning 
possible" except senses, and association: senses, to 'perceive that two 
facts are conjoined; association, as the law by which one of those two 
facts raises up the idea of the other. For these mental phenomena,. as- 
well as fot the belief or expectation which follows, and by which we 
recognize as having taken place, or as about to take place, that of 
which we have perceived a mark, there is evidently no need of lan- 
guage. And this inference of one particular fact firom another is a 
case of induction. It is of this sort of induction that brutes are capable ,* 
it is in this shape that uncultivated minds make almost all their induc- 
tions, and that we all do so in the- cases in which familiar experience 
forces our conclusions upon us without any active process of inquiry 
Dn our pfixt, and in which the belief or expectation follows the 



NAMING. ,, 399 

suggestion of the evidence, with the promptitude and certainty of an 
instinct. 

§ 3. But although inference of an inductive character is possible 
without the use of signs, it could never, without them, be carried much 
beyond the very simple cases which we have just described, and which 
form, in all probability, the limit of the reasonings of those animals to 
whom conventional language is unknown. Without language, or some- 
thing equivalent to it, there could only be as much of reasoning from 
experience, as can take place without the aid of general propositions. 
Now, although in strictness we may reason from past experience to a 
fresh individual case without the intermediate stage of a general pro- 
position, yet without general propositions we should seldom remember 
what experience we have had, and scarcely ever what conclusions that, 
experience will warrant. The division of the inductive process into 
two paits, the first ascertaining what is a mark of the given fact, the 
second whether in the new case that mark exists, is natural, and 
scientifically indispensable. , It is, indeed, in a majority of cases, 
rendered necessary by mere distance of time. The experience by 
which we are to guide our judgments may be other people's expe- 
rience, little of /vvhich can he communicated to us otherwise than by 
language: when it is our own, it is generally experience long "past ; 
unless, therefore, it were recorded by means of artificial signs, little of 
it (except in cases involving our intenser sensations or emotions, or the 
subjects of our daily and hourly contemplations) would be retained in 
the memory. It is hardly necessary to add, that when the inductive 
inference is of any but the most direct and obvious nature — when it 
requires several observations or experiments in varying circumstances, 
and the comparison of one of these with another — it is impossible to 
proceed a step, without the ' artificial memory which words bestow, 
without words, we should, if we had often seen A and B in imme- 
diate and obvious conjunction, expect B whenever we saw A; but to 
discover their conjunction when not obvious, or to determine whether 
it is really constant or only casual, and whether there is reason to ex-. 
pect it under any given change of circumstances, is a process far too 
complex to be performed without some contrivance to make our 
remembrance of our own mental operations accurate. Now, language 
is such a contrivance. Wlien that instrument is called to our aid, the 
difficulty is reduced to that of making our remembrance of the mean- 
ing of words accurate. This being secured, whatever passes through 
our minds may be remembered accurately, by putting it carefully into 
words, and committing the words either to writing or to memory. 

The function of Naming, and particularly of General Names, in In- 
duction, may be recapitulated as follows. Every inductive inference 
which is good at all, is good for a whole class of cases; and, that the 
inference may have any better wan-ant of its con-ectness than the mere 
clinging together of two ideas, a process of 'experimentation and com- 
parison is necessary ; in which the whole class of cases must be 
brought to \dew, and some unifoiTuity in the course of nature evolved 
and ascertained, since the existence of such an uniformity is required 
as a justification for drawing the inference in even a single case. This 
uniformity, therefore, may be ascertained once for all ; and if, being 
ascertained, it can be remembered, it will serve as a formula for 



400 OPERATIONS SUBSIDIARY TO INDUCTION. 

making in particular cases all such inferences as the previous experi- 
ence will warrant. But we can only secure its being remembered, 
or give ourselves even a chance of carrying in our memory any con- 
siderable number of such uniformities, by registeiing them through the 
medium of permanent signs; which (being from the nature of the case, 
signs not of an individual fact but of an uniformity, that is, of an indefi- 
nite number of facts similar to one another) are general signs ; uni- 
versals; general names, and general propositions. 

§ 4. And here I cannot omit to notice an oversight committed by 
some eminent metaphysicians ; who have said that the cause of our 
using general names is the infinite multitude of individual objects, which, 
making it impossible to have a name for each, compels us to make 
one name serve for many. This is a very limited view of the func- 
tion of general names. Even if there were a name for every individual 
object, we should require general names as much as we now do. 
Without them we could not express the result of a single comparison, 
nor record any one of the uniformities existing in nature ; and should 
be hardly better off in respect to Induction than if we had no names 
at all. With none but names of individuals (or, in other words, proper 
names), we might by pronouncing the name, suggest the idea of the ob- 
ject, but we could not assert a single proposition ; except the unmean- 
ing ones formed by predicating two proper names one of another. It is 
only by means of general names that we can convey any information, 
predicate any attribute, even of an individual, much more of a class. 
Rigorously speaking we could get on without any other general names 
than the abstract names of attributes ; all our propositions might be of 
the form " such an individual object possesses such an attribute," or 
" such an attribute is always (or never) conjoined with Such another 
attribute." In fact, however, mankind have always given general 
names to objects as well as attributes, and indeed before attributes : 
but the general names given to objects imply attributes, derive their 
whole meaning from attributes ; and are chiefly usefiil as the language 
by means of which we predicate the attributes which they connote. 

It remains to be considered what principles are to be adhered to in 
giving general names, so that these names, and the general propositions 
in which they fill a place, may conduce most to the purposes of Induc- 
tion. 



, • CHAPTER IV. 

OF THE REQUISITES OF A PHILOSOPHICAL LANGUAGE ; AND THE PRINCIPLES OF 

DEFINITION. 

§ 1. In order that we may possess a language perfectly suitable for 
the investigation and expression of general truths, there are two prin- 
cipal, and several minor, requisites. The first is, that every general 
name should have a meaning, steadily fixed, and precisely determined. 
When, by the fulfilment of this condition, such names as we possess 
are fitted for the due performance of their functions, the next requisite, 
and the second in order of importance, is that we should possess a 



EECIUISITES OF LANGUAGE. 401 

name wherever one is needed ; wherever there is anything to be desig- 
nated by it, which it is of importance to express. 

The former of these requisites is that to which our attention will be 
exclusively directed in the present chapter. 

§ 2. Every general name, then, must have a certain and knowable 
meaning. Now the meaning (as has so often been explained) of a 
general connotative name, resides in the connotation ; in the attribute 
on account of which, and to express which, the name is given. Thus, 
the name animal being given to all things which possess the attributes 
of sensation and voluntary motion, the word connotes those attributes 
exclusively, and they constitute the whole of its meaning. If the 
name be abstract, its denotation is the same with the connotation 
of the corresponding concrete : it designates directly the attribute, 
which the concrete term implies. To give a precise meaning to 
general names is, then, to fix with steadiness the attribute or attributes 
connoted by each concrete general name, and denoted by the corre- 
sponding abstract. Since abstract names, in the order of their creation, 
do not precede but follow concrete ones, as is proved by the etymolo- 
gical fact that they are almost always derived from them ; we may 
consider their meaning as determined by, and dependent upon, the 
meaning of their concrete : and thus the problem of giving a distinct 
meaning to general language, is all included in that of giving a precise 
connotation to all concrete general names. 

This is not difficult in the case of new names ; of the technical terms 
created by philosophic inquirers for the purposes of science or art. 
But when a name is in common use, the difficulty is greater ; the pro- 
blem in this case not being that of choosing a convenient connotation 
for the name, but of ascertaining and fixing the connotation with which 
it is already used. That this can ever be a matter of doubt, is a sort 
of paradox. But the vulgar (including in that term all who have not 
accurate habits of thought) seldom know exactly what assertion they 
intend to make, what common property they mean to express, when 
they apply the same name to a number of different things. All which 
the name expresses with them, when they predicate it of an object, is 
a confused feeling of resemblance between that object and some of the 
other things which they have been accustomed to denote by the name. 
They have applied the name Stone to various objects previously seen ; 
they see a new object, which appears to them something like the 
former, and they call it a stone, without asking themselves in what 
respect it is like, or what mode or degree of resemblance the best 
authorities, or even they themselves, require as a warrant for using 
the name. This rough, general impression of resemblance is, how- 
ever, made up of particular circumstances of resemblance ; and into 
these it is the business of the logician to analyze it ; to ascertain what 
points of resemblance among the different things commonly called by 
the name, have produced upon the common mind this vague feeling of 
likeness ; have given to the things the similarity of aspect, which has 
made them a class, and has caused the same name to be bestowed 
upon them. 

But although general names are imposed by the vulgar without any 
more definite connotation than that of a vague resemblance ; general 
propositions come in time to be made, in which predicates are applied 
3 E 



402 OPERATIONS SUBSIDIARY TO INDUCTION. 

to tliose names, that is, general assertions are made concerning the 
w7iole of the things which are denoted by the name. And since by each 
of these propositions some attribute, more or less precisely conceived, 
is of course predicated, the idea of these various attributes thus be- 
comes associated w^ith the name, and in a sort of uncertain v^ay it 
comes to connote them ; there is a hesitation to apply the name in any 
new case in which any of the attributes familiarly predicated of the 
class does not exist. And thus to common minds, the propositions 
which they are in the habit of hearing or uttering concerning a class, 
make up in a loose way a sort of connotation for the class-name. Let 
us take, for instance, the word Civilized. How few could be found, 
even among the most educated persons, who would undertake to say 
exactly what the term Civilized connotes. Yet there is a feeling in 
the minds of all who use it, that they are using it with a meaning; 
and this meaning is made up, in a confused manner, of everything 
whicli they have heard or read that civilized men or civilized commu- 
nities, are, or should be. 

It is at this stage, probably, in the progress of a concrete name, that 
the corresponding abstract name generally comes into use. Under 
the notion that the concrete name must of course convey a meaning, 
or in other words, that there is some property common, to all things 
which it denotes, men give a name to this common property ; from 
the concrete Civilized, they form the abstract Civilization. But since 
most people have never compared the different things which are called 
by the concrete name, in such a manner as to ascertain what- proper- 
ties these things have in common, or whether they have any ; each is 
thrown back upon the marks by which he himself has been accustomed 
to be guided in his application of the term : and these being merely 
vague hearsays and current phrases, are not the same in any two per- 
sons, nor in the same person at different times. Hence the word (as 
Civilization, for example,) which professes to be the designation of the 
unknown common property, conveys scarcely to any two minds the 
same idea. No two persons agree in the things they predicate of it ; 
and when it is itself predicated of anything, no other person knows, 
nor does the speaker himself know with precision, what he means 
to assert. Many other words which could be named, as the word 
ItonoT, or the word gentleman^ exemplify this uncertainty still more 
strikingly. 

It needs scarcely be observed, that general propositions of which 
tio one can tell exactly what they assert, cannot possibly have been 
brought to the test of a correct induction. Whether a name is to be 
used as an instrument of thinking, or as a means of communicating the 
result of thought, it is imperative to determine exactly the attribute or 
attributes which it is to express : to give it, in short, a fixed and ascer- 
tained connotation. 

§ 3. It would, however, be a complete misunderstanding of the 
proper office of a logician, in dealing with terms already in use, if he 
were to think that because a name has not at present an ascertained 
connotation, it is competent to any one to give it such a connotation at 
his own choice. The meaning of a term actually in use is not an ar- 
bitrary quantity to be fixed, but an unknown quantity to be sought. 

In the first place, it is obviously desirable to avail ourselves, as far 



REaUISITES OF LANGUAGE. 403 

as possible, of the associations already connected with the name ; not 
enjoining the employment of it in a manner which conflicts with all 
previous habits, and especially not so as to require the rupture of those 
strongest of all associations between names, which are created by 
familiarity with propositions in which they are predicated of one another. 
A philosopher would have little chance of having his example followed, 
if he were to give such a meaning to his terms as should require us to 
call the North American Indians a civilized people, or the higher classes 
in France or England savages ; or to say that civilized people live by 
hunting, and savages by agriculture. Were there no other reason, the 
extreme difficulty of effecting so complete a revolution in speech, would 
be more than a sufficient one. The endeavor should be, that all gen- 
erally received propositions into which the term enters, should be at 
least as ti'ue after its meaning is fixed, as they were before ; and that 
the concrete name (therefore) should not receive such a connotation as 
shall prevent it from denoting things which, in common language, it is 
cun'ently affirmed of. The fixed and precise connotation which it 
receives, should not be in deviation from, but in agreement (as far as 
it goes) with, the vague and fluctuating connotation which the term 
already had. 

To fix the connotation of a concrete name, or the denotation of the 
corresponding abstract, is to define the name. When this can be done 
without rendering any received assertions inadmissible, the name can 
be defined in accordance with its received use, which is vulgarly called 
defining not the name but the thing. What is meant by the improper 
expression of defining a thing (or rather a class of things — for nobody 
talks of defining an individual), is to define the name, subject to the 
condition that it shall denote those things. This, of course, supposes 
a comparison of the things, feature by feature and property by prop- 
erty, to ascertain what attributes they agree in ; and not unfrequently 
an operation still more strictly inductive, for the purpose of ascertain- 
ing sonie unobvious agreement which is the cause of the obvious 
agreements. 

For, in order to give a connotation to a name consistently with its 
denoting certain objects, we have to make our selection from among 
the various attributes in which those objects agree. To ascertain in 
what they do agree is, therefore, the first logical operation requisite. 
Wlien this has been done as far as is necessary or practicable, the 
question arises, which of these common attributes shall be selected to 
be associated with the name. For if the class which the name denotes 
be a Kind, the common properties are innumerable ; and even if not, 
they are often extremely numerous. Our choice is first limited by the 
preference to be given to properties which are well known, and 
familiarly predicated of the class ; but even these are often too numer- 
ous to be all included in the definition, and, besides, the properties 
most generally known may not be those which serve best to mark out 
the class from all others. We should therefore select from among the 
common properties (if among them any such are to be found), those 
on which it has been ascertained by experience, or proved by deduc- 
tion, that many others depend ; or at least which are sure marks of 
them, and from whence, therefore, many others will follow by inference. 
We thus see that to frame a good definition of a name already in use, 
is not a matter of choice but of discussion, and discussion not merely 



404 OPERATIONS SUBSIDIARY TO INDUCTION. 

respecting the usage of language, but respecting the properties of things, 
and even the origin of those properties. And hence every enlarge- 
ment of our knowledge of the objects to which the name is applied, 
is liable to suggest an improvement in the definition. It is impossible 
to frame a perfect set of definitions on any subject, until the theory of 
the subject is perfect : and as science makes progress, its definitions 
are also progressive. 

§ 4. The discussion of Definitions, in so far as it does not turn upon 
the use of words, but upon the properties of things, Mr. Whewell calls 
the Explication of Conceptions. The act of ascertaining, better than 
before, in what particulars any phenomena which are classed together 
agi'ee, Mr. Whewell in his technical phraseology calls, unfolding the 
general conception in virtue of which they are so classed. Making 
allowance for what appears to me the darkening and misleading ten- 
dency of this mode of expression, several of his remarks are so much 
to the purpose, that I shall take the liberty of transcribing them. 

He observes,* that many of the controversies which have had an 
important share in the formation of the existing body of science, have 
" assumed the form of a battle of Definitions. For example, the 
inquiry concerning the laws of falling bodies, led to the question 
w^iether the proper definition of a uniform force is that it generates a 
velocity proportional to the sjpace ^on\ rest, or to the time. The con- 
troversy of the vis viva was, what was the proper definition of the 
measure of force. A principal question in the classification of minerals 
is, what is the definition of a mineral species. Physiologists have 
endeavored to throw light on their subject by defining organization, 
or some similar teiTn." Questions of the same nature are still open 
respecting the definitions of Specific Heat, Latent Heat, Chemical 
Combination, and Solution. 

*' It is very important for us to observe, that these controversies 
have never been questions of insulated and arbitrary definitions, as 
men seem often tempted to imagine them to have been. In all cases 
there is a tacit assumption of some proposition which is to be expressed 
by means of the definition and which gives it its importance. The 
dispute concerning the definition thus acquires a real value, and be- 
comes a question concerning true and false. Thus in the discussion 
of the question, What is a uniform force ] it was taken for granted 
that gravity is a uniform force. In the debate of the vis viva, it was 
assumed that in the mutual action of bodies the whole effect of the 
force is unchanged. In the zoological definition of species (that it 
consists of individuals which have, or may have, sprung from the same 
parents,) it is presumed that individuals so related resemble each othei 
more than those which are excluded by such a definition ; or, perhaps, 
that species so defined have permanent and definite differences. A 
definition of organization, or of some other term, which was not em- 
ployed to express some principle, would be of no value. 

" The establishment, therefore, of a right definition of a term, may 
be a useful step in the explication of our conceptions ; but this will bo 
the case then only when we have under our consideration some prop- 
osition in which the term is employed. For then the question really 

♦ Phil, of the Ind. Sc. \l, 177-9. 



REaUlSITES OF LANGUAGE. 405 

is, how the conception shall be understood and defined in order that 
the proposition may be true." 

" To unfold our conceptions by means of definitions has never been 
serviceable to science, except v/hen it has been associated with an 
immediate use of the definitions. The endeavor to define a Unifomi 
Force was combined with the assertion that gravity is a uniform force : 
the attempt to define Accelerating Force was immediately followed by 
the doctrine that accelerating forces may be compounded : the process 
of defining Momentum was connected with the principle that momenta 
gained and lost are equal : naturalists would have given in vain the 
definition of Species which we have quoted, if they had not also given 

the characters of species so separated Definition may be the best 

mode of explaining our conception, but that which alone makes it 
worth while to explain it in any mode, is the opportunity of using it in 
the expression of truth. When a definition is propounded to us as a 
useful step in knowledge, we are always entitled to ask what principle 
it serves to enunciate." 

In giving an exact connotation to the phrase, " an uniform force," 
philosophers (as Mr. Whewell observes) restricted themselves by the 
condition, that the phrase should continue to denote gravity. The 
discussion, therefore, respecting the definition, resolved itself into this 
question. What is there of an uniform nature in the motions produced 
by gravity] By observations and comparisons it was found, that what 
was uniform in those motions was the ratio of the velocity required to 
the time elapsed ; equal velocities being added in equal terms. An 
uniform force, therefore, was defined, a force which adds equal veloci- 
ties in equal times. So, again, in defining momentum. It was already 
a received doctrine, that when two objects impinge upon one another, 
the momentum lost by the one is equal to that gained by the other. 
This proposition it was deemed necessary to preserve, not however 
from the motive (which operates in many other cases) that it was firmly 
fixed in popular belief; for the proposition in question had never been 
heard of by any but scientific men. But it was felt to contain a ti'uth : 
even a superficial observation of the phenomena left no doubt that in 
the propagation of motion from one body to another, there was some- 
thing of which the one body gained precisely what the other lost; and 
the word momentum had been invented to express this unknown some- 
thing. In the settlement, therefore, of the definition of momentum, was 
contained the determination of the question. What is that of which a 
body, when it sets another body in motion, loses exactly as much as it 
communicates] And when experiment had shown that this something 
was the product of the velocity of the body by its mass, or quantity of 
matter, this became the definition of momentum. 

Mr. Wliewell very justly adds,* ■" The business of definition is part 

of the business of discovery To define, so that our definition 

shall have any scientific value, requires no small portion of that saga- 
city by which truth is detected When it has been clearly seen 

what ought to be our definition, it must be pretty well known what 
truth we have to state. The definition, as well as the discovery, sup- 
poses a decided step in our knowledge to have been made. The 
writers on Logic, in the middle ages, made Definition the last stage in' 

* Phil, of the Ind. Sc, ii., 181-2. 



406 OPERATIONS SUBSIDIARY TO INDUCTION. 

the progress of knowledge ; and in this arrangement at least, the his- 
tory of science, and the philosophy derived from the history, confirm 
their speculative views." For in order to Judge how the name which 
denotes a class may best be defined, we must know all the properties 
common to the class, and all the relations of causation or dependence 
among those properties. , 

If the properties which are fittest to be selected as marks of other 
common properties are also obvious and familiar, and especially if they 
bear a gieat part in producing that general and superficial air of re- 
semblance which was the original inducement to the formation of the 
class, the definition will then be most felicitous. But it is often neces- 
sary to define the class by some property not familiarly known, provi- 
ded that property be the best mark of those which are known. M. de 
Blainville, for instance, has founded his definition of life, upon the 
process of decomposition and recomposition which incessantly goes on 
in every living body, so that the particles composing it are never for 
two instants the same. This is by no means one of the most obvious 
properties of living bodies ; it might escape altogether the notice of an 
unscientific observer. Yet great authorities (independently of M. de 
Blainville, who is himself a first-rate authority,) have thought, seem- 
ingly with much reason, that no other property so well answers the 
conditions required for the definition. 

§ 5. Having laid down the principles which ought for the most part 
to be observed in attempting to give a precise connotation to a term in 
use, I must now add, that it is not always practicable to adhere W 
those principles, and that even when practicable, it is occasionally not 
desirable. Cases in which it is impossible to comply with all the con- 
ditions of a precise definition of a name in agreement with usage, occur 
very frequently. There is often no one connotation capable of being 
given to a word, so that it shall still denote everything it is accustomed 
to denote ; or that all the propositions into which it is accustomed to 
enter, and which have any foundation in truth, shall remain true. In- 
dependently of accidental ambiguities, in which the different meanings 
have no connexion with one another; it continually happens that a 
word is used in two or more senses derived from each other, but yet 
radically distinct. So long as a term is vague, that is, so long as its 
connotation is not ascertained and permanently fixed, it is constantly 
liable to be applied by extension from one thing to another, until it 
reaches things which have little, or even no, resemblance to those which 
were first designated by it. 

Suppose, says Dugald Stewart, in his PhilosopJiical Essays* " that 
the letters A, B, C, D, E, denote a series of objects ; that A possesses 
some one quality in common with B ; B a quality in common with C ; 
C a quality in common with D ; D a quality in common vnth E ; while 
at the same time, no quality can be found which belongs in common 
to any three objects in the series. Is it not conceivable, that the affin- 
ity between A and B may produce a transference of the name of the 
first to the second ; and that, in consequence of the other affinities 
which connect the remaining objects together, the same name may pass 
in succession from B to C ; from C to D ; and from D to E ? In this 

* P. 217, 4to edition. 



EEQUISITES OF LANGUAGE. 407 

manner a common appellation will arise between A and E, although tlie 
two objects may, in their nature and properties, be so widely distant 
from each other, that no stretch of imagination can conceive how the 
tlioughts were led from the former to the latter. The transitions, never- 
theless, may have been all so easy and gradual, that, were they suc- 
cessfully detected by the fortunate ingenuity of a theorist, we should 
instantly recognize, not only the verisimilitude, but the truth of the 
conjecture : in the same way as we admit, with the confidence of intu- 
itive conviction, the certainty of the well-known etymological process 
which connects the Latin preposition e or ex with the English substan- 
tive stranger, the moment that the intermediate links of the chain are 
submitted to our examination."* 

The applications which a word acquires by this gradual extension 
of it from one set of objects to another, Stewart, adopting an expres- 
sion from Mr. Payne Knight, calls it transitive applications ; and after 
briefly illustrating such of them as are the result of local or casual 
associations, he proceeds as follows : — f 

" ]^ut although by far the gi-eater part of the transitive or derivative 
applications of words depend on casual and unaccountable caprices of 
the feelings or the fancy, there are certain cases in which they open a 
very mteresting field of philosophical speculation. Such are those, in 
which an analogous transference of the corresponding term may be 
remarked universally, or very generally, in other languages ; and in 
which, of course, the uniformity of the result must be ascribed to the 
essential principles of the human frame. Even in such cases, however, 
it will by no means be always found, on examination, that the various 
applications of the same term have arisen from any common quality 
or qualities in the objects to which they relate. In the greater number 
of instances, they may be traced to some natural and universal asso- 
ciations of ideas, founded in the common faculties, common organs, 

and common condition of the human race According to the 

different degrees of intimacy and strength in the associations on which 
the transitions of language are founded, very different effects may 
be expected to arise. Wliere the association is slight and casual, 
the several meanings will remain distinct from each other, and will 
often, in process of time, assume the appearance of capricious varieties 
in the use of the same arbitrary sign. Where the association is so 
natural and habitual, as to become virtually indissoluble, the transitive 
meanings will coalesce into one complex conception ; and every new 
transition will become a more comprehensive generalization of the term 
in question.'" 

I solicit particular attention to the law of mind expressed in the last 
sentence, and which is the source of the perplexity so often experienced 
in detecting these transitions of meaning. Ignorance of that law is 
the shoal upon which some of the greatest intellects which have adorned 
the human race have been wrecked. The inquiries of Plato into the 
definitions of some of the most general terms of moral speculation, 
are characterized by Bacon as a far nearer approach to a true induc- 

* " E, ex, extra, extraneus, etranger, stranger." 

Another etymological example sometimes cited is the derivation of the English uvcle 
from the Latin aviLs. It is scarcely possible for two words to bear fewer outward marks 
of relationship, yet there is but one step between them ; avtbs, avunculus, uncle. 

So pilgrim from ager : per agrum, peragrinvs, peregrinus, pellegrino, pilgrim. 

t Pp. 226-7. 



408 OPERATIONS SUBSIDIARY TO INDUCTION. 

tive method than is elsewhere to be found among the ancients, and are, 
indeed, almost perfect examples of the preparatory process of com- 
parison and abstraction ; but, from being unaware of the law just 
mentioned, he wasted the powers of this great logical instrument upon 
inquiries in which it could realize no result, since the phenomena 
whose common properties he so elaborately endeavored to detect, had 
not really any common properties. Bacon himself fell into the same 
error in his speculations on the nature of Heat, in which it is impossi- 
ble not to think, with Mr. Whewell, that he confounded under the 
name hot, classes of phenomena which had no property in common.* 
Dugald Stewart certainly overstates the matter when he speaks of "a 
prejudice which has descended to modern times from the scholastic 
ages, that when a word admits of a variety of significations, these 
different significations must all be species of the same genus, and 
must consequently include some essential idea common to every indi- 
vidual to which the generic term can be applied :"t for both Aristotle 
and his followers were well aware that there are such things as am- 
biguities of language, and delighted in distinguishing them. But they 
never suspected ambiguity in the cases where (as Stewart remarks) 
the association on which the transition of meaning was founded is so 
natural and habitual, that the two meanings blend together in the mind, 
and a real transition becomes an apparent generalization. Accordingly 
they wasted an infinity of pains in endeavoring to find a definition 
which would serve for several distinct meanings at once : as in an in- 
stance noticed by Stewart himself, that of " causation ; the ambiguity 
of the word which, in the Greek language, corresponds to the English 
word cause, having suggested to them the vain attempt of tracing the 
common idea which, in the case of any effect, belongs to the efficient, 
to the matter, to xkiQ form, and to the end. The idle generalities" (he 
adds) " we meet with in other philosophers, about the ideas of the good, 
the jit, and the becoming, have taken their rise from the same undue 
influence of popular epithets on the speculations of the learned. "| 

Among words which have undergone so many successive transitions 
of meaning that every trace of a property common to all the things 
they are applied to, or at least common and also peculiar to those 
things, has been lost, Stewart considers the word Beautiful to be one. 
And (without attempting to decide a question which in no respect 
belongs to logic) I cannot but feel, with him, considerable doubt, 
whether the word beautiful connotes the same property when we 
speak of a beautiful color, a beautiful face, a beautiful action, a beauti- 
ful character, and a beautiful solution of a mathematical problem. The 
word v/as doubtless extended from one of these objects to another on 
account of some resemblance between them, or, more probably, 
between the emotions they excited ; but, by this progressive extension, 
it has at last reached things very remote from those objects of sight to 
which there is no doubt that it was first appropriated ; and it is at 
least questionable whether there is now any property common to all 
the things we call beautiful, except the property of agreeableness, . 
which the term certainly does connote, but which cannot be all that we 
in any instance intend to express by it, since there are many agreeable 
thingi which we never call beautiful. If such be the case, it is 

* History of the Inductive Sciences, i., 48. 

t Philosophical Essays, p. 214. t Ibid, p. 215. 



REayiSITES OF LANGUAGE. 409 

impossible to give to the word beautiful any fixed connotation, such 
that it shall denote all the objects which in common use it now denotes, 
but no others. A fixed connotation, however, it ought to have ; for, 
so long as it has not, it is unfit to be used as a scientific term, and, 
even as a word in popular use, must be a perpetual source of false 
analogies and erroneous generalizations. 

This then, constitutes a case in exemplification of our remark, that 
even when there is a property common to all the things denoted by a 
name, to erect that property into the definition and exclusive connota- 
tion of the name is not always desirable. The various things called 
beautiful unquestionably resemble one another in being agreeable; 
but to make this the definition of beauty, and so extend the word 
Beautiful to all agreeable things, would be to drop altogether a portion 
of meaning which the word really, although indistinctly, conveys, and 
to do what depends upon us towards causing those qualities of the 
objects which the word previously, though vaguely, pointed at, to be 
overlooked and forgotten. It is better, in such a case, to give a fixed 
connotation to the term by restricting, than by extending its use ; rather 
excluding from the epithet beautiful some things to which it is com- 
monly considered applicable, than leaving out of its connotation any 
of the qualities by which, though occasionally lost sight of, the general 
mind may have been habitually guided in the commonest and most 
interesting applications of the term. For there is no question that 
when people call anything beautifhl, they think they are asserting more 
than that it is merely agreeable. They think they are ascribing a 
peculiar sort of agreeableness, analogous to that which they find in 
some other of the things to which they are accustomed to apply the 
same name. If, therefore, there be any peculiar sort of agreeableness 
which is common, though not to all, yet to the principal things which 
are called beautiful, it is better to limit the denotation of the term to 
those things, than to leave that kind of quality without a term to con- 
note it, and thereby divert attention fi:om its peculiarities. 

§ 6. The last remark exemplifies a rule of terminology, which is of 
great importance, and which has hardly yet been recognized as a rule, 
but by a few thinkers of the present generation. In attempting to 
rectify the use of a vague term by giving it a fixed connotation, we 
must take care not to discard (unless advisedly, and on the ground of 
a deeper knowledge of the subject,) any portion of the connotation 
which the word, in however indistinct a manner, previously carried 
with it. For otherwise language loses one of its inherent and most 
valuable properties, that of being the conservator of ancient experi- 
ence ; the keeper-alive of those thoughts and observations of by-gone 
ages, which may be alien to the tendencies of the passing time. This 
liinction of language is so often overlooked or undervalued, that a few 
observations upon it appear to be extremely required. 

Even when the connotation of a term has been accm^ately fixed, and 
still more if it has been left in the state of a vague unanalyzed feeling 
of resemblance ; there is a constant tendency in the word, through 
familiar use, to part with a portion of its connotation. It is a well- 
known law of the mind, that a word originally associated with a very 
complex cluster of ideas, is far from calling up all those ideas in the 
mind, every time the word is used : it calls up only one or two, from 
3F 



410 OPERATIONS SUBSIDIARY TO INDUCTION. 

which the mind runs on by fresh associations to another set of ideas, 
without waiting for the suggestion of the remainder of the complex 
cluster. If this were not the case, our processes of thought could not 
take place with anything like the rapidity which we know they possess. 
Very often, indeed, when we are employing a word in our mental 
operations, we are so far fi'om waiting until the complex idea which 
corresponds to the meaning of the word is consciously brought before 
us in all its parts, that we run on to new trains of ideas by the other 
associations which the mere word excites, without having realized in 
our imagination any part whatever of the meaning : thus using the 
word, and even using it well and accurately, and carrying on impor- 
tant processes of reasoning by means of it, in an almost mechanical 
manner : so much so, that some philosophers, generalizing from an 
extreme case, have fancied that all reasoning is but the mechanical 
use of a set of terms according to a certain form. We may discuss 
and settle the most important interests of towns or nations, by the 
application of general theorems or practical maxims previously laid 
dowm, without having had consciously suggested to us, once in the 
whole process, the houses and green fields, the thronged market- 
places and domestic hearths, of which not only those towns and nations 
consist, but which the words town and nation confessedly mean. 

Since, then, general names come in this manner to be used (and 
even to do a portion of their work well) without suggesting to the 
mind the whole of their meaning, and often with the suggestion of a 
very small, or no part at all of that meaning ; we cannot wonder that 
words so used come in time to be no longer capable of suggesting any 
other of the ideas appropriated to them, than those with which the 
association is most immediate and strongest, or most kept up by the 
incidents of life : the remainder being lost altogether ; unless the 
mind, by often consciously dwelling upon them, keeps up the associa- 
tion. Words naturally retain much more of their meaning to persons 
of active imagination, who habitually represent to themselves things in 
the concrete, with the detail which belongs to them in the actual world. 
To minds of a different description, the only antidote to this corruption 
of language is predication. The habit of predicating of the name, all 
the various properties which it originally connoted, keeps up the asso- 
ciation between the name and those properties. 

But in order that it may do so, it is necessary that the predicates 
should themselves retain their association with the properties which 
they severally connote. For the propositions cannot keep the mean- 
ing of the words alive, if the meaning of the propositions themselves 
should die. And nothing is more common than for propositions to be 
mechanically repeated, mechanically retained in the memory, and 
their truth entirely assented to and relied upon, while yet they can'y 
no meaning distinctly home to the mind; and while the matter of fact 
or law of nature which they originally expressed, is as much lost sight 
of, and practically disregarded, as if it never had been heard of at all. 
In those subjects which are at the same time familiar and complicated, 
and especially in those which are so much of both these things as moral 
and social subjects are, it is matter of common remark how many im- 
portant propositions are believed and repeated from habit, while no 
account could be given, and no sense is practically manifested, of the 
truths which they convey. Hence it is, that the traditional maxims of 



REaUISITES OF LANGUAGE. 411 

old experience, though seldom questioned, have so little effect on the 
conduct of life ; because their meaning is never, by most persons, 
really felt, until personal experience has brought it home. And thus 
also it is that so many principles of religion, ethics, and even politics, 
so full of meaning and reality to first converts, have manifested (after 
the association of that meaning with the verbal formulas has ceased to 
be kept up by the controversies w^hich accompanied their first intro- 
duction) a tendency to degenerate rapidly into lifeless dogmas; which 
tendency, all the efforts of an education expressly and skillfully 
directed to keeping the moaning alive, are barely found sufficient to 
counteract. 

Considering, then, that the human mind, in different generations, 
occupies itself with different things, and in one age is led by the cir- 
cumstances which surround it to fix more of its attention upon one of 
the properties of a thing, in another age »pon another ; it is natural 
and inevitable that in every age a certain portion of our recorded and 
traditional knowledge, not being continually suggested by the pursuits 
and inquiries with which mankind are at that time engrossed, should 
fall asleep, as it were, and fade from the memory. It would be utterly 
lost, if the propositions or formulas, the results of the previous expe- 
rience, did not remain, and continue to be repeated and believed in, 
as forms of words it may be, but of words that once really conveyed, 
and are still supposed to convey, a meaning : which meaning, though 
suspended, may be historically traced, and when suggested, is recog- 
nized by minds of the necessary endowments as being still matter ot 
fact, or truth. While the formulae remain, the meaning may at any 
time revive ; and as on the one hand the formulae progressively lose 
the meaning they were intended to convey, so on the other, when this 
forgetfulness has reached its height and begun to produce consequences 
of obvious evil, minds arise which from the contemplation of the for- 
mulae rediscover the whole truth, and announce it again to mankind, 
not as a discovery, but as the meaning of that which they have long 
been taught, and still profess to believe. 

Thus there is a perpetual oscillation in spiritual truths, and in 
spiritual doctrines of any significance, even when not truths. Their 
meaning is almost always in a process either of being lost or of being 
recovered ; a remark upon which all history is a comment. Wlioever 
has attended to the history of the more serious convictions of mankind 
— of the opinions by which the general conduct of their lives is, or as 
they conceive ought to be, more especially regulated— is aware that 
while recognizing verbally the very same doctrines, they attach to 
them at different periods a greater or a less quantity, and even a differ- 
ent kind, of meaning. The words in their original acceptation con- 
noted, and the propositions expressed, a complication of outward facts 
and inward feelings, to different portions of which the general mind is 
more particularly alive in different generations of mankind. To com- 
mon minds, only that portion of the meaning is in each generation 
suggested, of which that generation possesses the counterpart in its 
own habitual experience. But the words and propositions lie ready, 
to suggest to any mind duly prepared, the remainder of the meaning. 
Such individual minds are almost always to be found : and the lost 
meaning, revived by them, again by degrees works its way into the 
general mind. , 



412 OPERATIONS SUBSIDIARY TO INDUCTION. 

There s scarcely anything which can materially retard the arrival 
of this salutary reaction, except the shallov/ conceptions and incautious 
proceedings of mere logicians. It sometimes happens that towards 
the close of the downward period, when the words have lost part of 
their significance and have not yet begun to recover it, persons arise 
whose leading and favorite idea is the importance of clear conceptions 
and precise thought, and the necessity, therefore, of definite language. 
These persons, in examining the old formulas, easily perceive that 
words are used in them without a meaning ; and if they are not the 
sort of persons who are capable of rediscovering the lost signification, 
they naturally enough dismiss the formula, and define the name 
without any reference to it. In so doing they fasten down the name 
to what it connotes in common use at the time when it conveys the 
smallest quantity of meaning ; and introduce the practice of employing 
it, consistently and uniforifnly, according to that connotation. The 
word in this way acquires an extent of denotation far beyond what it 
had before ; it becomes extended to many things to which it was 
previously, in appearance capriciously, refused. Of the propositions 
in which it was formerly used, those which were true in virtue of the 
forgotten part of its meaning are now, by the clearer light which the 
definition diffuses, seen not to be true according to the definition ; 
which, however, is the recognized and sufficiently correct expression 
of all that is perceived to be in the mind of any one by whom the terra 
is used at the present day. The ancient formulas are consequently 
treated as prejudices; and people are no longer taught, as before, 
though not to understand them, yet to believe that there is truth in 
them. They no longer remain in men's minds surrounded by respect, 
and ready at any time to suggest their original meaning. The truths 
which they convey are not only, under these circumstances, redis- 
covered far more slowly, but, when rediscovered, the prejudice with 
which novelties are regarded is now, in some degree at least, against 
them, instead of being on their side. 

An example may make these remarks more intelligible. In all ages, 
except where moral speculation has been silenced by outward compul- 
sion, or where the feelings which prompt to it have received full satis- 
faction from an established faith unhesitatingly acquiesced in, one of 
the subjects which have most occupied the minds of thinking men is 
the inquiry, What is virtue ] or. What is a virtuous character ? Among 
the different theories on the subject which have, at different times, 
grown up and obtained currency, every one of which reflected as in 
the clearest mirror the express image of the age which gave it birth ; 
there was one, brought forth by the latter half of the eighteenth cen- 
tury, according to which virtue consisted in a correct calculation of our 
own personal interests, either in this world only, or also in the next. 
There probably had been no era in history, except the declining period 
of the Roman empire, in which this theory could have grown up and 
made many converts. It could only have originated in an age essen- 
tially unheroic. It was a condition of the existence of such a theory, 
that the only beneficial actions which people in general were much 
accustomed to see, or were therefore much accustomed to praise, should 
be such as were, or at least might without contradicting obvious facts 
be supposed to be, the result of the motive above characterized. 
Hence the words really connoted no more in common acceptation, 



REaUISITES OF LANGUAGE. 413 

than was set down in the definition : to which consequently no objec- 
tion lay on the score of deviation from usage, if the usage of that age 
alone was to be considered. 

Suppose, now, that the partisans of this theory had contrived to 
introduce (as, to do them justice, they showed themselves sufficiently 
inclined) a consistent and undeviating use of the term according to 
this definition. Suppose that they had succeeded in banishing the 
word disinterestedness from the language, in obtaining the disuse of 
all expressions attaching odium to selfishness or commendation to self- 
sacrifice, or which implied generosity or kindness to be anything but 
doing a benefit in order to receive a greater advantage in return. 
Need we say, that this abrogation of the old formulas for the sake of 
preserving clear ideas and consistency of thought, would have been an 
incalculable evil 1 while the very inconsistency incurred by the coexist- 
ence of the formulas with philosophical opinions which virtually con- 
demned them as absurdities, operated as a stimulus to the reexamina- 
tion of the subject; and thus the very doctrines originating in the oblivion 
into which great moral truths had fallen, were rendered indirectly, but 
powerfully, instrumental to the revival of those truths. 

The doctrine, therefore, of the Coleridge school, that the language of 
any people among whom culture is of old date, is a sacred deposit, the 
property of all ages, and which no one age should consider itself empow- 
ered to alter — is far from being so devoid of important truth as it 
appears to that class of logicians who think more of having a clear than 
of having a complete meaning; and who perceive that every age is 
adding to the truths which it has received from its predecessors, but 
fail to see that a counter-process of losing truths already possessed, is 
also constantly going on, and requiring the most sedulous attention to 
counteract it. Language is the depositary of the accumulated body of 
experience to which all former ages have contributed their part, and 
which is the inheritance of all yet to come. We have no right to pre- 
vent ourselves from transmitting to posterity a larger portion of this in- 
heritance than we may ourselves have profited by. We continually have 
cause to give up the opinions of our forefathers ; but to tamper with 
their language, even to the extent of a word, is an operation of much 
greater responsibility, and implies as an indispensable requisite, an 
accurate acquaintance with the history of the particular word, and of the 
opinions which in different stages of its progress it served to expi'ess. To 
be qualified to define the name, we must know all that has ever been 
known of the properties of the class of objects which are, or originally 
were, denoted by it. For if we give it a meaning according to which 
any proposition will be false which philosophers or mankind have ever 
held to be true, it is at least incumbent upon us to be sure that we 
know all which those who believed the proposition understood by it. 



414 OPERATIONS SUBSIDIARY TO INDUCTION. 

CHAPTER V. 

ON THE NATURAL HISTORY OF THE VARIATIONS IN THE MEANING OF TERMS. 

§ 1. It is not only in the mode which has now been pointed out, 
namely, by gradual inattention to a portion of the ideas conveyed, that 
words in common use are liable to shift their connotation. The truth 
is, that the connotation of such words is perpetually varying ; as might 
be expected from the manner in which words in common use acquire 
their connotation. A technical term, invented for purposes of art or 
science, has, from the first, the connotation given to it by its inventor ; 
but a name which is in every one's mouth before any one thinks of de- 
fining it, derives its connotation only from the circumstances which are 
habitually brought to mind when it is pronounced. Among these cir- 
cumstances, the properties common to the things denoted by the name, 
have naturally a principal place ; aud would have the sole place, if 
language were regulated by convention rather than by custom and ac- 
cident. But besides these common properties, which if they exist are 
necessarily present whenever the name is applied, any other circum- 
stance may casually be found along with it, so frequently as to become 
associated with it in the same manner, and as strongly as the common 
properties themselves. In proportion as this association forms itself, 
people give up using the name in cases in which those casual circum- 
stances do not exist. They prefer using some other name, or the same 
name with some adjunct, rather than employ an expression which will 
necessarily call up an idea they do not want to excite. The circum- 
stance originally casual, thus becomes regularly a part of the connota- 
tion of the word. 

It is this continual incorporation of circumstances originally acci- 
dental, into the permanent signification of words, which is the cause 
that there are so few exact synonyms. It is this also which renders 
the dictionary meaning of a word, by universal remark so imperfect an 
exponent of its real meaning. The dictionary meaning is marked out 
in a broad, blunt way, and probably includes all that was originally 
necessary for the coiTect employment of the term ; but in process of 
time so many collateral associations adhere to words, that whoever 
should attempt to use them with no other guide than the dictionary 
would confound a thousand nice distinctions and subtle shades of mean- 
ing which dictionaries take no account of; as we notice in the use of 
a language in conversation or vn:iting by a foreigner not thoroughly 
master of it. The history of a word, by showing the causes which de- 
tei-mined its use, is in these cases a better guide to its employment 
than any definition ; for definitions can only show its meaning at the 
particular time, or at most the series of its successive meanings, but its 
history may show the law by which 'the succession was produced. 
The word gentleman^ for instance, to the correct employment of which 
a dictionary would be no guide, originally meant simply a man of 
family. From this it came by degrees to connote all such qualities or ad- 
ventitious circumstances as were usually found to belong to persons of 
family. This consideration at once explains why in one of its vulgar 
acceptations it means any one who lives without labor, in another vnth- 



VARIATIONS IN MEANING OF TERMS. 415 

out manual labor, and in its more elevated signification it has in every 
age signified the conduct, character, habits, and outward appearance, in 
whomsoever found, which, according to the ideas of that age, belonged 
or were expected to belong to persons born and educated in a high so- 
cial position. 

It continually happens that of two words, whose dictionary mean- 
ings are either the same or very slightly different, one will be the 
proper word to use in one set of circumstances, another in another, 
without its being possible to show how the custom of so employing 
them originally grew up. The accident that one of the words was 
used and not the other on a particular occasion or in a particular social 
circle, will be sufficient to produce so strong an association between the 
word and some speciality of circumstances, that mankind abandon the 
use of it in any other case, and the speciality becomes part of its sig- 
nification. The tide of custom first drifts the word on the shore of a 
particular meaning, then retires and leaves it there. 

An instance in point is the remarkable change which, in the English 
language at least has taken place in the signification of the word loyal- 
ty. That word originally meant in English, as it still means in the 
language from whence it came, fair, open dealing, and fidelity to en- 
gagements : in that sense the quality it expressed was part of the ideal 
chivalrous or knightly character. By what process, in England, the 
term became restricted to the single case of fidelity to the throne, I am 
not sufficiently versed in the history of courtly language to be able to 
pronounce. The interval between a loyal chevalier and a loyal sub- 
ject is certainly great. I can only suppose that the word was, at some 
period, the favorite term at court to express fidelity to the oath of al- 
legiance, until at length those who wished to speak of any other, and 
as it was probably considered, inferior sort of fidelity, either did not 
venture t6 use so dignified a term, or found it convenient to employ 
some other in order to avoid being misunderstood. 

§ 2. Cases are not unfrequent in which a circumstance, at first cas- 
ually incorporated into the connotation of a word which originally had 
no reference to it, in time wholly supersedes the original meaning, and 
becomes not merely a part of the connotation, but the whole of it. 
This is exemplified in the word pagan, paganus ; which originally, as 
its etymology imports, was equivalent to villager ; the inhabitant of a 
pagus, or village. At a particular era in the extension of Christianity 
over the Roman empire, the adherents of the old religion, and the vil- 
lagers or country people, were nearly the same body of individuals, 
the inhabitants of the towns having been earliest converted ; as in our 
own day and at all times the greater activity of social intercourse ren- 
ders them the earliest recipients of new opinions and modes, while old 
habits and prejudices linger longest among the country people : not to 
mention that the towns were more immediately under the direct influ- 
ence of the government, which at that time had embraced Christianity. 
From this casual coincidence, the word paganus earned with it, and 
began more and more steadily to suggest, the idea of a worshiper of 
the ancient divinities ; until at length it suggested that idea so forcibly, 
that people who did not desire to suggest the idea avoided using the 
word. But when paganus had come to connote heathenism, the very 
unimportant circumstance, with reference to that fact, of the place of 



416 OPERATIONS SUBSIDIARY TO INDUCTION. 

residence, was soon disregarded in the employment of the word. As 
there was seldom any occasion for making separate assertion respect- 
ing heathens who lived in the country, there was no need for a separate 
word to denote them ; and pagan came not only to mean heathen, but 
to mean that exclusively. 

A case still more familiar to most readers is that of the word villain, 
or villein. This term, as everybody knows, had in the middle ages a 
connotation as strictly defined as a word could have, being the proper 
legal designation for those persons who were the subjects of the least 
onerous form of feudal bondage, those serfs who wei'e adscripti glebm. 
The scorn of the semibarbarous military aristocracy for these their ab- 
ject dependents, rendered the act of likening any person to this cla«s 
of men a mark of the greatest contumely ; the same scorn led them to 
ascribe to the same people all manner of hateful qualities, which doubt- 
less also, in the degrading situation in which they were held, were often 
not unjustly imputed to them. These circumstances combined to 
attach to the term villain, ideas of crime and guilt, in so forcible a 
manner, that the application of the epithet, even to those to whom it 
legally belonged, became an affront, and was abstained from whenever 
no affront was intended. From that time guilt was part of the conno- 
tation ; and soon became the whole of it, since mankind were not 
prompted by any urgent motive to continue making a distinction in 
their language between bad men of servile station and bad men of any 
other rank in life. 

These and similar instances in which the original signification of a 
term is totally lost — another and an entirely distinct meaning being 
first engrafted upon the former, and finally substituted for it— afford 
examples of the double movement which is always taking place in lan- 
guage : the counter-movements, one of Generalization, by which words 
are perpetually losing portions of their connotation and becoming of 
less meaning and more general acceptation ; the other of Specialization, 
by which other, or even these same words, are continually taking on 
fresh connotation ; acquiring additional meaning, by being restricted in 
their employment to a part only of the occasions on which they might 
properly be used before. This double movement is of sufficient im- 
portance in the natural history of language (to which natural history, 
the artificial modifications ought always to have some degree of refer- 
ence), to justify our dwelling for a little longer on the nature of the 
two-fold phenomenon, and the causes to which it owes its existence. 

§ 3. To begin with the movement of generalization. It is unneces- 
sary to dwell upon the changes in the meaning of names which take 
place merely from their being used ignorantly, by persons who, not 
having properly mastered the received connotation of a word, apply it 
in a looser and wider sense than belongs to it. This, however, is a 
real source of alterations in the language ; for when a word, from being 
often employed in cases where one of the qualities which it connotes 
does not exist, ceases to suggest that quality with certainty, then even 
those who are under no mistake as to the proper meaning of the word, 
prefer expressing that meaning in some other way, and leave the orig- 
inal word to its fate. The word 'Squire, as standing for an owner of 
a landed estate ; Parson, as denoting not the rector of the parish but 
clergymen in general; Artist, to denote only a painter or sculptor; are 



VARIATIONS IN MEANING OF TERMS. 417 

cases in point. Independently, however, of the generalization of 
names through their ignorant misuse, there is a tendency in the same 
direction, consistently with the most thorough knowledge of their 
meaning; arising from the fact, that the number of things known to 
us, and of which we feel a desire to speak, multiply faster than the 
names for them. Except on subjects for which there has been con- 
structed a scientific terminology, with which unscientific persons do 
not meddle, great difficulty is generally found in bringing a new name 
into use ; and independently of that difficulty, it is natural to prefer 
giving to a new object a name which at least expresses its resemblance 
to something already known, since by predicating of it a name entirely 
new we at first convey no information. In this manner the name of a 
species often becomes the name of a genus; as salt, for example, or 
oil ; the former of which words originally denoted only the muriate of 
soda, the latter, as its etymology indicates, only olive oil ; but which 
now denote larsre and diversified classes of substances resemblinor 
these in some of their qualities, and connote only those common quali- 
ties, instead of the whole of the distinctive properties of olive oil and 
sea salt. The words glass and soap are used by modern chemists in a 
similar manner, to denote genera of which the substances vulgarly so 
called are single species.* And it often happens, as in those instances, 
that the term keeps its special signification in addition to its more gen- 
eral one, and becomes ambiguous, that is, two names instead of one. 

These changes, by which words in ordinary use become more and 
more generalized, and less and less expressive, take place in a still 
greater degree with the words which express the complicated phe- 
nomena of mind and society. Historians, travellers, and in general 
those who speak or write concerning moral and social phenomena with 
which they are not familiarly acquainted, are the great agents in this 
modification of language. The vocabulary of all except unusually 
instructed persons, is, on such subjects, eminently scanty. They have 
a certain small set of words to which they are accustomed, and which 
they employ to express phenomena the most heterogeneous, because 
they have never sufficiently analyzed the facts to which those words 
correspond in their own country, to have attached perfectly definite 
ideas to the words. The first English conquerors of Bengal, for ex- 
ample, carried with them the phrase landed proprietor into a country 
where the rights of individuals over the soil were extremely different 
in degree, and even in nature, from those recognized in England. 
Applying the term with all its English associations in such a state of 
things ; to one who had only a limited right they gave an absolute right, 
from another because he had not an absolute right they took away all 
right, drove Vyhole classes of men to ruin and despair, filled the country 
with banditti, dieated a feeling that nothing was secure, and produced, 
with the best intentions, a disorganization of society which had not 
been produced in that country by the most ruthless of its barbarian 
invaders. Paul Louis Courier might well say, " Gardez-nous de I'equi- 
voque !" Yet the usage of persons capable of so gross a misappre- 
hension, determines the meaning of language : and the words they thus 

* " The term aXkali, in its original sense, signified that particular residuum which was 
alone obtained by lixiviating the ashes of the plant named kali, but the word is now so gen- 
eralized, that it denotes any body possessed of a certain number of properties." — Paris's 
Pharmacologia, vol. i., p. 68. - 

3G ' 



418 OPERATIONS SUBSIDIARY TO INDUCTION. 

misuse grow in generality, until the instructed are obliged to acquiesce; 
and to employ those words (first freeing them from vagueness by giv- 
ing them a definite connotation) as generic terms, subdividing the gen- 
era into species. • - " *. ) , - • « '/ ;,;- .'••■-. -,* 
— ^ ' ' '■ ^ ' - • . ' '* 

§ 4. While the more rapid growth of ideas than of names thus creates 
a perpetual necessity for making the same names serve, even if imper- 
fectly, on a greater number of occasions ; a counter-operation is going 
on, by which names become on the contrary restricted to fewer occa- 
sions, by taking on, as it were, additional connotation, from circum- 
stances not originally included in the meaning, but which have become 
connected with it in the mind by some accidental cause. We have 
seen above, in the words pagan and villain, remarkable examples of the 
specialization of the meaning of words from casual associations, as well 
as of the generalization of it in a new direction, which often follows. 

Similar specializations are of frequent occurrence in the history even 
of scientific nomenclature. " It is by no means uncommon," says Dr. 
Paris, in his Pharmacologia,^ " to find a word which is used to express 
general characters subsequently become the name of a specific sub- 
stance in which such characters are predominant ; and we shall find 
that some important anomalies in nomenclature may be thus explained. 
The term ApasvtKov, from which the word Arsenic is derived, was an 
ancient epithet applied to those natural substances which possessed 
strong and acrimonious properties, and as the poisonous quality of 
arsenic was found to be remarkably powerful, the term was especially 
applied to Orpiment, the form in which this metal most usually occur- 
red. So the term Verbena (quasi Herhcna) originally denoted all 
those herbs that were held sacred on account of their being employed 
in the rites of sacrifice, as we learn from the poets ; but as one herb 
was usually adopted upon these occasions, the word Verbena came to 
<denote that particular herb only, and it is transmitted to us to this day 
under the same title, viz. Verbena or Vervain, and indeed until lately 
it enjoyed the medical reputation which its sacred origin conferred 
upon it, for it was worn suspended around the neck as an amulet. 
Vitriol, in the original application of the word, denoted aiiy crystaline 
body with a certain degree of transparency {vitrum); it is hardly 
necessary to observe that the term is now appropriated to a particular 
species : in the same manner, Bark, which is a general term, is applied 
to express one genus, and by way of eminence, it has the article The 
prefixed, as The bark : the same observation will apply to the word 
Opium, which, in its primitive sense, signifies any ]mcG (0770^, Succus), 
while it now only denotes one species, viz. that of the poppy. So, 
again, Elaterium was used by Hippocrates to signify various internal 
applications, especially purgatives, of a violent and drastic nature 
(from the word E/lavi^w, agito, moveo, stimulo), but by succeeding 
authors it was exclusively applied to denote the active matter which 
subsides from the juice of the wild cucumber. The word Fecula, 
again, originally meant to imply any substance which was derived by 
spontaneous subsidence from; a liquid (from fcex, the grounds or 
settlement of any liquor) ; afterwards it was applied to Starch, which 
is deposited in this manner by agitating the flour of wheat in water; 

* Historical Introduction, vol. i., pp. 66-8, 



VARIATIONS IN MEANING OF TERMS. 419 

and lastly, it has been applied to a peculiar vegetable principle, which, 
like starch, is insoluble in cold, but completely soluble in boiling water, 
with which it forms a gelatinous solution. This indefinite meaning of 
the word Jecula h.Rs created nurnerous mistakes in pharmaceutic chem- 
istry; Elaterium, for instance, is said to hejecula, and, in the original 
sense of the word, it is properly so called, inasmuch as it is procured 
from a vegetable juice by spontaneous subsidence, but in the limited 
and modern acceptation of the term, it conveys an erroneous idea ; for 
instead of the active principle of the juice residing in Jecula, it is a 
peculiar proximate principle, sui generis, to which I have ventured to 
bestow the name of Elatln. For the same reason, much doubt and 
obscurity involve the meaning of the word Extract, because it is ap- 
plied generally to any substance obtained by the evaporation of a vege- 
table solution, and specifically to a peculiar proximate principle, pos- 
sessed of certain characters, by which it is distinguished from every 
other elementary body." 

A generic terra is always liable to become thus limited to a single 
species, or even individual, if people have occasion to think and speak 
of that individual or species much oftener than of anything else which 
is contained in the genus. Thus, by cattle, a stage coachman will 
understand horses ; beasts, in the language of agriculturists, stands for 
oxen ; and birds, with some sportsmen, for partridges only. The law 
of language which operates in these trivial instances, is the very same 
in conformity to which the terms Geof, Deus, and God, were adopted 
from Polytheism by Christianity, to express the single object of its 
own -adoration, in lieu of the ancient and specially appropriated name 
Jehovah. Almost all the terminology of the Christian Church is made 
up of words originally used in a much more general acceptation: 
jEJccZm<z, Assembly ; Bishop, Ej^iscopus, Overseer; Priest, Presbyter, 
Elder; Deacon, Diaconus, Administrator; Sacrament, a vow of alle- 
giance ; Evangelium, good tidings ; and some words, as Minister, are 
still used both in the general and in the limited sense. It would be 
interesting to trace the progress by which author, in its most familiar 
sense, came to signify a writer, and not7]TTjg, or Maker, a poet. 

Of the incorporation into the meaning of a term, of circumstances 
accidentally connected with it at some particular period, as in the case 
of Pagan, instances might easily be multiplied. Physician [cpvoLKog, or 
naturalist) became, in England at least, synonymous with a healer of 
diseases, because until a comparatively late period medical practitioners 
were the only naturalists. Clerc or Clericus, a scholar, came to signify 
an ecclesiastic, because the clergy were for many centuries the only 
scholars. 

Of all ideas, however, the most liable to cling by association to any- 
thing with which they have ever been connected by proximity, are 
those of our pleasures and pains, or of the things which we habitually 
contemplate as sources of our pleasures or pains. The additional con- 
notation, therefore, which a word soonest and most readily takes on, 
is that of agi'eeableness or painfulness, in their various kinds and de- 
grees : of'being a good or a bad thing ; desirable or to be avoided ; • 
an object of hati'ed, of dread, of contempt, admiration, hope, or love. 
Accordingly there is hardly a single name, expressive of any moral or 
social fact calculated to call forth strong affections either of a favorable 
or of a hostile nature, which does not carry with it decidedly and irre- 



420 OPERATIONS SUBSIDIARY TO INDUCTION. 

sistibly a connotation of those strong affections, or, at the least, of 
approbation or censure ; insomuch that to employ those names in 
conjunction with others by which the contrary sentiments were ex- 
pressed, would produce the effect of a paradox, or even a contradic- 
tion in terms. The baneful influence of the connotation thus acquired, 
on our reasonings and habits of thought, has been well pointed out on 
many occasions by Bentham, It gives "rise to the fallacy of '* question- 
begging names." The very property which we are inquiring whether 
a thing possesses or not, has become so associated with the name of the 
thing as to be part of its meaning, insomuch that by merely uttering 
the name we assume the point which was to be made out: one of the 
most frequent sources of apparently self-evident propositions. 

There is still another mode in which the meaning of a name is apt to 
be specialized, sufficiently frequent to be worthy of being pointed out. 
We have often the choice between a more and a less general name for 
designating an object, either of them sufficiently answering the pur- 
pose of distinction. Thus we may say either that dog, or that animal ; 
m many cases, that creature, or that object, would be sufficient. Now 
there is^ in many cases of frequent occurrence, a tendency, which 
grows as civilization advances, to adopt the practice of designating 
things by the most general words which with all the aids of context 
"and gesture will suffice to point them out. Natural good taste, and 
still more the conventional quality which usurps its name, consist to a 
great degree in keeping some aspects of things as much as possible out 
of sight ; speaking of disagreeable things with the least possible sug- 
gestion of their disagreeable details, and of agreeable things with as 
little obtrusion as possible of the mere mechanism of their production, 
which, except in our scientific observations, is not what interests us in 
them, and the close contemplation of which generally diminishes their 
charm to the imagination. The practice thus grows up among culti- 
vated people, of speaking of common things in a way much less literal 
and definite than is the custom of the vulgar ; in a way which indicates 
the thing meant, with the faintest possible suggestion of its character- 
istic qualities ; and the mere words used would often not suffice to 
convey the meaning, unless there were something in the accompanying 
circumstances to assist in exciting the idea. The vulgar, meanwhile, 
continue to use the appropriate, peculiar, a,nd, if scientific fitness were 
the only thing to be considered, the best phraseology, because unam- 
biguous ; while, for purposes of refinement, ambiguity is often the 
very quality desired. 

Now this practice of using more general terms where specific ones 
might have been employed, is constantly spoiling the general terms by 
rendering them specific. They become the terms particularly associ- 
ated with the very specialities of meaning which it was desired not to 
suggest. A ridiculous instance is the anecdote of a lady of the court 
of Louis XIV., who having stated to her confessor that she felt esteem 
for a certain cavalier, (this being, it seems, the phrase of the day to 
express a meaning which persons usually prefer to convey by a circum- 
locution,) was asked by the priest, " Combien de fois vous a-t-il 
estimee V which story, whether true or invented, got into circulation, 
and led to the abandonment of the phrase in that peculiar sense. If 
it had not been abandoned in that sense, it would soon have been 
discarded in any other sense; and finally, perhaps, lost altogether. 



TERMINOLOGY AND NOMENCLATURE. 421 

because when confined to that particular meaning, it would no longer 
have had the indistinctness which formed its recommendation. Many- 
terms, in many different languages, which originally had a more general 
meaning, have been unfitted for other uses by acquiring this very con- 
notation. And a vast variety of other words, without any relation to 
that peculiar subjept, have one after another fallen into disuse except 
among the coarse and uncultivated, because they had come to connote 
too directly and unequivocally something which people did not like to 
have brought very distinctly before their imagination. 

Without any farther multiplication of examples to illustrate the 
changes which usage is continually making in the signification of terms, 
I shall add, as a practical rule^ that the logician, not being able to pre- 
vent such transformations, should submit to them with a good grace 
when they are irrevocably effected, and if a definition is necessary, 
define the word according to its new meaning ; retaining the former as 
a second signification, if it is needed, and if there be any chance of 
being able to preserve it either in the language of philosophy or in 
common use. Logicians cannot make the meaning of any but scieu' 
tific terms : that of all other words is made by the collective human 
race. But logicians can ascertain clearly what it is which, working 
obscurely, has guided the general mind to a particular employment of 
a name ; and when they have found this, they can clothe it in such 
distinct and permanent terms, that mankind shall see the meaning 
which before they only felt, and shall not suffer it to be afterwards 
forgotten or misapprehended. And this is a power not lower in dignity, 
and far less liable to abuse, than the chimerical one of domineering 
over language. 



CHAPTER VI. 

THE PRINCIPLES OF A PHILOSOPHICAL LANGUAGE FURTHER CONSIDERED, 

§ 1. We have, thus far, considered only one of the requisites of a 
language adapted for the investigation of truth ; that its terms shall 
each of them convey a determinate and unmistakable meaning. There 
are, however, as we have already remarked, other requisites ; some of 
them important only in the second degree, but one which is funda- 
mental, and barely yields in point of importance, if it yields at all, to 
the quality which we have already discussed at so much length. That 
the language may be fitted for its purposes, not only should every 
word perfectly express its meaning, but there should be no important 
meaning without its word. Whatever we have occasioti to think of 
often, and for scientific purposes, ought to have a name appropriated 
to it. 

This requisite of philosophical language may be considered under 
three different heads ; that number of separate conditions being in- 
volved in it. 

§ 2. First; there ought to be all such names, as are needful for 
shaking such a record of individual observations that the words of the 



422 OPERATIONS SUBSIDIARY TO INDUCTION. 

record shall exactly show what fact it is which has been observed. Jn 
other words, there must be an accurate Descriptive Terminology. 

The only things which we can observe directly being our own sen- 
sations, or other feelings, a complete descriptive language would be 
one in which there should be a name for every variety of elementary 
sensation or feeling. Combinations of sensations or feelings may al- 
ways be described, if we have a name for each of the elementary 
feelings which compose them ; but brevity of description, as well as 
clearness (which often depends very much upon brevity,) is greatly 
promoted by giving distinctive names not to the elements alone, but also 
to all combinations which are of frequent recurrence. On this occasion 
I cannot do better than quote from Mr. Whewell some of the excellent 
remarks which he has made on this important branch of our subject. 

'* The meaning" (says he *) " of [descriptive] technical terms, can 
be fixed in the first instance only by convention, and can be made 
intelligible only by presenting to the senses that which the terms are 
to signify. The knowledge of a color by its name can only be 
taught through the eye. No description can convey to a hearer what 
we mean by apple-green or French-gray. It might, perhaps, be sup- 
posed that, in the first example, the term apple, refeiTing to so 
familiar an object, sufficiently suggests the color intended. But it may 
easily be seen that this is not true ; for apples are of many different 
hues of green, and it is only by a conventionaJ selection that we can 
appropriate the term to one special shade. When this appropriation 
is once made, the term refers to the sensation, and not to the parts of 
the term ; for these enter into the compound merely as a help to the 
memory, whether the suggestion be a natural connexion as in * apple- 
green,' or a casual one as in ' French-gray.' In order to derive due 
advantage fi:'om technical terms of this kind, they must be associated 
immediately with the perception to which they belong, and not con- 
nected with it through the vague usages of common language. The 
memory must retain the sensation ; and the technical word must be 
understood as directly as the most familiar word, and more distinctly. 
"When we find such terms as tin-white or pinchheck-hr own, the metallic 
color so denoted ought to start up in our memory without delay or 
search. 

" This, which it is most important to recollect with respect to the 
simpler properties of bodies, as color and form, is no less true with 
respect to more compound notions. In all cases the term is fixed to a 
peculiar meaning by convention ; and the student, in order to use the 
word, must be completely familiar with the convention, so that he has 
no need to frame conjectures from the word itself Such conjectures 
would always be insecure, and often erroneous. Thus the term papi- 
lionaceous applied to a flower is employed to indicate, not only a re- 
semblance to a butterfly, but a resemblance arising from five petals of 
a certain peculiar shape and arrangement ; and even if the resem- 
blance were much stronger than it is in such cases, yet if it were pro- 
duced in a different way, as, for example, by one petal, or two only, 
instead of a 'standard,' two 'wings,' and a ' keel' consisting of two 
parts more or less united into one, we should no longer be justified m 
speaking of it as a * papilionaceous' flower." 

'* Philosophy of the Inductive Scienees, i., 4.6i-^. 



TERMINOLOGY AND NOMENCLATURE. 423 

When, however, the thing named is, as in this last case, a combina- 
tion of simple sensations, it is not necessary in order to learn the 
meaning of the word, that the student should refer back to the sensa- 
tions themselves ; it may bo communicated to him through the medium 
of other words ; the terms, in short, may be defined. But the names 
of elementary sensations, or elementary feelings of any sort, cannot be 
defined ; nor is there any means of making their signification know^n 
but by making the learner experience the sensation, or referring him, 
through some known mark, to his remembrance of having experienced 
it before. Hence it is only the impressions on the outward senses, or 
those inward feelings which are connected in a very obvious and 
uniform manner with outward objects, that are really susceptible of 
an exact descriptive language. The countless variety of sensations 
which arise, for instance, from disease, or from peculiar physiological 
states, it would be in vain to attempt to name ; for as no one can judge 
whether the sensation I have is the same with his, the name may not 
have, to us two, any community of meaning. The same may be said, 
to a considerable extent, of purely mental feelings. But in some of 
the sciences which are conversant with external objects, it is scarcely 
possible to surpass the perfection to which this quality of a philosophi- 
cal langfuaofe has been carried. 

" The formation" (continues Mr. Whewell*) "of an exact and ex- 
tensive descriptive language for botany has been executed with a 
degree of skill andielicity, which, before it was attained, could hardly 
have been dreamed of as attainable. Every part of a plant has been 
named ; and the form of every part, even the most minute, has had a 
large assemblage of descriptive terms appropriated to it, by means of 
which the botanist can convey and receive knowledge of form and 
structure, as exactly as if each minute part were presented to him 
vastly magnified. This acquisition was part of the Linnaean reform .... 
* Tournefort,' says Decandolle, ' appears to have been the first who 
really perceived the utility of fixing the sense of terms in such a way 
as always to employ the same word in the same sense, and always to 
express the same idea by the same word ; but it was Linnasus who 
really created and fixed this botanical language, and this is his fairest 
claim to glory, for by this fixation of language he has shed clearness 
and precision over all parts of the science.' 

"It is not necessary liere to give any detailed account of the terms 
of botany. The fundamental ones have been gradually introduced, as 
the parts of plants were . more carefully and minutely examined. 
Thus the flower was necessarily distinguished into the calyx, the 
corolla, the stamens, and the jnstils; the sections of the corolla were 
termed petals by Columna; those of the calyx were called sepals by 
Necker. Sometimes terms of greater generality were devised ; as 
perianth to include the calyx and corolla, whether one or both of these 
were present ; pericarp, for the part inclosing the grain, of wdiatever 
kind it be, fi'uit, nut, pod, &c. And it may easily be imagined that 
descriptive terms may, by definition and combination, become very 
numerous and distinct. Thus leaves may be called pinnatijid, pinna- 
tipartite, pinnatisect, pinnatilobate, palmatijld, palmatipartite, &c., 
and each of these words designates different combinations of the mod^s 

* Philosophy of the InduQtive Sciences, i., 465-7. , 



424 OPERATIONS SUBSIDIARY TO INDUCTION. 

and extent of the divisions of the leaf with the divisions of its outhne. 
In some cases> arbiti'ary numerical relations are introduced into the 
definition : thus, a leaf is called bilobate, v\^hen it is divided into two 
parts by a notch ; but if the notch go to the middle of its length, it is 
hijid; if it go near the base of the leaf, it is bipartite; if to the base, 
it is bisect. Thus, too, a pod of a cruciferous plant is a silica, if it is 
four times as long as it is broad, but if it be shorter than this it is a 
silicula. Such terms being established, the form of the very complex 
leaf or frond of a fern* is exactly conveyed by the following phrase : — 
* fronds rigid pinnate, pinnae recurved subunilateral pinnatifid, the seg- 
ments linear undivided or bifid spinuloso-serrate.' 

** Other characters, as well as form, are conveyed with the like pre- 
cision: Color by means of a classified scale of colors This was 

done with most precision by Werner, and his scale of colors is still the 
most usual standard of naturalists. Werner also introduced a more 
exact terminology with regard to other characters which are impor- 
tant in mineralogy, as lustre, hardness. But Mohs improved upon 
this step by giving a numerical scale of hardness, in which talc is 1, 
gypsum 2, calc spar 3, and so on. . . . Some properties, as specific 
gravity, by their definition give at once a numerical measure ; and 
others, as crystaline form, require a very considerable array of math- 
ematical calculation and reasoning, to point out their relations and 
gradations." •• ^ -'■/- ' ; 

§ 3. Thus far of Descriptive Terminology, or of the language 
requisite for placing upon record our observation of individual in- 
stances. But when we proceed from this to Induction, or rather to 
that comparison of observed instances which is the preparatory step 
towards it, we stand in need of an additional and a different sort of 
general names. 

Whenever, for purposes of Induction, we find it necessary to intro- 
duce (in Mr. Whewell's phraseology) some new general conception; 
that is, whenever the comparison of a set of phenomena leads to the 
recognition in them of some common circumstance, which, our atten- 
tion not having been directed to it on any former occasion, is to us a 
new phenomenon ; it is of importance that this new conception, or this 
new result of abstraction, should have a name appropriated to it; 
especially if the circumstance it involves be one which leads to many 
consequences, or which is likely to be found also in other classes of 
phenomena. No doubt, in most cases of the kind, the meaning might 
be conveyed by joining together several words already in use. But 
when a thing has to be often spoken of, there are more reasons than 
the saving of time and space, for speaking of it in the most concise 
manner possible. What darkness would be spread over geometrical 
demonstration, if wherever the word circle is used, the definition of a 
circle were inserted instead of it. In mathematics and its applications, 
where the nature of the processes demands that the attention should 
be strongly concentrated, but does not require that it should be widely 
diffused, the importance of concentration also in the expressions has 
always been duly felt ; and a mathematician no sooner finds that he 
shall often have occasion to speak of the same two things together, 

* ^' Hi/menophyllum Wilaoiti,''* 



TERMINOLOGY AND NOMENCLATURE. 425 

than lie at once creates a term to express them whenever combined : 
just as, in his algebraical operations, he substitutes for (a"' + ^") f , or 

for - -| h -T + &c,, the single letter P, Q,, or S ; not solely to shorten 

bed 

his symbolical expressions, but to simplify the purely intellectual part 
of his operations, by enabling the mind to give its exclusive attention 
to the relation between the quantity S and the other quantities which 
enter into the equation, without being distracted by thinking unneces- 
sarily of the parts of which S is itself composed. 

But there is another reason, in addition to that of promoting perspi- 
cuity, for giving a brief and compact name to eacli of the more con- 
siderable results of abstraction which are obtained in the course of our 
intellectual phenomena. By naming them, we fix our attention upon 
them ; we keep them more constantly before the mind. The names are 
remembered, and being remembered, suggest their definition ; while if 
instead of specific and characteristic names,the meaning had been ex- 
pressed by putting together a number of other names, that particular 
combination of words already in common use for other purposes would 
have had nothing to make itself remembered by. If we want to ren- 
der a particular combination of ideas permanent in the mind, there is 
nothing which clenches it like a name specially devoted to express it. 
If mathematicians had been obliged to speak of " that to which a 
quantity, in increasing or diminishing, is always approaching nearer, 
so that the difference becomes less than any assignable quantity, but 
to which it never becomes exactly equal," instead of expressing all 
this by the simple phrase, " the limit of a quantity," we should probably 
have long remained without most of the important truths which have 
been discovered by means of the relation between quantities of various 
kinds and their limits. If instead of speaking of momentum^ it had 
been necessary to say " the product of the number of units of velocity 
in the velocity by the number of units of mass in the mass," many of 
the dynamical truths now apprehended by means of this complex idea, 
would probably have escaped notice for want of recalling the idea 
itself with sufficient readiness and familiarity. And on subjects less 
remote from the topics of popular discussion, whoever wishes to draw 
attention to some new or unfamiliar distinction among things, will find 
no way so sure as to invent or select suitable names for the express 
purpose of marking it. 

A volume devoted to explaining what civilization is and is not, does 
not raise so vivid a conception of it as the single expression, that Civi- 
lization is a different thing from Cultivation ; the compactness of that 
brief designation for the contrasted quality being an equivalent for a 
long discussion. So, if we would impress forcibly upon the under- 
standing and memory the distinction between what a representative 
government should be and what it often is, we cannot more effectually , 
do so than by saying that Representation is not Delegation. Dr. 
Chalmers, in order to distinguish his scheme of clerical superintend- 
ence of a parish from the mere keeping a church open which people 
might come to or not as they spontaneously chose, called very expres- 
sively the former the *' aggressive" system, the latter the " attractive." 
When the earlier electricians found that there were two different kmds 
of electrical excitement, they soon made the world familiar with them , 
by giving them the names of positive and negative, vitreous and resinous, 
3H 



426 OPERATIONS SUBSIDIARY TO INDUCTION.. 

Hardly any original tlioughts on mental or social subjects ever make 
their way among mankind or assume their proper importance in the 
minds even of their inventors, until aptly selected words or phrases 
have as it were nailed them down and held them fast. 

§ 4. Of the three essential parts of a philosophical language, we 
have now mentioned two : a terminology suited for describing with 
precision the individual facts observed ; and a name for every common 
property of any importance or interest, which we detect by comparing 
those facts : including (as the concretes coiTesponding to those abstract 
terms) names for the classes which we artificially construct in virtue of 
those properties, or as many of them, at least, as we have frequent 
occasion to predicate anything of. 

But there is a sort of classes, for the recognition of which no such 
elaborate process is necessary ; because each of them is marked out 
from all others not by some one property, the detection of which may 
depend upon a difficult act of abstraction, but by its properties generally. 
I mean, the Kinds of things, in the sense which, in this treatise, has 
been systematically attached to that term. By a Kind, it will be re- 
membered, we mean one of those classes which are distinguished from 
all others not by one or a few definite properties, but by an unknown 
multitude of them ; the combination of properties on which the class 
is grounded, being a mere index to an indefinite number of other dis- 
tinctive attributes. The class horse is a Kind, because the things which 
agree in possessing the characters by which we recognize a horse, 
agree in a great number of other properties as we know, and it cannot 
be doubted, in many more than we know. Animal, again, is a Kind, 
because no definition that could be given of the name animal could 
either exhaust the properties common to all animals, nor supply prem- 
isses from which the remainder of those properties could be inferred. 
But a combination of properties which does not give evidence of the 
existence of any other independent peculiarities, does not constitute a 
Kind, White horse, therefore, is not a Kind : because horses which 
agree in whiteness, do not agree in anything else, except in the quali- 
ties common to all horses, and in whatever may be the causes or effects 
of that particular color. 

On the principle that there should be a name for everything which 
we have frequent occasion to make assertions about, there ought evi- 
dently to be a name for every Kind ; for as it is the very nature of a 
Kind that the individuals composing it have an indefinite multitude of 
properties in common, it follows that, if not with our present knowl- 
edge, yet with that which we may hereafter acquire, the Kind is a 
subject to which there will have to be applied many predicates. The 
third component element of a philosophical language, therefore, is that 
there shall be a name for every Kind. In other words, there must 
not only be a terminology but also a nomenclature. i 

The words Nomenclature and Terminology are employed by most 
authors almost indiscriminately ; Mr. Whewell being, as far as I am 
aware, the first writer who has regularly assigned to the two words 
different meanings. The distinction however which he has drawn 
between them being a real and an important one, his example is likely 
to be followed ; and (as is apt to be the case when such innovations in 
language are felicitously made) a vague sense of the distinction is found 



TERMINOLOGY AND NOMENCLATURE.' > 427 

'to have influenced the employment of the terms in common practice, 
before the expediency had been pointed out of discriminating them 
philosophically. Every one would say that the reform effected by 
Lavoisier and Guyton-Morveau in the language of chemistry consisted 
in the introduction of a new nomenclature, not of a new terminology. 
Linear, lanceolate, oval, or oblong, serrated, dentate, or crenate leaves, 
are expressions forming part of the ternjinology of botany, while the 
names " Viola odorata," and " Ulex europaeus," belong to its nomen^ 
clature. 

A nomenclature may be defined, the collection of the names of all 
the Kinds with which any branch of knowledge is conversant, or more 
properly, of all the lowest Kinds, or mjimcE, species, those which may 
be subdivided indeed, but not into Kinds, and which generally accord 
with what in natural history are termed simply species. Science 
possesses two splendid examples of a systematic nomenclature ; that 
of plants and animals, constructed by Linnaeus and his successors, and 
that of chemistry, which we owe to the illustrious group of chemists 
who flourished in France towards the close of the eighteenth century. 
In these two departments, not only has every known species, or lowest 
Kind, a name assigned to it, but when new lowest Kinds are discovered, 
names are at once given to them upon an uniform principle. In other 
sciences the nomenclature is not at present constructed upon any sys- 
tem, either because the species to be named are not numerous enough 
to require one (as in geometry for example), or because no one has 
yet suggested a suitable principle for such a system, as in mineralogy ; 
in which the want of a scientifically constructed nomenclature is now 
the principal cause which retards the progress of the science. 

§ 5. A word which carries on its face that it belongs to a nomen- 
clature, seems at first sight to differ from other concrete general names 
in this — that its meaning does not reside in its connotation, in the 
attributes implied in it, but in its denotation, that is, in the particular 
group of things which it is appointed to designate ; and cannot, there- 
fore, be unfolded by means of a definition, but must be made known" in 
another way. Mr. Whewell seems to incline to this opinion, which, 
however, appears to me erroneous. Words belonging to a nomencla- 
ture differ, I conceive, from other words mainly in this, that besides 
the ordinary connotation, they have a peculiar one of their own: 
besides connoting certain attributes, they also connote that those attri- 
butes are distinctive of a Kind. The term "peroxide of iron," for 
example, belonging by its form to the systematic nomenclature of 
chemistry, bears upon its face that it is the name of a peculiar Kind 
of substance. It moreover connotes, like the name of any other class, 
some portion of the properties common to the class; in this instance 
the property of being a compound of iron and the largest dose of oxygen 
with which iron will combine. These two things, the fact of being 
such a compound, and the fact of being a Kind, constitute the conno- 
tation of the name peroxide of iron. When we say of the substance 
before us, that it is the peroxide of iron, we thereby assert, first, that 
it is a compound of iron and a maximum of oxygen, and next, that the 
substance so composed is a peculiar Kind of substance. 

Now, this second part of the connotation of any word belonging to 
a nomenclature is as essential a portion of its meaning as tlie first part, 



428 OPERATIONS SUBSIDIARY TO INDUCTION. 

while the definition can only declare the first : and hence the appear- 
ance that the signification of such terms cannot be conveyed by a 
definition : which appearance, however, is fallacious. The name Viold 
odorata denotes a Kind, of which a certain number of characters, 
sufficient to distinguish it, are enunciated in botanical works. This 
enumeration of characters is surely, as in other cases, a definition of the 
name. No, say some, it is not a definition, for the name Viola odorata 
does not mean those characters ; it means that particular group of 
plants, and the characters are selected from among a much greater 
number, merely as marks by which to recognize the group. By n*o 
means, I reply ; the name does not mean that group, for it would be 
applied to that group no longer than while the group is believed to be , 
an infima species; if it were to be discovered that several distinct 
Kinds have been confounded under this one name, no one would any 
longer apply the name Viola odorata to the whole of the group, but 
would apply it, if retained at all, to one only of the Kinds contained 
therein. What is imperative, therefore, is not that the name shall de- 
note one particular collection of objects, but that it shall denote a Kind, 
and a lowest Kind. The form of the name declares that, happen what 
will, it is to denote an injima species ; and that, therefore, the proper- ' 
ties which it connotes, and which are expressed in the definition, are 
to be connoted by it no longer than while we continue to believe that 
those properties, when found together, indicate a Kind, and that the 
whole of them are found in no more than one Kind. 

With the addition of this peculiar connotation, implied in the form 
of every word which belongs to a systematic nomenclature ; the set of 
characters which is employed to discriminate each Kind from all other 
Kinds (and which is a real definition) constitutes as completely as in 
any other case the whole meaning of the term. It is no objection to 
say that (as is ofi:en the case in natural history), the set of characters 
may be changed, and another substituted as being better suited for the 
purpose of distinction, while the word, still continuing to denote the 
same group of things, is not considered to have changed its meaning. 
For this is no more than may happen in the case of any other general 
name : we may, in reforming its connotation, leave its denotation un- 
touched ; and it is generally desirable to do so. The connotation, 
however, is not the less for this the real meaning, for we at once apply 
the name wherever the characters set down in the definition are found ; 
and that which exclusively guides us in applying the term, must con- 
stitute its signification. If we find, contrary to our previous belief, 
that the characters are not peculiar to one species, we cease to use the 
term coextensively with the characters ; but then it is because the 
other portion of the connotation fails ; the condition that the class must 
be a Kind. The connotation, therefore, is still the meaning ; the set 
of descriptive characters is a true definition: and the meaning is un- 
folded, not indeed (as in other cases) by the definition alone, but by 
the definition and the form of the word taken together. 

§ 6. We have now analyzed what is implied in the two principal 
requisites of a philosophical language ; first, precision or definiteness, 
and secondly, completeness. Any further remarks on the mode of 
constructing a nomenclature must be dcfeiTed until we treat of Classi- 
fication ; the mode of naming the Kinds of things being- necessarily 



TERMINOLOGY AND NOMENCLATURE. 429 

subordinate to tlie mode of arranging those Kinds into larger classes. 
With respect to the minor requisites of Terminology, some of them 
are well stated and copiously illustrated in the "Aphorisms on the 
Language of Science," included in Mr. Whewell's Philosophy of the 
Inductive Sciences. These, as being of secondary importance in the 
peculiar point of view of Logic, we shall leave the reader to seek in 
Mr. Whewell's pages, and shall confine our own observations to one 
more quality, which, next to the two already treated of, appears to be 
the most valuable which the language of science can possess. Of this 
quality a general notion may be conveyed by the following aphorism: 

Whenever the nature of the subject permits our reasoning process 
to. be, without danger, carried on mechanically, the language should 
be constructed on as mechanical principles as possible ; while in the 
contrary case, it should be so constructed that there shall be the gi'eatest 
possible obstacles to a merely mechanical use of it. 

I am conscious that this maxim requires much explanation, which I 
shall at once proceed to give. And first, as to what is meant by using 
a language mechanically. The complete or extreme case of the me- 
chanical use of language, is when it is used without any consciousness 
of a meaning, and with only the consciousness of using certain visible 
or audible marks in conformity to technical rules previously laid down. 
This extreme case is, so far as I am aware, nowhere realized except 
in the figures of arithmetic and the symbols of algebra, a language 
unique in its kind, and approaching as nearly to perfection, for the pur- 
poses to which it is destined, as can, perhaps, be said of any creation 
of the human mind. Its perfection consists in the completeness of its 
adaptation to a purely mechanical use. The symbols are mere coun- 
ters, without even the semblance of a meaning apart from the conven- 
tion which is renewed each time they are employed, and which is al- 
tered at each renewal, the same symbol a or x being used on different 
occasions to represent things which (except that, like all things, they 
are susceptible of being numbered) have no property in common. 
There is nothing, therefore, to. distract the mind from the set of mechani- 
cal operations which are to be performed upon the symbols, such as 
squaring both sides of the equation, multiplying or dividing by the 
same or by equivalent symbols, and so forth. Each of these opera-, 
tions, it is true, corresponds to a syllogism ; represents one step of a- 
ratiocination relating not to the symbols, but to the things signified by. 
them. But as it has been found practicable to frame a technical foim, 
by conforming to which we can make sure of finding the conclusion of 
the ratiocination, our end can be completely attained without our ever 
thinking of anything but the sym.bols. Being thus intended to work 
merely as mechanism, they have the qualities which mechanism ought 
to have. They are of the least possible bulk, so that they take up 
scarcely any room, and waste no time in their manipulation ; they are 
compact, and fit so closely together that the eye can take in the whole 
at once of almost every operation which they are employed to perfomi. 

These admirable properties of the symbolical language of mathe- 
matics have made so strong an impression on the minds of many phi- 
losophers, as to have led them to consider the symbolical language in 
question as the ideal type of philosophical language generally ; to 
think that names in general, or (as they are fond of calling them) signs, 
are fitted for the purposes of thought in proportion as they can be 



430 OPERATIONS SUBSIDIARY TO INDUCTION. 

made to approximate to the compactness, the entire unmeaningness, 
and the capabihty of being used as counters without a thought of what 
they represent, which are characteristic of the a and Z>, the x and y, of 
algebra. This notion has led to sanguine views of the acceleration of 
the progress of science by means which, as I conceive, cannot possi- 
bly conduce to that end, and forms part of that exaggerated estimate 
of the influence of signs, which has contributed in no small degree to 
prevent the real laws of our intellectual operations from being kept in 
view, or even rightly understood. 

In the first place, a set of signs by which we reason without con- 
sciousness of their meaning, can be serviceable, at most, only in our 
deductive operations. In our direct inductions we cannot for a mo- 
ment dispense with a distinct mental image of the phenomena, since 
the whole operation turns upon a perception of the particulars in which 
those phenomena agi'ee and differ. But, further, this reasoning by 
counters is only suitable to a very limited portion even of our deduc- 
tive processes. In our reasonings respecting numbers, the only gen- 
eral principles which we ever have occasion to introduce, are these, 
Things which are equal to the same thing are equal to one another, 
and The sums or differences of equal things are equal; with their 
various corollaries. Not only can no hesitation ever arise respecting 
the applicability of these principles, since they are true of all mag- 
nitudes whatever ; but every possible application, of which they are 
susceptible, may be reduced to a technical rule ; such as, in fact, the 
rules of the calculus are. But if the symbols represent any other 
things than mere numbers, let us say even straight or curve lines, we 
have then to apply theorems of geometry not true of all lines without 
exception, and to select those which are true of the lines we are rea- 
soning about. And how can we do this unless we keep completely in 
mind what particular lines these are 1 Since additional geometrical 
truths may be introduced into the ratiocination in any stage of its pro- 
gress, we cannot suffer ourselves, during even the smallest part of it, 
to use the names mechanically (as we use algebraical symbols) without 
an image annexed to them. It is only after ascertaining that the so- 
lution of a question concerning lines can be made to depend upon a 
previous question concerning numbers, or in other words after the 
question has been (to speak technically) reduced to an equation, that 
the unmeaning signs become available, and that the nature of the facts 
themselves to which the investigation relates can be dismissed from 
the mind. Up to the establishment of the equation, the language in 
which mathematicians cany on their reasoning does not differ in char- 
acter from that employed by close reasoners on any other kind of 
subject. 

I do not deny that every coiTect ratiocination, when thrown into the 
syllogistic shape, is conclusive from the mere form of the expression, 
provided none of the terms used be ambiguous; and this is one of the 
circumstances which have led some philosophers to think that if all 
names were so judiciously constructed and so carefully defined as not 
to admit of any ambiguity, the improvement thus made in language 
would not only give to the conclusions of every deductive science the 
same certainty with those of mathematics, but would reduce all reason- 
ings to the application of a technical form, and enable their conclu- 
siveness to be rationally assented to after a merely mechanical pro- 



TERMINOLOGY AND NOMENCLATURE. 431 

cess, as is undoubtedly the case in algebra. But, if we except geom- 
etry, the conclusions of which arc already as certain and exact as they 
can be made, there is no science but that of number, in which the prac- 
tical validity of a reasoning can be apparent to any person who has 
looked only at the form of the process. Whoever has assented to all 
that was said in the last Book concerning the case of the Composition 
of Causes, and the still stronger case of the entire supersession of one 
set of laws by another, is aware that geometry and algebra are the 
only sciences of which the propositions are categorically true : the 
general propositions of all other sciences are true, only hypothetically, 
sup2wsing that no counteracting cause happens to interfere. A con- 
clusion, therefore, however correctly deduced, in point of form, from 
admitted laws of nature, will have no other than a hypothetical cer- 
tainty. At every step we must assure ourselves that no other law of 
nature has superseded, or intermingled its operation with, those which 
are the premisses of the reasoning ; and how can this be done by 
merely looking at the words 1 We must not only be constantly think- 
ing of the phenomena themselves, but we must be constantly looking 
at them ; making ourselves acquainted with the peculiarities of every 
case to which we attempt to apply our general principles. 

The algebraic notation, viewed as a philosophical language, is per- 
fect in its adaptation to the subjects for which it is commonly employed, 
namely those of which the investigations have already been reduced 
to the ascertainment of a relation between numbers. But, admirable 
as it is for its own purpose, the properties by which it is rendered such 
are so far from constituting it the ideal model of philosophical language 
in general, that the mor^ nearly the language of any other branch of 
science approaches to it, the less fit that language is for its own proper 
functions. On all other subjects, instead of contrivances to prevent 
our attention from being distracted by thinking of the meaning of our 
signs, we require contrivances to make it impossible that we should 
ever lose sight of that meaning even for an instant. " 

With this view, as much meaning as possible should be thrown into 
the formation of the word itself; the aids of derivation and analogy 
being made available to keep alive a consciousness of all that is signi- 
fied by it. In this respect those languages have an immense advantage 
which form their .compounds and derivatives from native roots, like 
the German, and not from those of a foreign or a dead language, as is 
so much the case with English, French, and Italian : and the best are 
those which form them according to fixed analogies, corresponding to 
the relations between the ideas to be expressed. All languages do 
.this more or less, but especially, among modern European languages, 
. the German : while even that is inferior to the Greek, in which the 
relation between the meaning of a derivative word and that of its prim- 
itive, is in general clearly marked by its mode of formation ; except in 
the case of words compounded with prepositions, which, it must be 
acknowledged, are often, in both those languages, extremely anomalous. 

But all that can be done, by the mode of constructing words, to 
prevent them from degenerating into sounds passing through the mind 
without any distinct apprehension of what they signify, is far too little 
for the necessity of the case. Words, however well constructed origi- 
nally, are always tending, like coins, to have their inscription-wom off 
by passing from hand to hand; and the only possible mode of reviving 



432 OBSERVATIONS SUBSIDIARY TO INDUCTION. 

it is to be ever stamping it afresh, by living in the habitual contempla- 
tion of the phenomena themselves, and not resting in our familiarity 
with the words that express them. If any one, having possessed him- 
self of the laws of phenomena as recorded in words, whether delivered 
to him originally by others or even found out by himself, is content 
jfrom thenceforth to live in the midst of these formulae, to think exclu- 
sively of them, and of applying them to cases as they arise, without 
keeping up his acquaintance with the realities from which these laws 
were collected — not only will he continually fail in his practical efforts, 
because he will apply his formulae without duly considering whether, 
in this case and in that, other laws of nature do not modify or super- 
sede them ; but the formulae themselves will progressively lose their 
meaning to him, and he will cease at last even to be capable of recog- 
nizing with certainty whether a case falls within the contemplation of 
his formula or not. It is, in short, as necessary, on all subjects not 
mathematical, that the things on which we reason should be conceived 
by us in the concrete, and "clothed in circumstances," as it is in alge- 
bra that we should keep all individualizing peculiarities sedulously out 
of view. 

With this remark we shall close our observations on the Philosophy 
of Language. . ^ ^ . . y. , - ..,, ^ . v- - -'.■ 



/ 



4 w _ • o : 



.■- ■■ '' '^yy /*■* y , '. *.♦*"••'• ' •iv ' ■' r.^:. \ • ' •' " ••• ♦-'",-',■":♦ » •■'* 

'.* ■ •■••••. '.V/ &HAPTEK VII. ,.' ':•..•. V-'*" . -■'••'I 

■.^ •■ -v • ;fc>F CLASSIFICATION, AS SUBSIDIARY TO INDUCTION. " • *" 

■'*! ..* ->^ '...■ . '■•-.-.•,'' 

§ 1. There is, as we have frequently remarked in this work, a classi- 
fication of things, which is inseparable from the fact of giving them 
general names. Every name which connotes an att^L'ibute, divides, by 
that very fact, all things whatever into two classes, those which have 
the attribute and those which have not ; those of which the name can 
be predicated, and those of which it cannot. And the division thus 
made is not merely a division of such things as actually exist, or are 
known to exist, but of all such as may hereafter be discovered, and 
even of all such as can be imagined. 

On this kind of Classification we have nothing to add to what has 
previously been said. The Classification which requires to be dis- 
cussed as a separate act of the mind, is altogether different. In the 
one, the arrangement of objects in groups, and distribution of them into 
compartments, is a mere incidental effect consequent upon the use of 
names given for another purpose, namely, that of simply expressing 
some of their qualities. In the other, the arrangement and distribution 
are the main object, and the naming is secondary to, and purposely 
conforms itself to, instead of governing, that more important operation. 
Classification, thus regarded, is a contrivance for the best possible 
ordering of the ideas of objects in our minds; for causing the ideas to 
accompany or succeed one another in such a way as shall give us the 
greatest command over our knowledge already acquired, and lead most 
directly to the acquisition of more. The general problem of Classifi- 



CLASSIFICATION. , 433 

cation, in reference to these puiposes, may be stated as follows : To 
provide that things shall be thought of in such groups, and those groups 
in such an order, as will best conduce to the remembrance and to the 
ascertainment of their laws. 

Classification thus considered, differs from classification in the wider 
sense, in having reference to. real objects exclusively, and not to all 
that are imaginable : its object being the due coordination in our minds 
of those things only, with the properties of which we have actually 
occasion to make ourselves acquainted. But on the other hand it em- 
braces all really existing objects. We cannot constitute any one class 
properly, except in reference to a general division of the whole of 
nature; we cannot determine the group in which any one object can 
most conveniently be placed, without taking into consideration all the 
varieties of existing objects, all at least which have any degree of affinity 
with it. No one family of plants or animals could have been rationally 
constituted, except as part of a systematic arrangement of all plants or 
animals; nor could such a general aiTangement have been properly 
made, without first determining the exact place of plants and animals 
in a general division of nature. 

The theory of scientific classification, in its most general aspect, is 
now very well understood, owing chiefly to the labors of the distin- 
guished naturalists to whom science is indebted for what are called 
Natural Arrangements or Classifications, especially of the organized 
world. Mr. Whewell, in hh Fhilosopky of the Inductive- Sciences, has 
systematized a portion of the general logical principles which these 
classifications exemplify ; and this has been still more completely done 
by M. Comte, whose view of the philosophy of classification, in the 
third volume of his great work, is the most complete wdth which I am 
acquainted. 

§ 2. There is no property of objects which may not be taken, if we 
please, as the foundation for a classification or mental gi'ouping of 
those objects ; and in our first attempts we are likely to select for that 
purpose properties which are simple, easily conceived, and perceptible 
on a first view, without any previous process of thought. Thus Tour- 
nefort's aiTangement of plants was founded on the shape and divisions 
of the corolla; and that which is commonly called the Linngean (though 
Linnaeus also suggested another and more scientific arrangement) was 
grounded chiefly upon the number of the stamens and pistils. 

But these classifications, which are- at. first recommended by the 
facility they afford of ascertaining to what class any individual belongs, 
are seldom much adapted to the ends of that Classification which is 
the subject of our present remarks. The Linnaean arrangement an- 
swers the pui-jDose of making us think together of all those kinds of 
plants which possess the same number of stamens and pistils ; but to 
think of them in that manner is of little use, since we seldom have 
anything to affimi in common of the plants which have a given number 
of stamens and pistils. If plants of the class Pentandria, order Mono- 
gynia, agi-eed in any other properties, the habit of thinking and speak- 
ing of the plants under a common designation would conduce to our 
remembering those common properties so far as they were ascertained, 
and would dispose us to be on the look-out for such of them as are not 
yet known. But since this is not the case, the only purpose of thought 
31 



434 OPERATIONS SUBSIDIARY TO INDUCTION. 

whicli the Linrisean classification 'serves is that of causing us to re- 
member, better than we should otherwise have done, the exact number 
of stamens and pistils of every species of plants.- Now, as this prop- 
erty is of little importance or interest, the remembering it with any 
particular accuracy is of no moment. And inasmuch as, by habitually • 
' thinking of plants in those groups, we are prevented from habitually 
thinking, of them in groups which have a greater number of -properties 
in common, the effect of such a classification, when systematically 
adhered to, upon our habits of thought, must be regarded as mis- 
chievous. 

The ends of scientific classification are best '.answered, when the 
objects are formed into groups respecting which a greater number of 
general propositions can be made, and those propositions more impor- 
tant,, than could be. made respecting' any other groups into which the 
same, things could be distributed. The properties, therefore, according 
to which objects' are classified, should, if possible, be those which are 
causes of many other properties ; or at any rate, which are sure marks 
of them. Causes are preferable, both as being the surest and most 
direct of marks, and as being themselves the properties upon which it 
is of most use that our attention should be strongly fixed. But the 
property which is the cause of the chief peculiarities of a class, is 
unfortunately seldom fitted to serve also as the diagnostic of the class. 
Instead of the cause, we wiust generally select some of its more prom- 
inent effects, which may serve as marks of the other effects and of the 
cause itself. 

• A classification thus formed is properly scientific or philosophical, 
arid is commonly called a Natural, in contradistinction to a Technical 
or Artificial, classification or arrangement. The phrase Natural Clas- 
sification seems "most peculiarly appropriate- to such arrangements a,s 
correspond, in the groups which they form, to the spontaneous tenden- 
cies of the mind, by placing together the objects most similar in their 
general aspect ; in opposition to those technical systems which, ar- 
ranging things according to their agreement in some circumstance 
arbitrarily selected, often throw into the same group objects which in 
the general aggregate of their properties present no resemblance, and 
into different and remote groups, others which have the closest simi- 
larity. It is one of the most valid, reoomrpendations of any classifica- 
tioij "to the character of a scientific one, that it shall be a. natural 
classification in this sense also ; for the test of its scientific character is 
the number and importance of the properties which can be asserted in 
common of all -objects included in a group ; and- properties on which 
the .general aspect of the things depends, are, if only on tliat- ground, 
important, as well as, in most cases, numerous.. But, though a strong 
recommendation, this circumstance is not a sine qud non; since the 
more obvious properties of things may be of trifling. importance com- 
pared with others that are. not obvious. I have seen it mentioned as a 
great absurdity in the Linnaean classification, that it places (which by 
the way it does not) the violet by the side of the oak : it certainly dis- 
severs natural affinities, and brings together things quite as unlike as 
the oak and the violet are. But the difference, apparently so wide, 
which renders the juxtaposition of those two vegetables so suitable an 
illustration of a bad arrangement, depends, to the common eye, mainly 
upon mere size and texture j now if we made it our Study to adopt 



CLASSIFICATION. 435 

the classifiQation which would involve the least peril of similar rap- 
prochcmens, we should return to the obsolete division into trees, shrubs, 
and herbs, whieh although of primary importance with regard to mere 
general aspect, yet (compared 'even with so petty and unobvious a dis- 
tinction as that into dicotyledones and monocotyledones) answers to so 
few differences in the other properties of plants, that a classification 
founded on it (independently of- the indistinctness of the lines of 
demarkation,) would be as completely artificial and technical as the 
Linnaean. 

Our natural groups, therefore, must often be founded not upon the 
obvious, but upon the unobvious properties of things, when these are of ■ 
greater importance. But in such cases it is essential that there should 
be some other property or set of properties, more readiJy recognizable " 
by the observer, which coexist with, and may be received as marks of, 
the properties which are the real groundwork of the classification. A 
natural arrangement, for example, of animals, must be founded in the 
main upon their internal structure, but (as M. Comte justly remarks) it 
would be absurd that we should not be able to determine the genus and 
species of an animal without first killing it. On this ground, M. Comte 
gives the preference, among zoological classifications, to that of M. de 
•Blainville, founded upon the differences in the external integuments ; 
differences which correspond, much more accurately than might be sup- 
posed, to the really important varieties, both in the other parts of the" 
structure, and in the habits and history of the animals. 

This shows, more strongly than ever,* how extensive a knowledge of 
the properties of objects is necessary for making a good classification 
of them. And as it is one of the uses of such a classification that by 
drawing attention to the properties on which- it is founded, and which 
if the .classification be good are marks of many others, it facilitates the 
discovery of those others ; we' see in what manner our knowledge of 
things, and our classification of them, tend mutually and indefinitely to 
the- improvement of one another. 

"We said just now that the classification of objects should follow 
those of their properties vvhich indicate not only the most numerous, 
but also the most important peculiarities. What is here meant by 
importance % It has reference to the particular end in view : and the 
same objects, therefore, may admit with propriety of several different 
classifications. Each science or art forms its classification of things 
according to the properties which fall within its special cognizance, or 
of which it must take account in order to accomplish its peculiar prac- 
tical ends. A farmer does not divide plants, lik§ a botanist, into 
. dicotyledonous and monocotyledonous, but-into useful plants and weeds. 
A geologist divides fossils, not, like a zoologist, into families correspon-. 
ding to those of living species, but into fossils of the" secondary and of 
the tertiary periods, above the coal and below the coal, &c. ^Whales 
are or .are not fish,, according to the purpose for which we are consider- 
ing thein. "If we are speaking of the internal structure and physiology 
of the animal, we must no.t call them fish ;. for in these respects they 
deviate widely from fishes ; they have warm blood, and produce and 
suckle their young as land quadrupeds do. But this would not prevent 
our speaking of the tvJiale fishery, and calling such animals Jlsh on aU 
occasions connected with this employment;' for the relations thus arisino* 
depend upon the- aniriial's . living in the water, and being caught in a 



436 OPERATIONS SUBSIDIARY TO INDUCTION. 

manner similar to other fishes. A plea that human laws which mention 
fish do not apply to whales, would be rejected at once by an intelligent 
judge."* 

These different classifications are all good, for the purposes of their 
own particular departments of knowledge or practice. But when we 
are studying objects not for any special practical end, but for the sake 
of extending our knowledge of the whole of their properties and rela- 
tions, we must consider as the most important attributes, those which 
contribute most, either by themselves or by their effects, to render the 
things like one another, and unlike other things ; which give to the class 
composed of them the most marked individuality ; which fill, as it were, 
the largest space in their existence, and would most impress the atten- 
tion of a spectator who knew all their properties but was .not specially ' 
interested in any. Classes formed upon this principle may be called, 
in a more emphatic manner than any others, natural groups. 

§ 3. On the subject of these groups Mr. Whewell lays down a theo- 
ry, grounded on an important truth, which he has, in some respects, 
expressed and' illustrated very felicitously ; but also, as it appears to 
me, with some admixture of error. It will be advantageous, for both 
these reasons, to, extract the statement of his doctrine in the very* 
words he has used. 

"Natural groups," according to Mr. Whewell,t are "given by 
Type, not by Definition." And this consideration accounts for " that 
indefiniteness and indecision which we frequently find in the descrip- 
tions of such groups, and which must appear so strange and incon- 
sistent to any one who does not suppose these descriptions to assume 
any deeper ground of connexion than an arbitrary choice of the 
botanist. Thus in the family of the rose-tree, we are told that the 
ovules are very rarely erect, the stigmata usually simple. Of what 
use, it might be asked, can such loose accounts be 1 To which the 
answer is, that they are not inserted in order to distinguish the species, 
but in order to describe the family, and the total relations of the ovules 
and the stigmata of the family are better known by this general state- 
ment. A similar obsei'vation may be made with regard to the Anom- 
alies of each group, which occur so commonly, that Mr. Lindley, in his 
Introduction to the Natural System of Botany, makes the 'Anomalies' 
an article in each family. Thus, part of the character of the RosaceEe 
is, that they have alternate stipulate \g^Vg^^ and thdiX, the albumen \s 
obliterated ; but yet in Lowea, one of the genera of this family, the 
stipulae are absent ; and the albumen is present in another, Neillia. 
This implies, as we have already seen, that the artificial character (or 
diagnosis, as Mr. Lindley calls it), is imperfect. It is, though very 
nearly, yet not exactly, commensurate with the natural group : and 
hence in certain cases this character is made to yield to the general 
weight of natural affinities. 

" These views, — of classes determined by charactei-s which cannot 
be expressed in words, — ^of j)ropositions which state, not what hap- 
pens in all cases, but only usually, — -of particulars which are included 
in a class, though they transgress the definition of it, may probably 

* Aphorisms concerning the Language of Science, in Mr. Whewell's Philosophy of the 
Inductive Sciences, vol. i., p. Ixxv. 
■t Phil. Ind. Sc, i., 476-7. 



CLASSIFICATION. 437 

surprise the reader. They are so contrary to many of the received 
opinions respecting the use of definitions, and the nature of scientific 
propositions, that they will probably appear to many persons highly 
illogical and unphilosophical. But a disposition to such a judgment 
arises in a great measure from this, that the mathematical and 
mathematico-physical sciences have, in a great degree, determined 
men's views of the general nature and form of scientific truth ; while 
Natural History has not yet had time or opportunity to exert its due 
influence upon the current habits of philosophizing. The apparent 
indefiniteness and inconsistency of the classifications and definitions of 
Natural History belongs, in a far higher degree, to all other except 
mathematical speculations ; and the modes in which approximations 
to exact distinctions and general truths have been made in Natural 
History, may be worthy our attention, even for the light they throw 
upon the best modes of pursuing truth of all kinds." 

" Though in a Natural group of objects a definition can no longer 
be of any use as a regulative principle, classes are not therefore left 
quite loose, without any certain standard or guide. The class is 
steadily fixed, though not precisely limited; it is given, though not 
circumscribed; it is determined, not by a boundary line without, but 
by a central pointwit hin; not by what it strictly excludes, but by what it 
eminently includes ; by an example, not by a precept; in short, instead 
of Definition we have a Type for our director. 

" A Type is an example of any class, for instance a species of a 
genus, which is considered as eminently possessing the character of 
the class. All the species which have a greater affinity with this type- 
species than with any others, form the genus, and are ranged about 
it, deviating from it in various directions and different degrees. Thus 
a genus may consist of several species v/hich approach very near the 
type, and of which the claim to a place with it is obvious; while there 
may be other species which straggle further from this central knot, and 
which yet are clearly more connected with it than with any other. 
And even if there should be some species of which the place is dubi- 
ous, and which appear to be equally bound to two generic types, it is 
easily seen that this would not destroy the reality of the generic 
gi-oups, any more than the scattered trees of the intervening plain 
prevent our speaking intelligibly of the distinct forests of two sep- 
arate hills. 

" The type-species of every genus, the type-genus of every family, 
is, then, one which possesses all the characters and properties of the 
genus in a marked and prominent manner. The type of the Rose 
family has alternate stipulate leaves, wants the albumen, has the ovnles 
not erect, has the stigmata simple, and besides these features, which 
distinguish it from the exceptions or varieties of its class, it has the 
features which make it prominent in its class. It is one of those which 
possess clearly several leading attributes ; and thus, though we cannot 
say of any one genus that it must be the type of the family, or of any 
one species that it must be the type of the genus, we are still not 
wholly to seek ; the type must be connected by many affinities with 
most of the others of its group ; it must be near the centa'e of the 
crowd and not one of the stragglers." 

In this passage (the latter part of which especially I cannot help no- 
ticing as an "admirable example of philosophic style,) Mr. Wheweli 



438 OPERATIONS SUBSIDIARY TO INDUCTION. 

has stated very clearly and forcibly, but (I think) without making all 
necessary distinctions, one of the principles of a Natural Classification, 
What this principle is, what are its limits, and iii what manner, Mr, 
Whewell seems to me to have overstepped them, will appear when 
we have laid down another and more fundamental rule of Natural 
Arrangement, entitled to precedency over that which Mr. Whewell 
has here in view. • 

§ 4. The reader is by this time familiar with the general truth 
(which I restate so often on account of the -great confusion in which it 
is commonly involved), that there are in nature distinctions of Kind ; 
distinctions not consisting in a given number of definite properties, 
jplu^ the effects which follow from those properties, but ruiming through 
the whole nature, through the attributes generally, of the things so 
distinguished. . Our knowledge of the properties of a Kind is never 
complete. We are always discovering, eind expecting to discover, 
new ones. Where the distinction between things' is not one of kind, 
we expect to find their' properties alike, except where there is some 
reason for their being different. On the contrary, when the distinction 
is in kind, we expect to find the properties different unless there be 
some cause for their, being the same. All.knowledge of a Kind must 
be obtained by observation and experiment upon the Kind itself; no 
inference respecting its properties from the properties of things not 
connected withit by kind, goes for more than the sort of presumption 
usually characterized as an analogy, and generally in one' of its fainter 
degrees. . 

Since the common properties of a triie Kind, and consequently the 
general assertions which can be made respecting it, or which are cer- 
tain to be made hereafter as our knowledge extends, are indefinite. and 
inexhaustible '; and since the very first principle of natural classification 
is that of forming the classes so that the objects composing each may 
have the greatest number of properties in common ; this principle 
prescribes that every such classification shall recognize and adopt into 
itself all distinctions of Kind, which exist among the objects it pro- 
fesses to classify. To pass over any distinctions of Kind, and substitute 
definite distinctions, which, however considerable they may be, do not 
point to ulterior unknown differences, would be to replace classes with 
more by classes with fewer attributes in common ; and would be sub- 
versive of the Natural Method of Classification. 

Accordingly all natural arrangements, whether the reality of the 
distinction of Kinds was felt or not by their framers, have been led, by 
the mere pursuit of their own proper end, to conform themselves to 
the distinctions of Khid, so far. els these had been ascertained at the 
time. The Species of Plants are not only real Kinds, but are prob- 
ably,* all of them, real lowest Kinds, or Infimae Species ; which if we 
were to. subdivide, as of course it is open to us .to do, into sub-classes, 

* I say probably, not certainly, becaxise this is not the consideration by which a botanist 
determines what shall or shall not be admitted as, a species. In natural history those 
objects belong to the same species, which are, or consistently with experience might have 
been, produced from the same stock. ■ But this distinction in most, and probably in all 
cases, happily -accords with the other. It seems to be a law of physiology, thafanimab 
and plants do really, in the philosophical as well as .the popular sense, propagate their kind ; 
transmitting to their descendants all the distinctions of Kind (down to the most special OT 
lowest Kind), which they themselveg posses^. 



CLASSIFICATION. • 439 

the subdivision would necessarily be founded upon definite distinctions, 
not pointing (apart from what rnay be known of their causes or effects) 
to any difference beyond themselves. 

Iti so far as the natural classification is grounded upon real Kinds, 
its gi'oups are certainly not conventional ; Mr.- Wliewell is quite right 
in affirniing that they do not depend upon an arbitrary choice of the 
naturalist. But it does not follow, nor, I conceive, is it true, that 
these- 'classes are determined by a type, and not by characters. To 
determine them by 9, type would be as sure a way of missing the. Kind, 
as if we- were to select a set of characters arbitrarily. They are deter- 
mined by characters, but which are not arbitrary. The problem is, to 
find a. few definite characters which point to the multitude of indefinite ' 
ones. Kinds are Classes between which. there is an impassible bar- 
rier ; and what we have to seek is, marks whereby we may determine 
on which side of the barrier an object takes its place. The characters 
which will best do this are what should be chosen : .if they are also 
important in themselves, so. much the better. When we have selected 
the characters, we parcel out the objects according to those characters, 
and not, as Mr. WlieWell seems to suppose, according to resemblance 
to. a type. We do not compose the species Ranunculus acris, of all 
plants which bear a satisfactory degree of resemblance to a model-but- 
tercup, but of those which possess certain characters selected as marks 
by which we might recognize the possibility of a common parentage ; 
and the enumeration of those characters is the definition of the species. 

The question next arises, whether, as all Kinds must have a place 
among the classes, so all the classes in a natural arrangement must 
be Kinds'? And to this I answer, certainly not. The distinctions 
•of Kind are not numerous enough to supply the whole basis of 
a classification. Very few of the genera of plants, or even of the 
families, can be pronounced with certainty to be Kinds. The great 
distinctions of Vascular and Cellular, Dicotyledonous or Exogenous 
and Monocotyledonous or Endogenous, are perhaps differences of 
Jiind : the lines of demarkation which divide those classes seem (though 
even on this j would not pronounce positively) to go through the 
whole ■ nature of the plants. But the different species of a genus, or 
.genera of a family, usually have in common only a limited number of 
characters. A Rosa does not seem to differ from a Rubus, or the 
Umbelliferse from the Ranunculaceae,in much else than the characters 
■botanically assigiied to, those genera or those families. . Unenumerated 
differences certainly. do exist in some cases;- there • are families- of ' 
plants, which have peculiarities of chemical composition, or yield pro- 
ducts having peculiar effects on the animal economy.. The Cruciferge 
and Fungi contain an unusual proportion of azote ; tlie Labiatee are the 
chief sources of essential oils, the Solaneae are very commonly narcotic, 
&c. In these and sirhilar cases there are possibly distinctions of Kind ;. 
but it is by no means indispensable that there should be. Genera and 
Families ;may . be eminently natural, though marked out from one 
another by properties limited in" number-; provided those properties 
be important, and .tlK3 .objects .contained in each genus or family- re- 
semble 0ach other more tljan they- resemble anything which, is excluded 
Irom- the genus or .family. . • ._ "- • * . . 

After the recognition and definition, then,, of the infimcR species, the 
next &tep is to aiTangp these mfimcB species, into, larger groups : making 



440 OPERATIONS SUBSIDIARY TO INDUCTION. 

those groups correspond to Kinds wherever it is possible, but in most 
cases without any such guidance. And in doing- this it is true that we. ' 
are naturally and properly guided, in most cases at least, by resem- 
blance to a type. We form our groups round certain selected Kinds, 
each of which serves as a sort of exemplar of its group. But though 
the groups are suggested by types, I cannot agree with Mr, Whewell 
that a group when formed is determined by the type ; that in deciding 
whether a species belongs to the group, a reference is made to the 
type, and not to the characters; that the characters "cannot be ex- 
pressed in words." This assertion is inconsistent with Mr. Whewell's 
own statement of the fundamental principle of classification, namely, 
that " general assertions shall be possible." If the class did not possess 
any characters in common, what general assertions would be possible 
respecting it? Except that they all resemble each other more than 
they resemble anything else, nothing whatever could be predicated of 
the class. 

The truth is, on the contrary, that every genus or family is framed 
with distinct reference to certain characters, and is composed, first and 
principally, of species wliich agree in possessing all those characters. 
To these are added, as a sort of appendix, such other species, gener- 
ally, in small number, as possess nearly all the properties selected; 
wanting, some of them one property, some another, and which, while 
they agree with the rest almost as much as these agree with one 
another, do not resemble in an equal degree any other group. Our 
conception of the class continues to be grounded on the characters; 
and the class might be defined, those things which either possess that 
set of characters, or resemble the things that do so, more than they 
resemble anything else. 

^ And this resemblance itself is not, like resemblance between simple 
sensations, an ultimate fact unsusceptible of analysis. Even the inferior 
degree of resemblance is created by the possession of common char- 
acters. Whatever resembles the genus Rose more than it resembles 
any other genus, does so because it possesses a greater number of the 
characters of that genus, than of the characters of any other genus. 
Nor can there be the smallest difficulty in representing, by an enumera- 
tion of characters, the nature and degree of the resemblance which is 
strictly sufficient to include any object in the class. There are always 
some properties common to all things which are included. Others 
there often are, to which some things, which are nevertheless included, 
are exceptions. But the objects which are exceptions to one character 
are not exceptions to another: the resemblance which fails in some 
particulars must be made up for in others. The class, therefore, is 
constituted by the possession of all the characters which are universal, 
and most of those which admit of exceptions. If a plant had the 
ovules erect, the stigmata divided, the albumen not obliterated, and 
was without stipules, it probably would not be classed among the 
Rosaceae. But it may want any one, or more than one of these char- 
acters, and not be excluded. The ends of a scientific classification are 
better answered by including it. Since it agrees so nearly, in its known 
properties, with the sum of the characters of the class, it is likely to 
resemble that class more than any other in those of its properties which 
are still undiscovered. 
. Hot only, therefore,^ are natural groups, no less than any artificial 



CLASSIFICATION. 441 

classes, determined by characters; they are constituted in contempla- 
tion of, and by reason of, characters. But it is in contemplation not of 
those characters only which are rigorously common to all the objects 
included in the group, but of the entire body of characters, all of which 
are found in most of those, objects, and most of them in all. And 
hence our conception of the class, the image in our minds which is 
representative of it, is that of a specimen complete in all the charac- 
ters ; most naturally a specimen which, by possessing them all in the 
greatest degree in which they are ever found, is the best fitted to ex- 
hibit clearly, and in a marked manner, what they are. It is by a mental 
reference to this standard, not instead of, but in illustration of, the 
definition of the class, that we usually and advantageously determine 
whether any individual or species belongs to the class or not. And 
this, as it seems to me, is the amount of truth which is contained in 
Mr, Whewell's doctrine of Types. 

We shall see presently that where the classification is made for the 
express purpose of a special inductive inquiry, it is not optional, but 
necessary for fulfilling the conditions of a correct Inductive Method, 
that we should establish a type-species or genus, namely, the one which 
exhibits in the most eminent degree the particular phenomenon under 
investigation. But of this hereafter. It remains, for completing the 
theory of natural groups, that a few words should be said on the 
principles of the noinenclature adapted to them. 

§ 5.. A Nomenclature, as we have said, is a system of the names of 
Kind-s. These names, like other class-names, are defined by the 
enumeration of the characters distinctive of the class. The only merit 
which a set of names can have beyond this, is to convey, by the mode 
of their construction, as much information as possible : so that a per- 
son who knows the thing, may receive all the assistance which the 
name can give in, remembering what he knows, while he who knows 
it not, may receive as much knowledge respecting it as the case admits 
of, by merely being told its name. 

There are two modes of giving to the name of a kind this sort of 
significance. The best, but which unfortunately is seldom practicable, 
is when the word can be made to indicate, by its fomiation, the very- 
properties which it is designed to connote. The name of a kind does 
not, of course, connote all the properties of the kind, since these are 
inexhaustible, but such of them as are sufficient to distinguish it ; such 
as are sure marks of all the rest. Now, it is very rare that one 
property, or even any two or three properties, can answer this pur- 
pose. To distinguish the common daisy from all other species ot 
plants would require the specification of many characters. And a 
name cannot, without being too cumbrous for use, give indication, by 
its etymology or mode of construction, of more than a very small 
number of these. The possibility, therefore, of an ideally perfect 
Nomenclature, is. probably confined to the one case in which we are 
happily in possession of something nearly approacliing to it; I refer to 
the Nomenclature of Chemistry. The substances, whetlier simple or 
compound, with which chemistiy is conversant, are Kinds, and, as 
such, the properties which distinguish each of them from the rest, are 
innumerable ; but in the case of compound substances (the simple 
ones are not numerous enough to require a systematic nomenclature), 
3 K 



442 OPERATIONS SUBSIDIARY TO INDUCTION. 

there is one property, the chemical composition, which is of itself 
sufficient to distinguish the Kind ;• of itself a sure mark of all the other 
properties of the compound. All that was needful, therefore, was to 
make the name of every compound express, on the first hearing, its 
chemical composition; that is, to form the name of the compound, iri' 
some uniform manner, from' the names of the simple substances which 
enter into it as elements. This was done, most skillfully and success- 
fully, by the French chemists. The only thing .left unexpressed by 
them was the exact proportion in which the elements were combined.; 
and even this, since ' the establishment of the atomic theory, it has 
been found possible to express,, by a simple adaptation of their 
phraseology. • 

• But whero ,the characters which must .be taken into consideration in 
order sufficiently to designate the Kind, are too numerous to be all 
signified in the derivation of the name, and where no one of them is of 
such preponderant importance as to justify its being singled out to be 

. so indicated, we may avail ourselves of a subsidiary resource. Though 
we cannot indicate the distinctive properties of the kind, we may indi- 
cate its nearest natural affinities, by incorporating into its name the' 
name of the proximate natural group of which it is one of the. species. 
On this principle is founded the admirable binary nomenclature of • 
botany and zoology. . In this nomenclature the name, of every species 
consists of the name of the genus, or naturak group next above it, with 
g, word added to distinguish the particular species. This last portion 

"of the compound name is sometimes taken from some one of the pecu- 
liarities in which that species differs from others of the genus; as Cle- 
matis integrifolia,VotQTit\S\.d, alha,Yio\.3, palustris^ Artemisia vulgaris ; 
sometimes from a circumstance of a historical nature, as Narcissus j^oe- 
ticus, Potentilla tormentilla (indicating that the. plant was 'formerly 
known by the. latter name), Exacum Candpllii (from the fact that De^ 
CandoUe' was its first discoverer) ,^. and sometimes the word is purely 

. conventional, as Thlaspi hursa-pdstoris, Ranunculus tliora : it is of little . 
consequence which ; since the second, or as it is usually called the spe- 
cific name," could, at most, express, independently of convention, no 
more than a very small portion of the .connotation of the, term: But 
by adding to this the name of the superior genus, we make the best 
amends we can for the impossibility of so contrivhig the name as to 
express all the distinctive characters of the Kind, We make it, at all 
events, express as nla;ny of those characters as are common to the prox- 
irtiate natural group in which the Kind is included. If even those 
common characters are so numerous or so little familiar as to require a 
further extension of the same resource, we might, instead of a binary,, 
adopt a ternary nomenclature, employing not only the name of the 
geHus, but that of the next natural group in order of generality above 
the genus, commonly called the Family. This was done in the- min'e- 
ralogical nomenclature proposed by Professor Mohs. " The names 
•framed by him were," says Mr. Whewell,* ' *.' not composed of two, 
but of three elements, designating respectively the Species, the G'enus, 
and the Order; thus he has such species as Rliomhoheclral Lime Hd- 
leidc, Octahedral Fluor Haloide, IRrismatic Hal Baryte.''^- The binary 
construction, however, has been found sufficient iri botany and zoology, 

* Aphorisms concerning the Language of Science, p. Ixiv.. _ :. 



CLASSIFICATION BY SERIES. 443 

the only sciences in which this general principle has hitherto been sue- . 
cessfully adopted in the construction qif" a nomenclature. 

Besides the advantage which this principle of nomenclature possesses, 
in giving to the names of species the greatest quantity of independent ■ 
significance which the circumstances of the case admit of, it answers 
the further end of immensely economizing the use of names, and pre- 
venting ah otherwise intolerable burden upon the memory. When the 
naroes of species become extremely numerous, some artifice (as Mr. 
Whewell* obs.erves) becomes absolutely necessary to make it possible 
to recollect or apply them. . " The known species of plants, for ex- 
ample, were ten thousand in the time of. Linnaeus, and are now prob- 
ably sixty thousand. It would be useless to endeavor to" frame arid . 
employ separate names for each; of these- species. The division of the 
objects into a subordinated system of classification enables us to intro- 
duce a Nomenclature which does not require this enormous number of 
names. Each of the genera has its name, and the species are marked 
by the addition of some epithet to the name of the genus. In this 
manner about seventeen- hundred generic names, with a moderate 
number of specific names, were found by Linnaeus sufficient to desig- 
nate with precision all the species of vegetables known, at his time." 
And though the number of generic names has since' greatly increased, 
it has ■ not increased in anything like the proportion of the multiplica- 
tion of known Species. ~ y . . ■< ' 



CHAPTER VIII. 

OF CLASSIFICATION BY SERIES. 






§ 1. Thus far, we have considered the principles of scientific classi- 
fication so far only as relates to the formation of natural groups; and 
at this point most of those who have attempted a theory of natural ar- • 
rangenient, including, among the rest, Mr. Whewell, have stopped. 
There remains, however, another and a not less important portion of 
the theory, which has not yet, so farasT am aware, been systemati- 
cally treated of by any wTriter except M. Comte. This is, the aiTange- 
ment of 'the natural groups into a natural series. 

The end of Classification, as an instrument for the investigation of 
nature, is (as before stated) to make us think of those objects together, 
which have the greatest number of important-common properties ; and 
which therefore we have oftenest occasion, in the course of our induc- 
tions, for taking into joint consideration. Our ideas of objects are. thus 
brought into the order most conducive to the successful prosecution of 
inductive inquiries generally. But when the purpose is to facilitate • 
some particular inductive inquiry, more is required. To be instru- 
mental to that purpose, the classification must bring those objects to- 
gether, the simultaneous contemplation of which is likely to throw 
most light upon the particular subject. That subject being the laws 

• , ■■* Philosophy of the Inductive- Sciejices, i.jTp, i89.' 



444 OPERATIONS SUBSIDIARY TO INDUCTION. 

of some phenomenon, or some set of connected phenomena ; the very 
phenomenon or set of phenomena in question must be chosen as the 
groundwork of the classification. 

The requisites of a classification intended to facilitate the study of a 
particular phenomenon, are, first, to bring into one class all Kinds of 
things which exhibit that phenomenon, in whatever variety of forms or 
degrees ; and secondly, to arrange those Kinds in a series according 
to the degree in which they exhibit it, beginning with those w^hich 
exhibit most of it, and terminating with those which exhibit least. 
The principal example, as yet, of such a classification, is afforded by 
comparative anatomy and physiology, from which, therefore, our illus- 
trations shall be taken. 

§ 2. The object being supposed to be, the investigation of the laws 
of animal life ; the first step, after forming a distinct conception of the 
phenomenon itself, is to erect into one great class (that of animals) all 
the known Kinds of beings where that phenomenon presents itself; in 
however various combinations with other properties, and in however 
different degi'ees. As some of these Kinds manifest the general phe- 
nomenon. of animal life in a very high' degree, and others in an insig- 
nificant degree, barely sufficient for recognition ; we must, in the next 
place, arrange the various Kinds in a series, fallowing one another ac- 
cording to the degrees in which they severally exhibit the phenomenon ; 
beginning, therefore, with man, and ending with the most imperfect 
kinds of zoophytes. 

This is merely saying that we should put the instances, from which 
the law is to be inductively collected, into the order which is implied 
in one of the four Methods of Experimental Inquiry discussed in the 
preceding Book ; the fourth Method, that of Concomitant Variations. 
As we formerly remarked, this is often the only method to which re- 
course can be had, with assurance of a true conclusion, in cases in 
which we have but limited means of effecting, by artificial experiments, 
a separation of circumstances usually conjoined. The principle of the 
method is, that facts which increase or diminish together, and disappear 
together, are either cause and effect, or effects of a common cause. 
When it has been ascertained that this relation really subsists between 
the variations, a connexion between the facts themselves may be con- 
fidently laid down, either as a law of nature or only as an empirical 
law, according to circumstances. 

That the application of this Method must be preceded by the forrna- 
tion of such a series as we have described, is too obvious to need being 
pointed out; and the mere arrangement of a set of objects in a series,- 
according to the degrees in which they exhibit some fact of which we 
are seeking the law, is too naturally suggested by the necessities of 
our inductive operations, to require any lengthened illustration here. 
But there are cases in which the arrangement required for the special 
purpose, becomes the determining principle of the classification of the 
same objects for general pui'poses. This will naturally and properly 
happen, when those laws of the objects which are sought in the special 
inquiry enact so principal a part in the general character and histoiy 
of those objects — exercise so much influence in determining all the 
phenomena of which they are either the agents or the theatre-^ that 
all other diflerences existing among the objects are fittingly regarded aa 



CLASSIFICATION BY SERIES. • 445 

mere modifications of the one phenomenon sought; effects determined 
by the cooperation of some incidental circumstance with the laws of 
that phenomenon. Thus in the case of animated beings, the differences 
between one class of animals and another may reasonably be con- 
sidered as mere modifications of the general phenomenon, animal life ; 
modifications arising either from the different degrees in which that 
phenomenon is manifested in different animals, or firom the intermix- 
ture of the effects of incidental causes peculiar to the nature of each, 
with the effects produced by the general laws of life ; those laws still 
exercising a predominant influence over the result. Such being the 
case, no other inductive inquiry respecting animals can be successfully 
carried on, except in subordination to the great inquiry into the uni- 
versal laws of animal life. And the classification of animals best 
suited to that one purpose, is the most suitable to all the other pur- 



P 



OSes of zoological science. 



§ 3. To establish a classification of this sort, or even to comprehend 
it when established, requires the power of recognizing the essential 
similarity of a phenomenon, in its minuter degrees and obscurer forms, 
with what is called the sa7ne phenomenon in the greatest perfection ot 
its development; that is, of identifying with each other all phenomena 
which differ only in degree, and in properties which we suppose to be 
caused by difference of degree. In order to recognize this identity, 
or in other words, this exact similarity of quality, the assumption of a 
type-species is indispensable, We must consider as the type of. the 
class, that among the Kinds included in it, which exhibits the properties 
constitutive of the class, in the highest degree ; conceiving the other 
varieties as instances of degeneracy, as it were, from that type ; devia- 
tions from it by inferior intensity of the characteristic property or 
properties. For every phenomenon is best studied {ccRteris paribus) 
where it exists in the greatest intensity. It is there that the effects 
which either depend upon it, or depend upon the same causes with it, 
will also exist in the greatest degree. It is there, consequently, and 
only there, that those effects of it, or joint effects with it, can become 
fully knowni to us ; so that we may learn to recognize their smaller 
degrees, or even their mere rudiments, in cases in which the direct 
study would have been difiicult or even impossible. Not to mention 
that the phenomenon in its higher degrees may be attended by effects 
or collateral circumstances which in its smaller degrees do not occur at 
all, requiring for their production in any sensible amount a greater 
degi'ee of intensity of the cause than is there met with. In man, for 
example (the species in v/hich both the phenomenon of animal and that 
of organic life exist in the highest degree), many subordinate phe- 
nomena develop themselves in the course of his animated existence, 
which the inferior varieties of animals do not show. The knowledge 
of these properties may nevertheless be of great avail towards the 
discovery of the conditions and laws of the general phenomenon of life, 
which is common to man with those inferior animals. And they are, 
even, rightly considered as properties of animated nature itself; 
because they may evidently be affiliated to the general laws of ani- 
mated nature ; because we may fairly presume that some rudiments 
or feeble degrees of those properties would be recognized in all 
animals by more perfect organs, or even by more perfect instruments, 



446 OPERATIONS SUBSIDIARY TO INDUCTION. 

than one ; and because those may be correctly termed properties of a 
class, which a thing exhibits exactly in proportion as it belongs to the 
class, that is, in proportion as it possesses the main attributes con- 
stitutive of the class. ' . " , 

§ 4. It remains to consider how the internal distribution of the series 
may most properly take place : in what manner it should be divided 
into Orders, Families, and Genera. 

The main principle of division must of course be natural affinity ; 
the classes formed must be natural groups : and the formation of these 
has already been sufficiently treated of. But the "principles of natural 
grouping must be applied, in subordination to the principle of a natural 
series. The groups must not be so constituted as to place in the same 
gi-oup things which ought- to occupy different points of the general 
scale. The precaution necessary to be observed for this purpose is, 
that the primary divisions must be grounded not upon all distinctions 
indiscriminately, but upon those which correspond to. variations in the 
degree of the main phenomenon. The series of Animated Nature 
should be broken into parts at the exact points where the variation in 
the degree of intensity of the main phenomenon (as marked by its 
principal characters, Sensation, Thought, Voluntary Motion, &c.) be- 
gins to be attended by conspicuous changes in the miscellaneous prop- 
erties of the animal. Such well marked changes take place, for 
example, where the class Mammalia ends ;" at the points where Fishes 
are separated from Insects, Insects from MoUusca, &c. When so 
formed, the primary natural groups will compose the series by mere 
juxtaposition, without redistribution ; each of them corresponding to 
a definite division of the scale. In like manner each family should, if 
possible, be so subdivided, that one portion of it shall stand higher atid 
the other lower, though of course contiguous, in. the general .scale ; 
.and only when. this is- impossible is it allowable to ground the remain- 
ing subdivisions upon characters having no determinable connexion 
with the main phenomenon. 

Where the principal phenomenon so far transcends in importance all 
•other properties on which a classification could be grounded, as it does 
in the case of animated existence, any considerable deviation from the 
rule last laid down is in general sufficiently guarded against by the first 
principle of a natural arrangement, that of forming thfe groups ag- 
cordingto the most important characters. All attempts at a sci"entific 
classification of animals, since first their anatomy and physiology were 
successfully studied, have been framed with a certain degree of in- 
stinctive reference to a natural series, and have accorded, in many 
more points than they have differed, with the classification which 
would most naturally have been grounded upon such a series. But- 
the accordance has not. always been complete, and it still is often a 
inatter of discussion which of several classifications best accords- with 
the true scale of intensity of the main phenomenon. M. Comte, for 
example, blames Cuvier forhaving formed his natural groups with aii 
undue degree of- reference to the mode .of alimentation, a circumstance 
directly connected only with organic life, and leading to an arrange- 
ment most -inappropriate for the purposes of an investigation of the 
laws of animal life, since both carnivorous and herbivorous or frugivo- 
rous animals are found at almost every degree in the scale of animal 



CLASSIFICATION BY SERIES, 447 

perfection. M. Comte, with much apparent reason, gives, on these 
gronnds, gi'eatly the preference to the classification framed by M. de 
Blainville ; as representing correctly, by the mere order of the groups, 
the successive degeneracy of aninial nature from its highest to its most 
itnperfect exemplification. 

§ 5. A classification of any large portion of the field of nature, in con- 
formity to the foregoing principles, has hitheito been found practicable 
only in one gi'eat instance, that of animals. In the case, even of vege- 
tables, thenatm-al arrangement has not been carried beyond the forma- 
tion of natural gi'oups. Naturalists have found and probably vs^ill 
continue to find it impossible to form those groups into any series, the 
terms of v^hich correspond to real gi^adations in the phenomenon of 
vegetative or organic life. Such a difference of degree may be traced 
between the class of Vascular Plants and that of Cellular, which 
includes lichens, algae, and other substances whose organization is 
simpler and more, rudimentary than that of the higher order of vegeta- 
bles, and which therefore approach nearer to mere inorganic' nature. 
But when we rise much above this point, we do not find any recogniz- 
able difference in the degree in which different plants possess the 
properties of organization and life. The dicotyledones and the mono- 
cotyledpnes are distinct natural groups, but it cannot be said, even by 
a metaphor, that the former are more or less plants than the latter. 
The palm-tree and the oak, the rose and the tulip, are organized and 
vegetate in a different manner, but certainly not in a different degree. 
The natural classification of vegetables must therefore continue to be 
made without reference to any scale or series ; and the whole vegetable 
kingdom must form, as it does. in M. Comte's arrangement, one single 
step or gradation, the lowest of all in the series of organized beings, 
scientifically constructed for the purpose of facilitating the investiga- 
tion .of the laws of organic life. . 

. Although the scientific arrangements of organic nature afford as yet 
.the only complete example of the true principles of rational classifica- 
tion, whether as to the formation of gTOups or. of series, those principles 
are applicable to all cases in which mankind are called upon- to bring 
the various parts of any extensive subject into mental coordination. 
Th-ey are as much to the point when objects are to be classed for 
purposes of 'art or business, as for those of science. . The proper 
arrangement, for example, of a code of laws, depends upon the same 
scientific conditions as the classifications in natural history ; nor could 
there be a better preparatory discipline for that important function, 
than the study of the principles of a natural arrangement, not only in 
the abstract, but in their actual application to the class of phenomena 
for which they were first elaborated, and which are still the best school 
for learning their use. Of this the great authority on codification, 
Bentham, was perfectly aware : -and his early Fragment on Government, 
the admirable introduction to' a series of writings unequaled in their 
•peculiar department, contains clear and just views (as far as they go) 
on the meaning of a natural arrangement, such as could scarcely have 
occuiTed to any one who lived a,nterior to.' the age of Linnaeus and 
•Bernard de Jussieu. 



BOOK V. 

ON FALLACIES. 



^ II leur semble qu'il n'y a qu'a douter par fantaisie, et qu'il n'y a qu'^ dire en gen6ral 
que notre nature est infirme ; que notre esprit est plein d'aveuglement ; qu'il faut avoir un 
grand soin de se defaire de ses pr6juges, et autres choses seinblables. lis pensent que cela 
suffit pour ne plus se laisser seduire a ses sens, et pour ne plus se tromper du tout. II ne 
suffit pas de dire que I'esprit est foible, il faut lui faire sentir ses foiblesses. Ce n'est pas 
assez de dire qu'il est sujet a I'erreur, il faut lui decouvrir en quoi consistent ses erreurs." 
— Malebranche, Recherche de la Verite. 

" Errare non modo affirmando et negando, sed etiam sentiendo, et in tacita hominum 
cogitatione contingit." — Hobbes, Computatio sive Logica, ch. v. 



CHAPTER I. 

OF FALLACIES IN GENERAL. 



§ 1. It is a maxim of the schoolmen, that " contrariorum eadem est 
scientia :" we never really know what a thing is, unless we are also 
able to give a sufficient account of its opposite. Conformably to this 
maxim, one considerable section, in most treatises on Logic, is devoted 
to the subject of Fallacies; and the practice is too well worthy of 
observance, to allow of our departing from it. The philosophy of rea- 
soning, to be complete, ought to comprise the theory of bad as well as 
of good reasoning. 

We have endeavored to ascertain the principles by which the suffi- 
ciency of any proof can be tested, and by which the nature and amount 
of evidence needful to prove any given conclusion can be determined 
beforehand. If these principles were adhered to, then although the 
number and value of the truths ascertained would be limited by the 
opportunities, or by the industry, ingenuity, and patience, of the indi- 
vidual inquirer, at least error would not be embraced instead of truth. 
But the general consent of mankind, founded upon all their experience, 
vouches for their being far indeed from even this negative kind of 
perfection in the employment of their reasoning powers. 

In the conduct of life — in the ordinary business of mankind — wrong 
inferences, incorrect interpretations of experience, unless after much 
culture of the thinking faculty, are absolutely inevitable : and with 
most people after the highest degree of culture they ever attain (unless 
where the events of their daily life supply an immediate corrective), 
such erroneous inferences are as frequent if not more frequent than 
coiTcct inferences, correct interpretations of experience. Even in the 
speculations to which the highest intellects systematically devote them- 
selves, and in reference to which the collective mind of the scientific 
world is always at hand to aid the efforts and control the aberrations 



FALLACIES IN GENERAL. 449 

of individuals, it is only from the more perfect sciences, from those of 
which the subject matter is the least complicated, that opinions not 
resting upon a correct induction have at length, generally speaking, 
been expelled. In the departments of inquiry relating to the more 
complex phenomena of the universe, and especially those of which the 
subject is man, whether as a moral and intellectual, a social, or even 
as a physical being ; the diversity of opinions still prevalent among 
instructed persons, and the equal confidence with which those of the 
most contrary ways of thinking cling to their respective tenets, are a 
proof not only that right modes of philosophizing are not yet generally 
adopted on those subjects, but that wrong ones are ; that philosophers 
have not only in general missed the truth, but have often embraced 
error ; that even the most cultivated portion of our species have not 
yet learned to abstain from dravnng conclusions for which the evidence 
is insufficient. 

The only complete safeguard against reasoning ill, is the habit of 
reasoning well ; familiarity with the principles of correct reasoning, 
and practice in applying those principles. It is, however, not unim- 
portant to consider what are the inost commpn modes of bad reasoning ; 
by what appearances the mind is most likely to be seduced from the 
observance of true principles of induction ; what, in short, are the most 
common and most dangerous varieties of Apparent Evidence, v\^hereby 
men are misled into opinions for wJiich there does not exist evi- 
dence really conclusive. 

A catalogue of the varieties ^)f apparent evidence which are not real 
evidence, is' an enumeration of Fallacies. "Without such an enumera- 
tion, therefore, the present work would be wanting in an essential 
point. And while writei'S '^ho included in their theory of reasoning 
nothino- more than ratiocination, have, in consistency with this limita- 
tion confined their retiiarks to the fallacies which have their seat in 
that portion of the process of investigation ; we, who profess to treat 
of the whole process, must add to our directions for perfonning it 
rigttly, warping-s against performing it vn^ong in any of its parts : 
whether the ratiocinative or the experimental portion of it be in 
fault, or the fault lie in dispensing with ratiocination and induction 
altoget2ier. 

I 2. In considering the sources of unfounded inference, it is un- 
necessary to reckon the errors which arise, not from a wrong method, 
or even from ignorance of the right one, but from a casual lapse, 
through hurry or inattention, in the application of the true principles 
of induction. Such eiTors, like the accidental mistakes in casting up 
a sum, do not call for philosophical analysis or classification; theo- 
retical considerations can throw no light upon the means of avoiding 
them. In the present treatise our attention is required, not to mere 
inexpertness in performing the operation in the right way, (the only 
remedies for which are increased attention and more sedulous prac- 
tice,) but to the modes of performing it in a way fundamentally 
v^n^-ong ; the conditions under which the human mind persuades itself 
that it has sufficient grounds for a conclusion which it has not arrived 
at by any of the legitimate methods of induction — which it has not, 
even carelessly or overhastily, endeavored to test by those legitimate 
methods. 

3L 



450 FALLACIES. 

§ 3. There is another branch of what may be called the Philosophy 
of Error, which must be mentioned here, though only to be excluded 
from our subject. The sources of erroneous opinions are two-fold, 
moral and intellectual. Of these, the moral do not fall within the com- 
pass of this work. They may be classed under two general heads ; 
Indifference to the attainment of truth, and Bias : of which last the 
most common case is that in which we are biased by our wishes ; but 
the liability is almost as great to the undue adoption of a conclusion 
which is disagreeable to us as of one which is agreeable, if it be of a 
nature to bring into action any of the stronger passions. Persons of 
timid character are the more predisposed to believe any statement, the 
more it is calculated to alarm them. Indeed, it is a psychological law, 
deducible from the most general laws of the mental constitution ot 
man, that any strong passion renders us credulous as to the existence 
of objects suitable to excite it. 

But the moral causes of our opinions, though real and most powerful, 
are but remote causes : they do not act immediately, but by means ot 
the intellectual causes- to which they bear the same relation that the 
circumstances called, In the theory of medicine, predisposing causes, 
bear to exciting causes. Iixdifference to truth cannot, in and by itself, 
produce erroneous belief; it operates by preventing the mind from 
collecting the proper evidences, or from applying to them the test of a 
legitimate and rigid induction ; b^ which omission it is exposed unpro- 
tected to the influence of any species of apparent evidence which 
occurs spontaneously, or which is elicited by that smaller quantity of 
trouble which the mind may be not uriwilling to take. As Httle is 
Bias a direct source of wrong conclusions. We cannot believe a 
proposition only by wishing, or only by drehding, to beHeve it. The 
most violent inclination to find a set of propositions true will not enable 
the weakest of mankind to believe them vdtl^oMt a vestige of intel- 
lectual grounds, without any, even apparent, evidence. It can only 
act indirectly, by placing the intellectual grounds of belief in an in- 
complete or distorted shape before his eyes. It make.s him shi'ink 
from the irksome labor of a rigorous induction, when he has a mis- 
giving that its result may be disagreeable ; and in such examination as 
he does institute, it makes him exert that which is in a certain measure 
voluntary, his attention, unfairly, giving a larger share of it to the 
evidence which seems favorable to the desired conclusion, a smbller 
to that which seems unfavorable. And the like when the bias arises 
not from desire but fear. Although a person afraid of ghosts believes 
that he has seen one on evidence wonderfully inadequate, he does not 
believe it altogether without evidence ; he has perceived some unusual 
appearance, while passing through a church-yard : he saw something 
start up near a grave, which looked white in the moonshine. Thus 
eveiy erroneous inference, though originating in moral causes, involves 
the intellectual operation of admitting insufficient evidence as sufficient; 
and whoever was on his guard against all kinds of inconclusive evidence 
which can be mistaken for conclusive, would be in no danger of being 
led into error even by the strongest bias. There have been minds so 
strongly fortified on the intellectual side, that they could not blind 
themselves to the light of truth, however really desirous of doing so ; 
they could not, with all the inclination in the world, pass off upon 
themselves bad arguments for good ones. If the sophistry of the in- 



CLASSIFICATION OF FALLACIES. 451 

telle ct could be rendered impossible, that of the feelings, having no 
instrument to work with, would be powerless. A comprehensive 
classification of all those things which, not being evidence, ai'e liable 
to appear such to the understanding, will, therefore, include all errors 
of judgment arising from moral causes, to the exclusion only of errors 
of practice committed against better knowledge. 

To examine, then, the various kinds of apparent evidence which are 
not evidence at all, and of apparently conclusive evidence which do not 
really amount to conclusiveness, is the object of that part of our inquiry 
into which we are about to enter. 

The subject is not beyond the compass of classification and compre- 
hensive survey. The things, indeed, which are not evidence of any 
given conclusion, are manifestly endless, and this negative property, 
having no dependence upon any positive ones, cannot be made the 
groundwork of a real classification. But the things ^vhich, not being 
evidence, are susceptible of being mistaken for it, are capable of a 
classification having reference to the positive property which they 
possess, of appearing to be evidence. We may arrange them, at our 
choice, on either of two principles ; according to the cause which makes 
them appear evidence, not being so ; or according to the particular 
kind of evidence which they simulate. The Classification of Fallacies 
which will be attemped in the ensuing chapter, is founded upon these 
considerations jointly. 



CHAPTER II. 

CLASSIFICATION OF FALLACIES. 

§ 1. In attempting to establish certain general distinctions which shall 
mark out from one another the various kinds of Fallacious Evidence, 
we propose to ourselves an altogether different aim from that of sev- 
eral eminent thinkers, who have given, under the name of Political or 
other Fallacies, a mere enumeration of a certain number of erroneous 
opinions; false general propositions which happen to be often met with ; 
loci communes of bad arguments on some particular subject. Logic is 
not concerned with the false opinions which men happen to entertain, 
but with the manner in which they come to entertain them. The ques- 
tion for us is not, what facts men have at any time erroneously supposed 
to be proof of certain other facts, but what property in the facts it was 
which led them to this mistaken supposition. 

When a fact is supposed, although incoiTectly, to be evidentiary of, 
or a mark of, some other fact, there must be a cause of the error ; the 
supposed evidentiaiy fact must be connected in some particular manner 
with the fact of which it is deemed evidentiary, must stand in some 
paiticular relation to it, without which relation it would not be regarded 
m that light. The relation may either be one resulting from the simple 
contemplation of the two facts side by side with one another, or it may 
depend upon some process of our own mind, by which a previous asso- 
ciation has been established between them. Some peculiarity of rela- 
tion, however, there must be \ the fact which can, even by the wildest 



452 t'ALLACIES. 

aberration, be supposed to prove another fact, must stand in som6 
special position with regard to it; and if we could ascertain and define 
that special position, we should perceive the origin of the error. 

We cannot regard one fact as evidentiary of another unless we 
believe that the two are always, or in the majority of cases, conjoined. 
If we believe A to be evidentiary of B, if when we see A we are 
inclined to infer B from it, the reason is because we believe that where- 
ever A is, B also either always or for the most part exists, either as an 
antecedent, a consequent, or a concomitant. If when we see A we are 
inclined not to expect B, if we believe A to be evidentiary of the absence 
of B, it is because we believe that where A is, B either is never, or at 
least seldom, found. Erroneous conclusions, in short, no less than 
correct conclusions, have an invariable relation to a general formula, 
either expressed or tacitly implied. When we infer some fact from 
sorne othei: fact which does not really prove it, we either have admitted, 
or if we maititained consistency, ought to admit, some groundless gen- 
eral proposition respecting the conjunction of the two phenomena. 

For every property, therefore, in facts, or in our mode of considering 
facts, which leads us to believe that they are habitually conjoined when 
they are not, or that they are not when in reafity they are, there is a 
corresponding kind of Fallacy; and an enumeration of Fallacies would 
consist in a specification of those properties in facts, and those pecu- 
liarities in our mode of considering them, which give rise to this en'O- 
neous opinion. 

§ 2. To begin, then; the supposed connexion, or repugnance, between 
the two facts, may either be a conclusion from evidence (that is, from 
some other proposition or propositions) or may be admitted without 
any such ground ; admitted, as the phrase is, on its ovm evidence : em- 
braced as self-evident, as an axiomatic truth. This gives rise to the first 
great distinction, that between Fallacies of Inference, and Fallacies of 
Simple Inspection. In the latter division must be included not only 
all cases in which a proposition is believed and held for true, literally 
without any extrinsic evidence, either of specific experience or general 
reasoning ; but those more frequent cases in which simple inspection 
creates a presumption in favor of a proposition ; not sufficient for belief 
but sufficient to cause the strict principles of a regular induction to be 
dispensed with, and creating a predisposition to believe it on evidence 
which would be seen to be insufficient if no such presumption existed. 
This class, comprehending the whole of what may be termed Natural 
Prejudices, and which I shall call indiscriminately Fallacies of Simple 
Inspection or Fallacies a priori^ shall be placed at the head of our list. 

Fallacies of Inference, or erroneous conclusions from supposed 
evidence, must be subdivided according to the nature of the apparent 
evidence from which the conclusions are drawn ; or (what is the same 
thing,) according to the particular kind of sound argument which the 
fallacy in question simulates. But there is a distinction to be first 
drawn, which does not answer to any of the divisions of sound argu- 
ments, but arises out of the nature of bad ones. We may know 
exactly what our evidence is, and yet draw a false conclusion from it; 
we may conceive precisely what our premisses are, what alleged mat- 
ters of fact, or general principles, are the foundation of our inference ; 
and yet, because the premisses are false, or because we have inferred 



CLASSIFICATION OP FALLACIES. 453 

from them what they will not support, our conclusion may be erro- 
neous. But a case, perhaps even more frequent, is that in which 
the error arises from not conceiving our premisses with due clearness, 
that is, (as shown in the preceding book,*) with due fixity : forming 
one conception of our evidence when we collect or receive it, and 
another when we make use of it ; or unadvisedly and in general un- 
consciously substituting, as we proceed, different premisses in the 
place of those with which we set out, or a different conclusion for that 
which we undertook to prove. This gives existence to a class of fal- 
lacies which may be justly termed Fallacies of Confusion ; compre- 
hending, among others, all those which have their source in language, 
whether arising from the vagueness or arabiguity of our terms, or from 
casual associations with them. 

When the fallacy is not one of Confusion, that is, when the propo- 
sition believed, and the evidence on which it is believed, are steadily 
apprehended and unambiguously expressed, there remain to be made 
two cross divisions, giving rise to four classes. The Apparent Evidence 
may be either particular facts, or foregone generalizations ; that is, 
the process may simulate either simple Induction, or Deduction : and 
again, the evidence, whether consisting of facts or general propositions, 
may be false in itself, or, being true, may fail to bear out the conclu- 
sion attempted to be founded upon it. This gives us, first, Fallacies 
of Induction and Fallacies of Deduction, and then a subdivision of 
each of these, according as the supposed evidence is false, or true but 
inconclusive. 

Fallacies of Induction, where the facts upon which the induction 
proceeds are erroneous, may be termed Fallacies of Observation. The 
term is not strictly accurate, or rather, not accurately coextensive with 
the class of fallacies which I propose to designate by it. Induction is 
not always grounded upon facts immediately observed, but sometimes 
upon facts inferred : and when these last are erroneous, the error is not, 
in the literal sense of the term, an instance of bad observation, but of 
bad inference. It will be convenient, however, to make only one class 
of all the inductions of which the en-or lies in not sufficiently ascer- 
taining the facts on which the theory is grounded ; whether the cause 
of failure be mal-observation, or simple non-observation, and whether 
the mal-observation be direct, or by means of intermediate marks 
which do not prove what they are supposed to prove. And in the 
absence of any comprehensive term to denote the ascertainment, by 
whatever means, of the facts on which an induction is grounded, I will 
venture to retain for this class of fallacies, under the explanation already 
given, the title, Fallacies of Observation. 

The other class of inductive fallacies, in which the facts are correct, 
but the conclusion not warranted by them, are properly denominated 
Fallacies of Generalization : and these, again, fall into various subor- 
dinate classes, or natural groups, some of which will be enumerated 
in their proper place. 

When we now turn to Fallacies of Deduction, namely, those modes 
of incorrect argumentation in which the premisses, or some of them, are 
general propositions, and the argument a ratiocination ; we may of 
course subdivide these also into two species, similar to the two preced- 

* Supra, p. 396. 



454 FALLACIES. 

ing, namely, those which proceed on false premisses, and those of 
which the premisses, though true, do not support the conclusion. But 
of these species, the first must necessarily fall within some one of the 
heads already enumerated. For the error must be either in those 
premisses which are general propositions, or in those which assert 
individual facts. In the former case it is an Inductive Fallacy, of one 
or the other class ; in the latter it is a Fallacy of Observation : unless, 
in either case, the erroneous premiss has been assumed on simple 
inspection, in which case the fallacy is a priori. Or, finally, the prem- 
isses, of whichever kind they are, may never have been conceived in 
80 distinct a manner as to produce any clear consciousness by what 
means they were arrived at ; as in the case of what is called reasoning 
in a circle : and then the fallacy is of Confusion. 

There remains, therefore, as the only class of fallacies having prop- 
erly their seat in deduction, those in which the premisses of the ratio- 
cination do not bear out its conclusion ; the various cases, in short, 
of vicious argumentation, provided against by the rules of the syllogism. 
We shall call these, Fallacies of Ratiocination. 

We have thus five distinguishable classes of fallacy, which may be 
expressed in the following synoptic table : — 

of Simple Inspection ... 1. Fallacies a priori. 

/ Inductive |2. Fallacies of Observation, 

from evidence V Fallacies \ 3. Fallacies of Generalization, 
distinctly con- I 



Fallacies 



ceived ^ ^^^;^^2 \ 4. Fallacies of Ratiocination. 



Fallacies 
from evidence ) 
indistinctly > ... 5. Fallacies of Confusion. 
of Inference j I. conceived ) 

§ 3. We must not, however, expect to find that men's actual errors 
always, or even commonly, fall so unmistakably under some one of 
these classes, as to be incapable of being referred to any other. Erro- 
neous arguments do not admit of such a sharply cut division as valid 
arguments do. An argument fiiUy stated, with all its steps distinctly 
set out, in language not susceptible of misunderstanding, must, if it be 
eiToneous, be so in some one, and one only, of these five modes ; or 
indeed of the first four, since the fifth, on such a supposition, would 
vanish. But it is not in the nature of bad reasoning to express itself 
thus unambiguously. When a sophist, whether he is imposing upon 
himself or attempting to impose upon others, can be constrained to 
throw his sophistry into so distinct a form, it needs, in a large propor- 
tion of cases, no further exposure. 

In all arguments, everywhere but in the schools, some of the links 
are suppressed ; a fortiori when the arguer either intends to deceive, 
or is a lame and inexpert thinker, little accustomed to bring his rea- 
soning processes to any test : and it is in those steps of the reasoning 
which are made in this tacit and half- conscious, or even wholly uncon- 
scious manner, that the error oftenest lurks. In order to detect the 
fallacy, the proposition thus silently assumed must be supplied ; but the 
reasoner, most likely, has never really asked himself what he was as- 
suming : his confuter, if unable to extort it from him by the Socratic 
mode of interrogation, must himself judge what the suppressed premiss 
ought to be in order to support the conclusion. And hence, in the 
words of Archbishop Whately, " it must be often a matter of doubt, or 



CLASSIFICATION OF FALLACIES. 455 

ratlier of arbitrary choice, not only to which genus each kind of fallacy 
should be referred, but even to which kind to refer any one individual 
fallacy ; for since, in any course of argument, one premiss is usually 
suppressed, it frequently happens in the case of a fallacy, that the hear- 
ers are left to the alternative of supplying cither a premiss which is not 
true, or else, one which does not prove the conclusion: e.g., if a man 
expatiates on the distress of the country, and thence argues that the 
government is tyrannical, we must suppose him to assume either that 
* every distressed country is under a tyranny,' which is a manifest 
falsehood, or, merely that ' every country under a tyranny is distressed,' 
which, however true, proves nothing, the middle term being undis- 
tributed." The former would be ranked, in our distribution, among 
fallacies of generalization, the latter among those of ratiocination. 
*' Which are we to suppose the speaker meant us to understand % 
Surely" (if he understood himself) "just whichever each of his hearers 
might happen to prefer : some might assent to the false premiss ; 
others allow the unsound syllogism." 

Almost all fallacies, therefore, might in strictness be brought under 
our fifth class, Fallacies of Confusion. A fallacy can seldom be abso- 
lutely referred to any of the other classes ; we can only say, that if all 
the links were filled up which should be capable of being supplied in 
a valid argument, it would either stand thus (forming a fallacy of one 
class), or thus (a fallacy of another) ; or at furthest we may say, that 
the conclusion is most likely to have originated in a fallacy of such 
and such a class. Thus in Archbishop Whately's illustration, the 
error committed may be traced with most probability to a fallacy of 
generalization ; that of mistaking an uncertain mark, or piece of evi- 
dence for a certain one ; concluding from an effect to some one of its 
possible causes, when there are others which would have been equally 
capable of producing it. 

Yet, though the five classes run into each other, and a particular 
error often seems to be arbitrarily assigned to one of them rather than 
to any of the rest, there is considerable use in so distinguishing them. 
We shall find it convenient to set apart, as Fallacies of Confusion, 
those of which confusion is the most obvious characteristic ; in which 
no other cause can be assigned for the mistake committed, than neg- 
lect or inability to state the question properly, and to apprehend the 
evidence with definiteness and precision. In the remaining four 
classes I shall place not only the comparatively few cases in which the 
evidence is clearly seen to be what it is, and yet a wrong conclusion 
drawn from it, but also those in which, although there be confusion, 
the confusion is not the sole cause of the en*or, but there is some 
shadow of a ground for it in the nature of the evidence itself And in 
distributing these cases of partial confusion among the four classes, I 
shall, when there can be any hesitation as to the precise seat of the 
fallacy, suppose it to be in that part of the process in which from the 
nature of the case, and the known infirmities of the human mind, an 
eiTor would in the particular circumstances be the most probable. 

After these observations we shall proceed, without further pream- 
ble, to consider the five classes in their order. 



456 FALLACIES. 

CHAPTER III. 

FALLACIES OF SIMPLE INSPECTION ; OR ^ PRIORI FALLACIES. 

§ 1. The tribe of errors of which we are to treat in the first instance, 
are those in which no actual inference takes place at all ; the proposi- 
tion (it cannot in such cases be called a conclusion) being embraced, 
not as proved, but as requiring no proof; as a self-evident truth ; or 
else as having such intrinsic verisimilitude, that external evidence not 
in itself amounting to proof, is sufficient in aid of the antecedent pre- 
sumption. 

An attempt to treat this subject comprehensively would be a trans- 
gression of the bounds prescribed to this work, since it would necessi- 
tate the inquiry which, more than any other, is the grand question of 
transcendental metaphysics, viz.. What are the propositions which may 
reasonably be received without proof? That there must be some such 
propositions all are agreed, since there cannot be an infinite series of 
proof, a chain suspended from nothing. But to determine what these 
propositions are, is the opus magnum of the higher mental philosophy. 
Two principal divisions of opinion on the subject have divided the 
schools of philosophy from its first dawn. The one recognizes no 
ultimate premisses but the facts of our subjective consciousness ; our 
sensations, emotions, intellectual states of mind, and volitions. These 
and whatever by the strict rules of Induction can be derived from these 
it is possible, according to this theory, for us to know j of all else we 
must remain in ignorance. The opposite school hold that there are other 
existences suggested indeed to our minds by these subjective phenom- 
ena, but not inferrible from them,' by any process either of deduction 
or of induction ; which, however, we must by the constitution of our 
mental nature, recognize as realities ; and realities, too, of a higher 
order than the phenomena of our consciousness, being the efficient 
causes and necessary substrata of all Phenomena. Among these en- 
tities they reckon Substances, whether matter or spirit; from the 
dust under our feet to the soul, and fi:om that to the Deity, All these 
according to them are preternatural or supernatural beings, having no 
likeness in experience, although experience is entirely a manifestation 
of their agency. Their existence, together with more or less of the 
laws to which they conform in their operations, are, on this theory, 
apprehended and recognized as real by the mind itself, intuitively : 
experience (whether in the form of sensation, or of mental feeling) 
having no other part in the matter than as affording a multitude of facts, 
which are consistent with these necessary postulates of reason, and 
which are explained and accounted for by them. 

As it is foreign to the purpose of the present treatise to determine 
on which side the truth lies as between these theories, we are pre- 
cluded from inquiring into the existence, or defining the extent and 
limits, of knowledge a priori, and from characterizing the kind of cor- 
rect assumption (if any such there be), which the fallacy of incorrect 
assumption, now under consideration, simulates. Yet since it is allowed 
on both sides that such assumptions are occasionally made improperly, 
we may find it practicable, without entering into the ultimate "neta- 



FALLACIES OF SIMPLE INSPECTION. 457 

physical grounds of the discussion, to state some speculative proposi- 
tions, and suggest some practical cautions (not absolutely inconsistent 
with either view of the philosophical question) respecting the forms in 
which such unwarranted assumptions are most likely to be made. 

§ 2. In the cases in which, according to the philosophers of the onto- 
logical school, the mind apprehends, by intuition, things, and the laws 
of things, not cognizable by our sensitive faculty ; those intuitive, or 
supposed intuitive, perceptions are undistinguishable from what the 
opposite school are accustomed to call ideas of the mind. When they 
themselves say that they perceive the things by an immediate act of 
a faculty given for that purpose at their creation, it would be said of 
them by their opponents that they find an idea or conception in their 
own minds, and from the idea or conception infer the existence of 
a corresponding objective reality. Nor would this be an unfair state- 
ment, but a mere version into other words of the account given by 
themselves ; and one to which the more clear-sighted of them might, 
and generally do, without hesitation subscribe. Since, therefore, in the 
cases which lay the strongest claim to be examples of knowledge a 
priori, the mind proceeds from the idea of a thing to the reality of the 
thing itself, we cannot be surprised by finding that illicit assumptions 
a priori, consist in doing the same thing erroneously : in mistaking 
subjective facts for objective, laws of the percipient mind for laws of 
the perceived object, properties of the ideas or conceptions for prop- 
erties of the things conceived. 

Accordingly, a large proportion of the erroneous thinking which exists 
in the world proceeds upon a tacit assumption, that the same order 
m.ust obtain among the objects in nature which obtains among our 
ideas of them. That if we always think of two things together, the 
two things must always exist together. That if one thing makes us 
think of another as preceding or following it, that other must precede 
it or follow it in actual fact. And conversely, that when we cannot 
conceive two things together they cannot exist together and that their 
combination may, without further evidence, be rejected from the list 
of possible occurrences. 

Few persons, I am inclined to think, have reflected upon the great 
extent to which this fallacy has prevailed, and prevails, in the actual 
beliefs and actions of mankind. For a first illustration of it, we may 
refer to a large class of popular susperstitions. If any one will 
examine in what circumstance most of those things agree, which in 
different ages and by different portions of the human race have been 
considered as omens or prognostics of some interesting event, whether 
calamitous or fortunate ; he will find them very generally characterized 
by this peculiarity, that they cause the mind to think of that, of which 
they are therefore supposed to forebode the actual occurrence. '* Talk 
of the devil, and he will appear," has passed into a proverb. Talk of 
the devil, that is, raise the idea, and the reality will follow. In times 
when the appearance of that personage in a visible form was thought 
to be no uncommon occurrence, it has doubtless often happened to per- 
sons of vivid imagination and susceptible nerves, that talking of the 
devil has caused them to fancy they saw him ; as, even in our incred- 
ulous days, listening to ghost stories predisposes us to see ghosts : 
and thus, as a prop to the d priori fallacy, there might come to be 
3M 



458 FALLACIES. 

added an auxiliary fallacy of mal-observation, with one of false genera- 
lization gi-ounded upon it. Fallacies of different orders often herd or 
cluster together in this fashion. But the origin of the superstition is 
evidently that which we have assigned. In like manner it has been 
universally considered unlucky to speak of misfortune. The day on 
which any calamity happened has been considered an unfortunate day, 
and there has been a feeling everywhere, and in some nations a 
religious obligation, against transacting any important business on 
that day. For on such a day our thoughts are likely to be of misfor- 
tune. For a similar reason, any untoward occurrence in commencing 
an undertaking has been considered ominous of failure ; and often, 
doubtless, has really contributed to it, by putting the persons engaged 
in the enterprise more or less out of spirits : but the belief has equally 
prevailed where the disagreeable circumstance was, independently of 
superstition, too insignificant to depress the spirits by any influence of 
its own. All know the story of Caesar's accidentally stumbling in the 
act of landing on the African coast ; and the presence of mind with 
which he converted the direful presage into a favorable one by ex- 
claiming, "Africa, I embrace thee !" Such omens, it is true, were of- 
ten conceived as warnings of the future, given by a friendly or a hostile 
deity : but this very superstition grew out of a preexisting tendency ; 
the god was supposed to send, as an indication of what was to come, 
something which men were already inclined to consider in that light. 
So in the case of lucky or unlucky names. Herodotus tells how the 
Greeks, on the way to Mycale, were encouraged in their enterprise by 
the arrival of a deputation from Samos, one of the members of which 
was named Hegesistratus, the leader of armies. 

Cases may be pointed out in which something which could have no 
real effect but to make persons thinh of misfortune, was regarded not 
merely as a prognostic but as something approaching to an actual 
cause of it. The k.v(\>i\\iEi of the Greeks, and favete Unguis, or bona 
verha qucRso^ of the Romans, evince the care with which they endeav- 
ored to repress the utterance of any word expressive or suggestive 
of ill fortune ; not from notions of delicate politeness, to which their 
general mode of conduct and feeling had very little reference, but fi'om 
hona fide alarm lest the event so suggested to the imagination should in 
fact occur. Some vestige of a similar superstition has been known to 
exist among uneducated persons even in our own day : it is thought an 
unchristian thing to talk of, or suppose, the death of any person while 
he is alive. It is known how careful the Romans were to avoid, by an 
indirect mode of speech, the utterance of any word directly expressive 
of death or other calamity : how instead of mortuus est they said vixit ; 
and *' be the event fortunate or otherwise'^ instead of adverse. The 
neime Maleventum, of which Salmasius so sagaciously detected the 
Thessalian origin (Ma/loei^, MaXoevroq), they changed into the highly 
propitious denomination, Beneventum ; and Epidamnus, a name so 
pleasant in its associations to the reader of Thucydides, they ex- 
changed for Dyrrhachium, to escape the perils of a word suggestive 
of damnum or detriment. 

" If a hare cross the highway," says Sir Thomas Browne,* " there 
are few above threescore that are not perplexed thereat ; which not- 

* Vulgar Errors^ book v., hap. 21. 



FALLACIES OF SIMPLE INSPECTION. 459 

withstanding is but an augurial teiror, according to that received ex- 
pression, Inauspicatum dat iter ohlatus lepus. And the ground of the 
conceit was probably no gi'eater than this, that a fearful animal passing 
by us portended unto us something to be feared ; as upon the like 
consideration the meeting of a fox presaged some future imposture." 
Such superstitions as these last must be the result of study; they are 
too recondite for natural or spontaneous growth. But when the at- 
tempt was once made to construct a science of predictions, any asso- 
ciation, though never so faint or remote, by which an object could be 
connected in however far-fetched a manner with ideas either of pros- 
perity or of danger and misfortune, was enough to determine its being 
classed among good or evil omens. 

An example of rather a different kind from any of these, but falling 
under the same principle, is the famous attempt, on which so much 
labor and ingenuity were expended by the alchemists, to make gold 
potable. The motive to this was a conceit that potable gold could be 
no other than the universal medicine : and why gold % Because it was 
so precious. It must have all marvelous properties as a physical 
substance, because the mind was already accustomed to marvel at it. 

From a similar feeling, " every substance," says Dr. Paris,* "whose 
origin is involved in mystery, has at different times been eagerly ap- 
plied to the purposes of medicine. Not long since, one of those 
showers which are now known to consist of the excrements of insects, 
fell in the north of Italy ; the inhabitants regarded it as manna, or 
some supernatural panacea, and they swallowed it with such avidity, 
that it was only by extreme address that a small quantity was obtained 
for a chemical examination." The superstition, in this instance, though 
doubtless partly of a religious character, probably in part also arose 
from the prejudice that a wonderful thing must of course have wonder- 
ful properties. 

§ 3. The instances of d priori fallacy which we have hitherto cited, 
belong to the class of vulgar errors, and do not now, nor in any but a 
rude age ever could, impose upon minds of any considerable attain- 
ments. But those to which we are about to proceed, have been, and 
still are, all but universally prevalent even among philosophers. The 
same disposition to give objectivity to a law of the mind — to suppose 
that what is true of our ideas of things must be true of the things them- 
selves — exhibits itself in many of the most accredited modes of philo- 
sophical investigation, both on physical and on metaphysical subjects. 
In one of its most undisguised manifestations, it embodies itself in two 
maxims, which lay claim to axiomatic truth : Things which we cannot 
think of together, cannot coexist ; and. Things which we cannot help 
thinking of together, must coexist. I am not sure that the maxims 
were ever expressed in these precise words, but the history both of 
philosophy and of popular opinions abounds with exemplifications of 
both forms of the doctrine. 

To begin with the latter of them : Things which we cannot think of 
except together, must exist together. This is assumed in the many 
reasonings of philosophers which conclude that A must accompany B 
in point of fact, because ** it is involved in the idea." Such thinkers 

* Pharmacologia, Historical Introduction, p. 16. 



460 FALLACIES. 

do not reflect that the idea, being a result of abstraction, ought to 
confoi-m to the facts, and cannot make the facts conform to it. The 
argument is at most admissible as an appeal to authority ; a surmise, 
that what is now part of the idea must, before it became so, have been 
found by previous inquirers in the facts. Nevertheless, the philoso- 
pher who more than all others has made profession of rejecting author- 
ity, Descartes, constructed his philosophical system on this very basis. 
His favorite device for arriving at truth, even in regard to outward 
things, was by looking into his own mind for it. " Credidi me," says 
his celebrated maxim, " pro regula generali sumere posse, omne id 
quod vald^ dilucide et distincte concipiebam, verum esse :" vrhatever 
can be very clearly conceived, must certainly exist ; that is, as he af- 
terwards explains it, if the idea includes existence. And upon this 
ground he infers that geometrical figures really exist, because they 
can be distinctly conceived. Whenever existence is " involved in an 
idea," a thing conformable to the idea must really exist ; which is as 
much as to say, whatever the idea contains must have its equivalent in 
the thing ; and what we are not able to leave out of the idea cannot 
be absent from the reality. This assumption pervades the philosophy 
not only of Descartes, but of all the thinkers who received their im- 
pulse mainly from him, in particular the two most remarkable among 
them, Leibnitz and Spinosa, from whom the modern German meta- 
physical philosophy is essentially an emanation. The esteemed author 
of one of the Bridgewater Treatises (which for its accumulation of 
scientific facts, and even for some of its generalizations, is worthy of 
all praise) has fallen, as it seems to me, into a similar fallacy when, 
after arguing in rather a curious way to prove that matter may exist 
without any of the known properties of matter, and may therefore be 
changeable, he concludes that it cannot be eternal, because " eteraal 
(passive) existence necessarily involves incapability of change." I 
believe it would be difficult to point out any other connexion between 
the facts of eternity and unchangeableness, than a strong association 
between the two ideas. 

The other form of the fallacy ; Things which we cannot think of 
together cannot exist together — including as one of its branches, that 
what we cannot think of as existing, cannot exist at all — may be thus 
briefly expressed : Whatever is inconceivable must be false. 

Against this prevalent doctrine I have sufficiently argued in a former 
Book,* and nothing is required, in this place, but examples. It was 
long held that Antipodes were impossible, because of the difficulty 
which men found in conceiving persons with their heads in the same 
direction as our feet. And it was one of the received arguments 
against the Copernican system, that we cannot conceive so great a 
void space as that system supposes to exist in the celestial regions. 
When men's imaginations had always been used to conceive the stars 
as firmly set in solid spheres, they naturally found much difficulty in 
imagining them in so different, and, as it doubtless appeared to them, 
so unsafe a situation. But men had no right to mistake the limitation 
(whether natural, or, as it in fact proved, only artificial) of their own 
faculties, for an inherent limitation of the possible modes of existence 
in the universe. 

* Supra, pp. 156-161. 



FALLACIES OP SIMPLE INSPECTION. 461 

It may be said in objection, that the error in these cases was in the 
minor premiss, not the major ; an error of fact, not of principle ; that 
it did not consist in supposing that what is inconceivable cannot be 
true, but in supposing Antipodes to be inconceivable, when present 
experience so fully proves that they can be conceived. Even if this 
objection were allowed, and the proposition that what is inconceivable 
cannot be true were suffered to remain unquestioned as a speculative 
truth, it would be a truth upon which no practical consequence could 
ever be founded, since, upon this showing, it is impossible to affirm of 
any proposition, not being a contradiction in terms, that it is inconceiva- 
ble. Antipodes were really, not fictitiously, inconceivable to our 
ancestors : they are indeed conceivable to us ; and as the limits of our 
power of conception have been so largely extended, by the extension 
of our experience and the more varied exercise of our imagination, so 
may posterity find many combinations perfectly conceivable to them 
which are inconceivable to us. But, as beings of limited experience, 
we must always and necessarily have limited conceptive powers ; while 
it does not by any means follow that the same limitation obtains in the 
possibilities of nature, nor even in her actual manifestations. 

Rather more than a century and a half ago it was a philosophical 
maxim, disputed by no one, and which no one deemed to require any 
proof, that " a thing cannot act where it is not." With this weapon 
the Cartesians waged a formidable war against the theory of gravita- 
tion, which, according to them, involving so obvious an absurdity, 
must be rejected in limine ; the sun could not possibly act upon the 
earth, not being there. It was not surprising that the adherents of the 
old systems of astronomy should urge this objection against the new ; 
but the false assumption imposed equally upon Newton himself, who 
in order to turn the edge of the objection, imagined a subtle ether 
which filled up the space between the sun and the earth, and by its 
intermediate agency was the proximate cause of the phenomena of 
gravitation. *' It is inconceivable," said Newton, in one of his letters 
to Dr. Bentley,* **that inanimate brute matter should, without the 
mediation of something else, which is not material, operate upon and 

affect other matter without mutual contact That gravity should be 

innate, inherent, and essential to matter, so that one body may act on 
another, at a distance, through a vacuum, without the mediation of 
anything else, by and through which their action and force may be 
conveyed from one to another, is to me so great an absurdity, that I 
believe no man, who in philosophical matters has a competent faculty 
of thinking, can ever fall into it." This passage should be hung up in 
the cabinet of every man of science who is ever tempted to pronounce 
a fact impossible because it appears to him inconceivable. In our own 
day one would be more inclined, though with equal injustice, to reverse 
the concluding observation, and consider the seeing any absurdity at 
all in a thing so simple and natural, to be what really marks the ab- 
sence of " a competent faculty of thinking." No one now feels any 
difRculty in conceiving gravity to be, as much as any other property 
is, " innate, inherent, and essential to matter," nor finds the compre- 
hension of it facilitated in the smallest degree by the supposition of 
an ether ; nor thinks it at all incredible that the celestial bodies can 

* I quote this passage from Playfair's celebrated Dissertation on the Progress of Mathemat- 
ical aind Physical Science. 



462 FALLACIES. 

and do act where tliey, in actual bodily presence, are not. To us it is 
not more wonderful that bodies should act upon one another ''without 
mutual contact," than that they should do so when in contact : we are 
familiar with both these facts, and we find them equally inexplicable, 
but equally easy to believe. To Newton the one, because his imagi- 
nation was familiar with it, appeared natural and a matter of course, 
while the other, for the contrary reason, seemed too absurd to be cred- 
ited. If a Newton could err thus grossly in the use of such an argu- 
ment, who else can trust himself with it ] 

It is strange that any one, after such a warning, should rely implicitly 
upon the evidence, d priori, of such propositions as these, that matter 
cannot think ; that space, or extension, is infinite ; that nothing can be 
made out of nothing (ex nihilo nihil Jit). Whether these propositions 
are true or no this is not the place to determine, nor even whether the 
questions are soluble by the human faculties. But such doctrines are 
no more self-evident truths, than the ancient maxim that a thing cannot 
act where it is not, which probably is not now believed by any educated 
person in Europe. Matter cannot think ; why % because w^e cannot 
conceive thought to be annexed to any arrangement of material parti- 
cles. Space is infinite, because having never known any part of it 
w^hich had not other parts beyond it, we cannot conceive an absolute 
termination. Ex nihilo nihil Jit, because having never known any 
physical product without a preexisting physical material, we cannot, or 
think we cannot, imagine a creation out of nothing. But these things 
may in themselves be as conceivable as gravitation without an inter- 
vening medium, which Newton thought too great an absurdity for any 
man of a competent faculty of philosophical thinking to admit : and 
even supposing them not conceivable, this, for aught we know, may be 
merely one of the limitations of our very limited minds, and not in 
nature at all. 

, Coleridge has attempted, with his usual ingenuity, to establish a dis- 
tinction which would save the credit of the common mode of thinking 
on this subject, declaring that the unimaginahle, indeed, may possibly 
be true, but that the inconceivable cannot : and he would probably have 
said that the three supposed impossibilities last spoken of are not cases 
of mere unimaginableness, but of actual inconceivableness ; while the 
action of the sun upon the earth without an intervening medium, was 
merely unimaginable. I am not aware that Coleridge has anywhere 
attempted to define the distinction between the two ; and I am per- 
suaded that, if he had, it would have broken dov^ni under him. But if 
by unimaginableness he meant, as seems likely, mere inability on our 
part to represent the phenomenon, like a picture of something visible, 
to the internal eye, antipodes were not unimaginable. They were 
capable of being imaged ; capable even of being drawn, or modeled 
in plaster. They were, however, inconceivable : the imagination could 
paint, but the intellect could not recognize them as a believable thing. 
Things may be inconceivable, then, wdthout being incredible : and 
Coleridge's distinction, whether it have any foundation or not, wiU in 
no way help the maxim out. 

No philosopher has more directly identified himself with the fallacy 
now under consideration, or has embodied it in more distinct terms, 
than Leibnitz. In his view, unless a thing was not merely conceivable, 
but even explainable, it could not exist in nature. All natural phe- 



FALLACIES OF SIMPLE INSPECTION. 468 

nomena, according to him, must be susceptible of being accounted for 
a priori. The only facts of which no explanation could be given but 
the will of God, were miracles properly so called. ** Je reconnais,'* 
says he,* " qu'il n'est pas permis de nier ce qu'on n'entend pas ; raais 
j'ajoute qu'on a droit de nier (au moins dans I'ordre naturel) ce qui 
absolument n'est point intelligible ni explicable. Je soutiens aussi .... 
qu'enfin la conception des creatures n'est pas la mesure du pouvoir de 
Dieu, mais que leur conceptivite, ou force de concevoir, est la mesure 
du pouvoir de le nature, tout ce qui est conforme a I'ordre naturel 
pouvant etre con^u ou entendu par quelque creature." 

Not content with assuming that nothing can be true which we are 
unable to conceive, philosophers have frequently given a still further 
extension to the doctrine, and contended that, even of things not alto- 
gether inconceivable, that which we can conceive with the greatest 
ease is likeliest to be true. It was long an admitted axiom, and is not 
yet entirely discredited, that ** nature always acts by the simplest 
means," i. e. by those which are most easily conceivable. A large pro- 
portion of all the errors ever committed in the investigation of the 
laws of nature, have arisen from the assumption that the most familiar 
explanation or hypothesis must be the truest. One of the most in- 
structive facts in scientific history is the pertinacity with which the 
human mind clung to the belief that the heavenly bodies must move 
in circles, or be carried round by the revolution of spheres ; merely 
because those were in themselves the simplest suppositions : although, 
to make them accord with the facts which were ever contradicting 
them more and more, it became necessary to add sphere to sphere and 
circle to circle, until the original simplicity was converted into almost 
inextricable complication. 

§ 4. We pass to another d priori fallacy or natural prejudice, allied. 
to the former, and originating as that does, in the tendency to pre- 
sume an exact correspondence between the laws of the mind and those 
of things external to it. The fallacy may be enunciated in this general 
form — Whatever can be thought of apart exists apart : and its most 
remarkable manifestation consists in the personification of abstractions. 
Mankind in all ages have had a strong propensity to conclude that 
wherever there is a name, there must be a distinguishable separate 
entity corresponding to the name ; and every complex idea which the 
mind has formed for itself by operating upon its conceptions of indi- 
vidual things, was considered to have an outward objective reality 
answering to it. Fate, Chance, Nature, Time, Space, were real 
beings, nay, even gods. If the analysis of qualities in the earlier part 
of this work be correct, names of qualities and names of substances 
stand for the very same sets of facts or phenomena ; whiteness and a 
white thing are only different phrases, required by convenience for 
speaking, under different circumstances, of the same external fact. 
Not such, however, was the notion which this verbal distinction sug- 
gested of old, either to the vulgar or to philosophers. Whiteness was 
an entity, inhering or sticking in the white substance : and so of all 
other qualities. So far was this carried, that even concrete general 
terms were supposed to be, not names of indefinite numbers of indi- 

* Nouveatuv Essais sur V Entendement Humain — Avant-propos. (CEuvres, Paris ed. 1842. 
vol. i., p. 19.) 



464 FALLACIES. 

vidual substances, but names of a peculiar kind of entities termed 
Universal Substances. Because we can think and speak of man in 
genera], that is, of all men in so far as possessing the common attri- 
butes of the species, without fastening our thoughts permanently on 
some one individual man ; therefore man in general was supposed to 
be, not an aggregate of individual men, but an abstract or universal 
man, distinct from these. 

It may be imagined what havoc metaphysicians trained in these 
habits made with philosophy, when they came to the largest generali- 
zations of all. Suhstantice Secundce of any kind were bad enough, but 
such Substantise Secundae as to ov, for example, and ro ev, standing for 
peculiar entities supposed to be inherent in all things which exist, or 
which are said to be one, were enough to put an end to all intelligible 
discussion; especially since, wdth a just perception that the truths 
which philosophy pursues are general truths, it was soon laid dovni 
that these general substances were the only objects of science, being 
immutable, while individual substances cognizable by the senses, 
being in a perpetual flux, could not be the subject of real knowledge. 
This misapprehension of the import of general language constitutes 
Mysticism, a word so much oftener written and spoken than under- 
stood. Whether in the Vedas, in the Platonists, or in the Hegelians, 
mysticism is neither more nor less than ascribing objective existence to 
the subjective creations of the mind's own faculties, to mere ideas of 
the intellect ; and believing that by watching and contemplating these 
ideas of its own making, it can read in them what takes place in the 
world without. 

§ 5. Proceeding with the enumeration of d priori fallacies, and 
endeavoring to arrange them with as much reference as possible to 
their natural affinities, we come to another, which is also nearly allied 
to the fallacy preceding the last, standing in the same relation to one 
variety of it as the fallacy last mentioned does to the other. This, too, 
represents nature as bound to conform herself to the incapacities of 
our intellect; but instead of only asserting that nature cannot do a 
thing because we cannot conceive it done, goes the still greater length 
of avening that nature does a particular thing, on the sole ground 
that we can see no reason why she should not. Absurd as this seems 
when so plainly stated, it is a received principle among philosophers 
for demonstrating a priori the laws of physical phenomena. A phe- 
nomenon must fBllow a certain law, because we see no reason why it 
should deviate from that law in one way rather than in another. This 
is, called the principle of the Sufficient Reason; and by means of it 
philosophers often flatter themselves that they are able to establish, 
without any appeal to experience, the most general truths of experi- 
mental physics. 

Take, for example, two of the most elementary of all laws, the law 
of inertia and the first law of motion. A body at rest cannot, it is 
affirmed, begin to move unless acted upon by some external force : 
because, if it did, it must either move up or down, forward or back- 
ward, and so forth ; but if no outward force acts upon it, there can be 
no reason for its moving up rather than down, or down rather than 
up, &c., ergo it will not move at all. Q. E. D. 

This reasoning I conceive to be entirely fallacious, as indeed Pr. 



FALLACIES OF SIMPLE INSPECTION. 465 

Brown, in his treatise on Cause and Effect, has shown with great 
acuteness and justness of thought. We have before remarked, that 
almost every fallacy may be referred to diflcrcnt genera by different 
modes of filling up the suppressed steps, and this particular one may, 
at our option, be brought under pctitio 2)rincipii. It supposes that 
nothing can be a " sufficient reason" for a body's moving in one par- 
ticular direction, except some external force. But this is the very 
thing to be proved. Why not some internal force 1 Why not the law 
of the thing's own nature 1 Since these philosophers think it neces- 
sary to prove the law of inertia, they of course do not suppose it to he 
self-evident ; they must, therefore, be of opinion that, j^reviously to all 
proof, the supposition of a body's moving by internal impulse is an 
admissible hypothesis : but if so, why is not the hypothesis also admis- 
sible, that the internal impulse acts naturally in some one particular 
direction, not in another ] If spontaneous motion might have been 
the law of matter, why not spontaneous motion towards the sun, 
towards the earth, or towards the zenith % Why not, as the ancients 
supposed, towards a particular place in the universe, appropriated to 
each particular kind of substance % Surely it is not allowable to say 
that spontaneity of motion is credible in itself, but not credible if sup- 
posed to take place in any determinate direction. 

Indeed, if any one chose to assert that all bodies when uncontrolled 
set out in a direct line towards the north pole, he might equally prove 
his point by the principle of the Sufficient Reason. By w^hat right is 
it assumed that a state of rest is the particular state which cannot be 
deviated from without special cause ] Why not a state of motion, and 
of some particular sort of motion 1 Why may we not say that the 
natural state of a horse left to himself is to amble, because otherwise 
he must either trot, gallop, or stand still, and because we know no 
reason why he should do one of these rather than another] If this is 
to be called an unfair use of the " sufficient reason," and the other a 
fair one, there must be a tacit assumption that a state of rest is more 
natural to a horse than a state of ambling. If this means that it is the 
state which the animal will assume when left to himself, that is the 
very point to be proved ; and if it does not mean this, it can only mean 
that a state of rest is the simplest state, and therefore the most likely 
to prevail in nature, which is one of the fallacies or natural prejudices 
we have already examined. 

So again of the First Law of Motion; that a body once moving 
-will, if left to itself, continue to move uniformly in a straight line. An 
attempt is made to prove this law by saying, that if not, the body must 
deviate either to the right or to the left, and that, there is no reason 
why it should do one more than the other. But who could know, an- 
tecedently to experience, whether there was a reason or not % Might 
it not be the nature of bodies, or of some particular bodies, to deviate 
towards the right 1 or if the supposition is preferred, towards the east, ' 
or south ] It Avas long thought that bodies, terrestrial ones at least, 
had a natural tendency to deflect do^vniwards ; and there is no shadow 
of anything objectionable in the supposition, except that it is not true. 
The pretended proof of the law of motion is even more manifestly un- 
tenable than that of the law of inertia, for it is flagi'antly inconsistent ; 
it assumes that the continuance of motion in the direction first taken is 
more natural than deviation either to the right or to the left, but denies 
3N 



466 FALLACIES. 

that one of these can possibly be more natural than the other. All 
these fancies of the possibility of knowing what is natural or not natural 
by any other means than experience, are, in truth, entirely futile. The 
real and only proof of the laws of motion, or of any other law of the 
universe, is experience ; it is simply that no other suppositions explain 
or are consistent with the facts of universal nature. 

Geometers have, in all ages, been open to the imputation of en- 
deavoring to prove the most general facts of the outward world by 
sophistical reasoning, in order to avoid appeals to the senses. Archi- 
medes, says Professor Playfair,* established some of the elementary 
propositions of statics by a process in which he "borrows no principle 
from experiment, but establishes his conclusion entirely by reasoning 
d priori. He assumes, indeed, that equal bodies, at the ends of the 
equal arms of a lever, will balance one another ; and also that a cylin- 
der or parallelepiped of homogeneous matter, vnll be balanced about 
its centre of magnitude. These, however, are not inferences from 
experience ; they are, properly speaking, conclusions deduced from 
the principle of the Sufficient Reason." And to this day there are 
few geometers who would not think it far more scientific to establish 
these or any other premisses in this way, than to rest their evidence 
upon that familiar experience which in the case in question might have 
been so safely appealed to. 

§ 6. Another natural prejudice, of most extensive prevalence, and 
which lay at the root of the en'ors fallen into by the ancient philoso- 
phers in their physical inquiries, was this : That the differences in 
nature must con-espond to our received distinctions; that eflfects which 
we are accustomed, in popular language, to call by different names, 
and arrange in different classes, must be of different natures, and have 
different causes. This prejudice, so evidently of the same origin with 
those already treated of, marks more especially the earliest stage of 
science, when it has not yet broken loose from the ti'ammels of every- 
day phraseology. The extraordinary prevalence of the fallacy among 
the Greek philosophers may be accounted for by their generally know- 
ing no other language than their own; from which it was a consequence 
that their ideas followed the accidental or arbitrary combinations of 
that language, more completely than can happen among the modems 
to any but illiterate persons. -They had great difficulty in distinguish- 
ing between things which their language confounded, or in putting 
mentally together things which it distinguished ; and could hardly com- 
bine the objects in nature into any classes but those which were made 
for them by the populur phrases of their own country ; or at least 
could not help fancying those classes to be natural, and all others 
arbitrary and artificial. Accordingly, as is remarked by Mr. Whewell, 
scientific investigation among the Greek philosophers and their fol- 
lowers in the middle ages, was little more than a mere sifting and 
analyzing of the notions attached to common language. They thought 
that by determining the meaning of words, they could become ac- 
quainted with facts. " They took for granted," says Mr. Whewell, t 
*' that philosophy must result from the relations of those notions which 
are involved in the common use of language, and they proceeded to 

* Dissertation, ut supra, pp. 298-9. 
' t History of the Inductive Sciences, Book i., chap. 1. 



FALLACIES OF SIMPLE INSPECTION. 467 

seek it by studying such notions." In his next chapter Mr. Whewell 
has so well illustrated and exemplified this error, that we shall take 
the liberty of quoting him at some length. 

*' The propensity," says he, "to seek for principles in the common 
usages of language, may be discerned at a very early period. Thus 
we have an example of it in a saying which is reported of Thales, the 
founder of Greek philosophy. When he was asked, 'What is the 
greatest thing?' he replied ''Place; for all other things are in the 
world, but the world is in it.' In Aristotle we have the consummation 
.of this mode of speculation. The usual point from which he starts in 
his inquiries is, that we say thus or thus in common language. Thus, 
when he has to discuss the question whether there be, in any part of 
the universe, a void, or space in which there is nothing, he inquires first 
in how many senses we say that one thing is in another. He enumer- 
ates many of these ; we say the part is in the whole, as the finger is in 
the hand ; again we say, the species is in the genus, as man is included 
in animal ; again, the government of Greece is in the king ; and various 
Other senses are described and exemplified, but of all these the most 
proper is when we say a thing is in a vessel, and generally in place^ 
He next examines what place is, and comes to this conclusion, that 'if 
, about a body there be another body including it, it is in place, and if 
'iio.t, Xiot.' A body moves when it changes its place; but he adds, that 
if water be in a vessel, the vessel being at rest, the parts of^the water 
may still move, for they are included by each other; so that while the 
whole does not change its place, the parts may change their place in a 
circular order. Proceeding then to the question of a void, he as usual 
examines the different senses in which the term is used, and adopts, as 
the most proper, place without matter; with no useful result." 

" Again, in a question concerning mechanical action, he says, ' When 
a man moves a stone by pushing it with a stick, we say both that the 
man moves the stone, and that the stick moves the stone, but the latter 
more properly.' 

" Again, we find the Greek philosophers applying themselves'to ex- 
tract their dogmas frOm the most general and abstract notions which 
they could detect ; for example, from the conception of the Universe 
as One or as Many things. They tried to determine how far we may, 
or must, combine with these conceptions that of a whole, of parts, of 
number, of limits, of place, of beginning or end, of full or void, of rest 
or motion, of cause and effect, and the like. The analysis of such con- 
ceptions with such a view, occupies, for instance, almost the whole of 
Aristotle's Treatise on the Heavens." 

The following paragraph merits particular attention : — "Another 
mode of reasoning, very widely applied in these attempts, was the doc- 
trine of contrarieties, in which it was assumed, that adjectives or sub- 
stantives which are in common language, or in some abstract mode of 
conception, opposed to each other, must point at some fundamental 
antithesis in nature, which it is important to study. Thus Aristotle 
says, that the Pythagoreans, from the contrasts which number sug- 
gests, collected ten principles — Limited and Unlimited, Odd and Even, 
One and Many, Right and Left, Male and Female, Rest and Motion, 
Straight and Curved, Light and Darkness, Good and Evil, Square and 
Oblong .... Aristotle himself deduced the doctrine of four elements and 
other dogmas by oppositions of the same kind." 



468 ' FALLACIES. 

Of tlie manner in whicb, from premisses obtained in this way, the 
ancients attempted to deduce laws of nature, one example is given by 
Mr. Whewell a few pages further on. "Aristotle decides that there is 
no void, on such arguments as this. In a void there could be no dif- 
ference of up and down ; for as in nothing there are no differences, so 
there are none in a privation or negation ; but a void is merely a priva- 
tion or negation of matter ; therefore, in a void, bodies could not move 
up and down, which it is in their nature to do. It is easily seen" (Mr. 
Whewell very justly adds) ** that such a mode of reasoning elevates . 
the familiar forms of language, and the intellectual connexions of term's^,' 
to a supremacy over facts ; making truth depend upon whether terms 
are or are not privative, and whether we say that bodies fall naturally P 
The propensity to assume that the same relations obtain between 
objects themselves, which obtain between our ideas of them, is here 
seen in the extreme stage of its development. For the mode of phi- 
losophizing, exemplified in the foregoing instances, assumes no less 
than that the proper way of arriving at knowledge of nature, is to' 
study nature herself subjectively ; to apply our observation and anal- 
ysis not to the facts, but to the common notions entertained of those 
facts. 

Many other equally striking examples may be given of the tendency 
to assume that things which for the convenience of pommon life are 
placed in different classes, must differ in every respect. Of this nature 
was the universal and deeply-rooted prejudice of antiquity and the mid- 
dle ages, that celestial and terrestrial phenomena must be essentially 
different, and could in no manner or degree depend upon the same 
laws. Of the same kind, also, was the prejudice against which Bacon 
contended, that nothing produced by nature could be successfully 
imitated by man : *' Calorem solis et ignis toto genere differre ; ne 
scilicet homines putent se per opera ignis, aliquid simile iis quae in 
Naturafiunt, educere et formare posse:" and again, " Composition em 
tantum opus Hominis, Mistionem vero opus solius Naturae esse : ne 
scilicet homines sperent aliquam ex arte Corporum naturalium genera- 
tionem aut transformationem." * The grand distinction in the ancient 
philosophy, between natural and violent motions, though not without 
a plausible foundation in the appearances themselves, was doubtless 
greatly recommended to adoption by its conformity to this prejudice. 

§ 7. From the fundamental error of the scientific inquirers of anti- 
quity, we pass, by a natural association, to a scarcely less fundamental 
one of their great rival and successor, Bacon. It has excited the 
surprise of philosophers that the detailed system of inductive logic, 
which this extraordinary man labored to construct, has been turned to 
so little direct use by subsequent inquirers, having neither continued, 
except in a few of its generalities, to be recognized as a theory, nor 
having conducted in practice to any great scientific results. But this, 
though not unfrequently remarked, has scarcely received any plausible 
explanation ; and some, indeed, have preferred to assert that all rules 
of induction are useless, rather than suppose that Bacon's rules are 
grounded upon an insufficient analysis of the inductive process. Such, 
however, will be seen to be the fact, as soon as it is considered, that 

. * .Novum Organum, Aph. 75, 



FALLACIES OP SIMPLE INSPECTION. 469 

Bacon entirely overlooked Plurality of Causes. All his rules tacitly 
imply the assumption, so contrary to all we now know of nature, that 
a phenomenon cannot have more than one cause. 

When Bacon is inquiring into what he terms the forma calidi aut 
Jrigidi, gravis aut Icvis, sicci aut hum,idi, and the like, he never for an 
instant doubts that there is some one thing, some invariable condition 
or set of conditions, which is present in all cases of heat, or of cold, or 
of whatever other phenomenon he is considering ; the only difficulty 
being to find what it is ; which accordingly he tries to do by a process 
of elimination, rejecting or excluding, by negative instances, whatever 
is not the forma or cause, in order to arrive at what is. But, that this 
forma or cause is one thing, and that it is the same in all hot objects, 
he has no more doubt of, than another person has that there is always 
some cause or other. In the present state of knowledge it could not 
be necessary, even if we had not already treated so fully of the question, 
to point out how widely this supposition is at variance with the truth. 
It is particularly unfortunate for Bacon that, falling into this error, he 
should have fixed almost exclusively upon a class of inquiries in which 
it was particularly fatal ; namely, inquiries into the causes of the 
sensible qualities of objects. For his assumption, groundless in every 
case, is false in a peculiar degree with respect to those sensible quali- 
ties. In regard to scarcely any of them has it been found possible to 
trace any unity of cause, any set of conditions invariably accompanying 
the quality. The conjunctions of such qualities with one another 
constitute the variety of Kinds, in which, as already remarked, it has 
not been found possible to ti^ace any law. Bacon was seeking for 
what did not exist. The phenomenon of which he sought for the one 
cause has oftenest no cause at all, and when it has, depends (as far as 
hitherto ascertained) upon an unassignable variety of distinct causes. 

And upon this rock every one must split, who, like Bacon, repre- 
sents to himself as the first and fundamental problem of science to 
ascertain what is the cause of a given effect, rather than what are the 
effects of a given cause. It was shown, in an early stage of our in- 
quiry into the nature of Induction,* how much more ample are the 
resources which science commands for the latter than for the former 
inquiry, since it is upon the latter only that we can throw any direct 
light by means of experiment ; the power of artificially producing an 
effect, implying a previous knowledge of at least one of its causes. If 
we discover the causes of effects, it is generally by having previously 
discovered the effects of causes : the greatest skill in devising crucial 
instances for the former purpose may only end, as Bacon's physical 
Inquiries did, in no result at all. Was it that his eagerness to acquire 
the power of producing for man's benefit effects of practical importance 
to human life, rendering him impatient of pursuing that end by a cir- 
cuitous route, made even him, the champion of experiment, prefer the 
direct mode, though one of mere observation, to the indirect, in which 
alone experiment was possible 1 Or had even Bacon not entirely 
cleared his mind from the notion of the ancients, that "rerum cognos- 
cere causas^' was the sole object of philosophy, and that to inquire into 
!;he effects of things belonged to servile and mechanical arts? 

It is worth remarking that, while the only efficient mode of cultivating 

"■ • '\ ^y. . •.. . * Supra, p. 221. 



470 ' FALLACIES. : 

speculative science was missed from an undue contempt of manual 
operations, the false speculative views thus engendered gave in their 
turn a false direction to such practical and mechanical aims as were 
still suffered to exist. The assumption universal among the ancients, 
and in the middle ages, that there were principles of heat and cold, 
dryness and moisture, &c., led directly to a belief in alchemy ; in a 
transmutation of substances, a change from one Kind into another. 
Why should it not be possible to make gold 1 Each of the charac- 
teristic properties of gold had its forma, its essence, its set of condi- 
tions, which if we could discover, and learn how to realize, we could 
superinduce that particular property upon any other substance, upon 
wood, or iron, or lime, or clay. If, then, we could effect this with 
respect to every one of the essential properties of the precious metals, 
we should have converted the other substance into gold. Nor did this, 
if once the premisses were granted, appear to transcend the real pow- 
ers of man. For daily experience showed that almost every one of 
the distinctive sensible properties of any object, its consistence, its 
color, its taste, its smell, its shape, admitted of being totally changed 
by firej or water, or some other chemical agent. The formcB of all 
those qualities seeming, therefore, to be within human power either to 
produce or to annihilate, not only did the transmutation of substances 
appear abstractedly possible, but the employment of the power, at our 
choice, for practical ends, seemed by no means hopeless. 

A prejudice universal in the ancient world, and from which even 
Bacon was so far from being free, that it pervaded and vitiated the 
whole practical part of his system of logic, may with good reason be 
ranked high in the order of Fallacies of which we are now ti^eating. 

§ 8. There remains one a priori fallacy or natural prejudice, the 
most deeply-rooted, perhaps, of all which we have enumerated : one 
which not only reigned supreme in the ancient world, but still possesses 
almost undisputed dominion over many of the most cultivated minds ; 
and some of the most remarkable of the numerous instances by which 
I shall think it necessary to exemplify it, will be taken from the writings 
of recent philosophers. This is, that the conditions of a phenomenon 
must, or at least probably will, resemble the phenomenon itself. 

Conformably to what we have before remarked to be of frequent 
occurrence, this fallacy might without much impropriety have been 
placed in a different class, among Fallacies of Generalization : for 
experience does afford a certain degree of countenance to the assump- 
tion. The cause does, in very many cases, resemble its effect ; like 
produces like. Many phenomena have a direct tendency to perpetuate 
their own existence, or to give rise to other phenomena similar to them- 
selves. Not to mention forms actually moulded upon one another, as 
impressions on wax and the like, in which the closest resemblance 
between the effect and its cause is the very law of the phenomenon ; 
all motion tends to continue itself, with its own velocity, and in its own 
original direction ; and the motion of one body tends to set others in 
motion, which is indeed the most common of the modes in which the 
motions of bodies originate. We need scarcely refer to contagion, 
fermentation, and the like ; or to the production of effects by the 
growth or expansion of a germ or i-udiment resembling on a smaller 
scale the completed phenomenon — as in the growth of a plant or anitna'l 



FALLACIES OF SIMPLE INSPECTION. 471 

from an embryo, that embryo itself deriving its origin from another 
plant or animal of the same kind. Again, the thoughts, or reminis- 
cences, which are effects of our past sensations, resemble those sensa- 
tions ; feelings produce similar feelings by way of sympathy ; acts 
produce similai acts by involuntary or voluntary imitation. With so 
many appearances in its favor, no wonder if a presumption naturally 
grew up in men'^s minds, that causes must necessarily resemble their 
effects, and that like could only be produced by like. 

This principle of fallacy has usually presided over the fantastical 
attempts to influence the course of nature by conjectural means, the 
choice of which was not directed by previous obsei-vation and experi- 
ment. The guess almost always fixed upon some means which pos- 
sessed features of real or apparent resemblance to the end in view. 
If a charm was wanted, as by Ovid's Medea, to prolong life, all long- 
lived animals, or what were esteemed such, were collected and brewed 
into a broth : — 

nee defuit illic 

Squamea Cinyphii tenuis membrana chelydri 
Vivacisque jecur cervi : quibus insuper addit 
Ora caputque novem cornicis saecula passae. 

A similar notion was embodied in the celebrated medical theory 
called the ** Doctrine of Signatures," '* which is no less," says Dr. 
Paris,* " than a belief that every natural subtance which possesses 
any medicinal virtue, indicates by an obvious and well-marked ex- 
ternal character the disease for which it is a remedy, or the object 
for which it should be employed." This outward character was 
generally some feature of resemblance, real or fantastical, either to 
the effect it was supposed to produce, or to the phenomenon over 
which its power was thought to be exercised, " Thus the lungs 
of a fox must be a specific for asthma, because that animal is re- 
markable for its strong powers of respiration. Turmeric has a 
brilliant yellow color, which indicates that it has the power of curing 
the jaundice ; for the same reason poppies must relieve diseases of the 
head ; Agaricus those of the bladder ; Cassia Jistula the affections of 
the intestines, and Aristolochia the disorders of the uterus: the polish- 
ed surface and stony hardness which so eminently characterize the 
seeds of the Lithospermum officinale (common gi'omwell) were deemed 
a certain indication of their efficacy in calculous and gravelly dis- 
orders : for a similar reason, the roots of the Saxifraga granulata 
(white saxifrage) gained reputation in the cure of the same disease ; 
and the Euplrrasia (eye-bright) acquired fame, as an application in 
complaints of the eye, because it exhibits a black spot in its corolla 
resembling the pupil. The blood-stone, the Heliotropium of the an- 
cients, from the occasional small specks or points of a blood-red color 
exhibited on its green surface, is even at this day employed in many 
parts of England and Scotland, to stop a bleeding from the nose; and 
nettle tea continues a popular remedy for the cure of Urticaria. It is 
also asserted that some substances bear the signatures of the humors, 
as the petals of the red rose that of the blood, and the roots of rhubarb 
and the flowers of saffron that of the bile." 

The early speculations respecting the chemical composition of bodies 
were rendered abortive by no circumstance more, than by their inva- 

* Pharmacologia, ut supra, pp. 306-7. 



472 FALLACIES. 

riably taking for granted that the properties of the elements must re- 
semble those of the compounds which were formed from them. 

To descend to more modern instances ; it was long thought and was 
stoutly maintained by the Cartesians and even by Leibnitz against the 
Newtonian philosophy, (not did Newton himself, as we have seen, 
contest the assumption, but eluded it by an arbitrary hypothesis,) that 
nothing (of a physical nature at least) could account for motion, except 
previous motion ; the impulse or impact of some other body. It was 
very long before the scientific world could prevail upon itself to admit 
attraction and repulsion (^. e. spontaneous tendencies of particles to ap- 
proach or recede from one another) as ultimate laws, no more requiring 
to be accounted for than impulse itself, if indeed the latter were not, 
in truth, resolvable into the former. From this same source arose the 
innumerable hypotheses to explain those classes of motions which ap- 
peared more mysterious than others because there was no obvious 
mode of attributing them to imj)ulse, as for example the voluntary mo- 
tions of the human body. Such were the interminable systems of 
vibrations propagated along the nerves, or animal spirits rushing up 
and down between the muscles and the brain : which, if the facts 
could have been proved, would no doubt have been an important ad- 
dition to our knowledge of physiological laws ; but the mere invention, 
or arbitrary supposition of them, could not unless by the strongest de- 
lusion be supposed to render the phenomena of animal life more com- 
prehensible or less mysterious. Nothing, however, seemed satisfacto- 
ry, but to make out that motion was caused by motion ; by something 
like itself. If it was not one kind of motion it must be another. In 
like manner it was supposed that the physical qualities of objects 
must arise fi'om some similar quality, or perhaps only some quality 
bearing the same name, in the particles or atoms of which the objects 
were composed ; that a sharp taste, for example, must arise from sharp 
particles. And reversing the inference, the effects produced by a 
phenomenon must, it was supposed, resemble in their physical attri^ 
butes the phenomenon itself. The influences of the planets were sup- ' 
posed to be analogous to their visible peculiarities : Mars, being of a 
red color, portended fire and slaughter ; and the like. 

Passing from physics to metaphysics, we may notice among the most 
remarkable fruits of this a priori fallacy, two closely analogous theories, 
employed in ancient and in modern times to bridge over the chasm 
between the world of mind and that of matter: the species sensihiles of 
the Epicureans, and the modern doctrine of perception by means of 
ideas. These theories are indeed, probably, indebted for their exist- 
ence not solely to the fallacy in question, but to that fallacy combined 
with another natural prejudice already adverted to, that a thing cannot 
act where it is not. In both doctrines it is assumed that the phenom- 
enon which takes place in us when we see or touch an object, and 
which we regard as an effect of that object, or rather of its presence to 
our organs, must of necessity resemble very closely the outward object 
itself. To fulfill this condition, the Epicureans supposed that objects 
were constantly projecting in all directions impalpable images of them- 
selves, which entered at the eyes and penetrated to the mind : while 
modem philosophers, though they rejected this hypothesis, agi'eed in 
deeming it necessary to suppose that not the object itself, but a mental 
image or representation of it, was the direct object of perception. Dr. 



FALLACIES OF SIMPLE INSrECTION. 473 

Reid had to employ a world of argiimont and illustration to familiarize 
people with the truth, that the sensations or impressions on our minds 
need not necessarily be copies of, or have any resemblance to, the 
causes which produce them; in opposition to the. natural prejudice 
which led men to assimilate the action of bodies upon our senses, and 
through them upon our minds, to the transfer of a given form from one 
. object to another by actual moulding. The works of Dr. Reid are 
even now the most effectual course of study for detaching the mind 
from the prejudice of which this was an example. And the value of 
the service which he thus rendered to popular philosophy, is not much 
diminished although we may hold, with Brown, that he went too far 
in imputing the " ideal theory" as an actual tenet, to the generality of 
the philosophers who preceded him, and especially to Locke and 
Hume : for if they did not themselves consciously fall into the error, 
unquestionably they often led their readers into it. 

The prejudice, that the conditions of a phenomenon must resemble 
the phenomenon, is occasionally exaggerated, at least verbally, into a 
still more palpable absurdity ; the conditions of the thing are spoken 
of as if they were the very thing itself. In Bacon's model-inquiry, 
which occupies so great a space in the Novum Grgaiium, the inquisitio 
informam calidi, the conclusion which he favors is that heat is a kind 
of motion ; meaninof of course not the feeling^ of heat, but the conditions 
of the feeling ; meaning, therefore, only, that wherever there is heat, 
there must first be a particular kind of motion ; but he makes no dis- 
tinction in his language between these two ideas, expressing himself as 
if heat, and the conditions of heat, were one and the same thing. So 
Darwin, in the beginning of his Tjoonomia, says, " The word idea has 
various meanings in the writers of metaphysics : it is here used simply 
for those notions of external things which our organs of sense bring us 
acquainted with originally" (thus far the proposition, though vague, is 
unexceptionable in meaning), " and is defined a contraction, a motion, 
or configuration, of the fibres which constitute the immediate organ of 
sense." Our notions, a configuration of the fibres! What kind of 
philosopher must he be who thinks that a phenomenon is defined to he 
the condition on which he supposes it to depend ] Accordingly he 
says soon after, not that our ideas are caused by, or consequent upon, 
certain organic phenomena, but " our ideas are animal motions of the 
organs of sense." And this confusion runs through the four volumes of 
the Zoonomia ; the reader never knows whether the wi^iter is speaking 
of the effect, or of its supposed cause; of the idea, a state of mental 
consciousness, or of the state of the nerves and brain, which he consid- 
ers it to presuppose. 

I have given a variety of instances in which the natural prejudice, , 
that causes and their effects must resemble one another, has operated 
in practice so as to give rise to grievous errors. I shall now go fmther, 
and produce from the writings, even of recent philosophers, instances 
in which the prejudice itself is laid dowTi as an established principlei 
M. Victor Cousin, in the last of his very remarkable lectures on Locke 
(which as a resume of the objections of the opposite school to that great 
man's doctiines, is a work of eminent merit), enunciates this maxim in 
the following unqualified terms : " Tout ce qui est vrai de I'effet est 
vrai de la cause." A doctrine to which, unless in some peculiar and 
technical meaning of the words cause and effect, it is not to be ima- 
30 



474 FALLACIES. 

gined that any person would literally adhere : but he who could so 
write must be far enough from seeing, that the very reverse might be 
the fact'; that there is nothing impossible in the supposition that no one 
property which is true of the effect might be true of the cause. Without 
going quite so far in point of expression, Coleridge, in his Biogra2'>hia 
Literaria* affirms as an *' evident truth," that " the law of causality 
holds only between homogeneous things, i. e., things having some 
common property," and therefore, " cannot extend from one world 
into another, its opposite :" hence, as mind and matter have no com- 
mon property, mind cannot act upon matter nor matter upon mind. 
What is this but the a priori fallacy of which we are speaking] The 
doctrine, like many others of Coleridge, is taken from Spinosa, in the 
first book of whose Ethica (De Deo) it stands as the Third Proposi- 
tion : " Quae res nihil commune inter se habent, earum una alterius 
causa esse non potest," and is there proved from two so-called axioms, 
equally gi'atuitous with itself; but Spinosa, ever systematically con- 
sistent, pursued the doctrine to its inevitable consequence, the materi- 
ality of God. 

The same conception of impossibility led the ingenious and subtle 
mind of Leibnitz to his celebrated doctrine of a preestablished har- 
mony. He, too, thought that mind could not act upon matter, nor 
especially matter upon mind, and that the two, therefore, must have 
been arranged by their Maker like two clocks, which, though uncon- 
nected with one another, strike simultaneously, and always point to 
the same hour. Malebranche's equally famous theory of Occasional 
Causes was a further refinement upon this conception : instead of sup- 
posing the clocks originally arranged to strike together, he held that 
when the one strikes, God interposes, and makes the other strike in 
cori'espondence with it. 

Descartes, in like manner, whose works are a rich mine of almost 
every description of a priori fallacy, says that the Efficient Cause must 
at least have all the perfections of the effect, and for this singular 
reason : *' Si enim ponamus aliquid in idea reperiri quod non fuerit in 
ejus causa, hoc igitur habet a nihilo;" of which it is scarcely a parody 
to say, that if there be pepper in the soup there must be pepper in the 
cook who made it, since otherwise the pepper would be without a 
cause. A similar fallacy is committed by Cicero in his second book 
De Finihus, where, speaking in his own person against the Epicureans, 
he charges them with inconsistency in saying that the pleasures of the 
mind had their origin from those of the body, and yet that the former 
were more valuable, as if the effect could surpass the cause. "Animi 
voluptas oritur propter voluptatem corporis, et major est animi voluptas 
quam corporis ^ ita fit ut gratulator laetior sit quam is^ cui gratulatur." 
Even that, surely, is no absolute impossibility : a man's good fortune 
has been known to give more pleasure to others than it gave to the 
man himself 

Descartes, with no less readiness, applies the same principle the 
converse way, and infers the nature of the effects from the assumption 
that they must, in this or that property, or in all their properties, 
resemble their cause. To this class belong his speculations, and those 
of so many others after him, tending to infer the order of the universe, 

* Vol i., chap. 8. 



FALLACIES OF OBSERVATION. 475 

not from observation, but from the notion we think ourselves able to 
foiTQ of the qualities of the Godhead. This sort of inference was 
probably never carried to a greater length than it was in one particular 
instance by Descartes, when, as a proof of one of his physical princi- 
ples, that the quantity of motion in the universe is invariable, he had 
recourse to the immutability of the Divine Nature. Optimism, in all 
its shapes, is an example of the same species of fallacy: God is per- 
fect, therefore what we think perfection must obtain in nature. Even 
in our own time men do not cease to oppose the divine benevolence to 
the evidence of physical facts, to the principle of population for ex- 
ample. As if the subjection of mankind to physical suffering, often 
entirely unavoidable, and, when capable of being warded off, capable 
only by means of forethought and self-restraint, were more difficult to 
reconcile with the ways of Providence in some one of its particular 
manifestations than in so many others. As if, in so far as pain is an 
imperfection, any one day's experience were not sufficient to con- 
vince the devoutest mind that imperfection, in that sense, in the work, 
entered into the plans of the Creator, and that no attribute really 
incompatible with it can be correctly ascribed to him. 

Although several other varieties of a priori fallacy might probably 
be added to those here specified, these are all against which it seems 
necessary to give any special caution. Our object is to open, without 
attempting or affecting to exhaust the subject. Having illustrated, 
therefore, this first class of Fallacies at sufficient length, I shall pro- 
ceed to the second. 



CHAPTER IV. 

FALLACIES OF OBSERVATION, 



§ 1. From the fallacies which are properly Prejudices, or presump- 
tions antecedent to, and superseding, proof, we pass to those which lie 
in the incorrect performance of the proving process. And as Proof, 
in its widest extent, embraces one or more or all of three processes, 
Obsei-vation, Generalization, and Deduction; we shall consider in their 
order the eiTors capable of being committed in these three operations. 
And first, of the first mentioned. 

A fallacy of misobservation may be either negative or positive ; 
either Non-observation or Mal-observation. It is non-observation, 
when all the error consists in overlooking, or neglecting, facts or par- 
ticulars which ought to have been observed. It is mal-obsei-vation, 
when something is not simply unseen, but seen wrong ; when the fact 
or phenomenon, instead of being recognized for what it is in reality, 
is mistaken for something else. 

§ 2. Non-observation may either take place by overlooking instances, 
or by overlooking some of the circumstances of a given instance. If 
we were to conclude that a fortune-teller was a true prophet, from not 
adverting to the cases in which his predictions had been falsified by 
the event, this would be non-observation of instances : but if we over- 



476 FALLACIES. 

« 

looked or remained ignorant of the fact that in cases where the pre- 
dictions had come true, he had been in collusion with some one who 
had given him the information on which they were gTounded, this 
would be non-obsei'vation of circumstances. 

The former case, in so far as the act of induction from insufficient 
evidence is concerned, does not fall under this second class of Fallacies, 
but under the third, Fallacies of Generalization. In every such case, 
however, there are two defects or errors instead of one : there is the 
eiTor of treating the insufficient evidence as if it were sufficient, which 
is a Fallacy of the third class; and there is the insufficiency itself; the 
not having better evidence ; which, when such evidence, or in other 
words, when other instances, were to be had, is Non-observation ; and 
the erroneous inference, so far as it is to be attributed to this cause, is 
a Fallacy of the second class. 

It belongs not to our purpose to treat of non-observation as arising 
from casual inattention, from general slovenliness of mental habits, want 
of due practice in the use of the observing faculties, or insufficient in- 
terest in tlie subject. The question pertinent to logic is — Granting 
the want of complete competency in the observer, on what points 
is that insufficiency on his pait likely to lead him wrong] or rather, 
what sorts of instances, or of circumstances in any given instance, 
are most likely to escape the notice of observers generally ; of mankind 
at large 1 

: § 3. First, then, it is evident that when the instances on one side of 
a question are more likely to be remembered and recorded than those 
on the other ; especially if there be any strong motive to preserve the 
memory of the first but not of the latter; these last are likely to be 
overlooked, and escape the observation of the mass of mankind. This 
is the recognized explanation of the credit given, in spite of reason 
and evidence, to many classes of impostors ; to quack doctors, and for- 
tune-tellers in all ages ; to the " cunning man" of modem times, and 
the oracles of old. Few have considered the extent to which this 
fallacy operates in practice, even in the teeth of the most palpable 
negative evidence. A striking example of it is the faith which the 
uneducated portion of the agricultural classes, in this and other coun- 
tries, continue to repose in the prophecies as to weather supplied by 
almanac makers : although every season affijrds to them numerous 
cases of completely erroneous prediction ; but as every season also 
furnishes some cases in which the prediction is verified, this is enough 
to keep up the credit of the prophet, with people who do not reflect on 
the number of instances requisite for what we have called, in our in- 
ductive terminology, the Elimination of Chance ; .since a certain num- 
ber of casual coincidences not only may but will happen, between any 
two unconnected events. , ■ ' 

Coleridge, in one of the essays in the Friend, has very happily 
illustrated the matter we are now considering, in discussing the origin 
of a proverb, " which, diffi^rently worded, is to be found in all the 
languages of Europe," viz., "Fortune favors fools." This proverb, 
says he, ** admits of various explanations. It may arise from pity, and 
the soothing persuasion that Providence is eminently watchful over the 
helpless, and extends an especial care to those who are not capable of 
caring for themselves. So used, it breathes the same feeling as * God, 



FALLACIES OF OBSERVATION. 477 

tempers the wind to the shorn lamb,' or the more sportive adage, that 
* the fairies take care of children and tipsy folk.' " So far, the notion 
partakes of the character of a fallacy of Generalization. But he con- 
tinues, " The persuasion itself, in addition to the general religious 
feeling of mankind, and the scarcely less general love of the marvelous, 
may be accounted for from our tendency to exaggerate all effects, that 
seem disproportionate to their visible cause, and all circumstances that 
are in any way strongly contrasted with our notions of the persons 
under them." Omitting some further explanations which would refer 
the error to mal-observation, or to the other species of non-observation 
(that of circumstances), I take up the quotation further on. " Unfore- 
seen coincidences may have gi'eatly helped a man, yet if they have 
done for him only what possibly from his own abilities he might have 
effected for himself, his good work will excite less attention, and the 
instances be less remembered. That clever men should attain their 
objects seems natural, and we neglect the circumstances that perhaps 
produced that success of themselves, without the intervention of skill 
or foresight ; but we dwell on the fact and remember it, as something 
strange, when the same happens to a weak or ignorant man. So too, 
though the latter should fail in his undertakings from concurrences 
that might have happened to the wisest man, yet his failure being no 
more than might have been expected and accounted for from his folly, 
it lays no hold on our attention, but fleets away among the other undis- 
tinguished waves in which the stream of ordinary life murmurs by us, 
and is forgotten. Had it been as true as it was notoriously false, that 
those all-embracing discoveries, which have shed a dawn o^ science on 
the art of chemistry, and give no obscure promise of some one great 
constitutive law, in the light of which dwell dominion, and the power 
of prophecy; if these discoveries, instead of*having been, as they really 
were, preconcerted by meditation, and evolved out of his own intellect, 
had occurred by a set of lucky accidents to the illustrious father and 
founder of philosophic alchemy; if they had presented themselves to 
Professor Davy exclusively in consequence of his luck in possessing a 
particular galvanic battery; if this battery, as far as Davy was con- 
cerned, had itself been an accident, and not (as in point of fact it was) 
desired and obtained by him for the purpose of insuring the testimony 
of experience to his principles, and in order to bind down material 
nature under the inquisition of reason, and force from her, as by tor- 
ture, unequivocal answers to prepared and preconceived questions, — 
yet still they would not have been talked of or described as instances 
of luck, but as the natural results of his admitted genius and known 
skill. But should an accident have disclosed similar discoveries to a 
inechanic at Birmingham or Sheffield, and if the man should gi'ow rich 
in consequence, and partly by the envy of his neighbors and partly 
with good reason, be considered by them as a man belotv par in the 
general powers of his understanding; then, 'O what a lucky fellow! 
Well, Fortune does favor fools — that's for certain! — It is always so!* 
And forthwith the excl aimer relates half a dozen similar instances. 
Thus accumulating the one sort of facts and never collecting the other, 
we do, as poets in their diction, and quacks of all denominations do in 
their reasoning, put a part for the whole, and at once soothe our envy 
and gratify our love of the marvelous, by the sweeping proverb, 
Fortune favors fools." ;. ' . . 



478 FALLACIES. 

This passage very liappily sets forth the manner in which, under the 
loose mode of induction which proceeds per enumerationem simplice?)!^ 
not seeking for instances of such a kind as to be decisive of the ques- 
tion, but generalizing from any which occur, or rather which are 
remembered, opinions grow up with the apparent sanction of experi- 
rcnce, which have no foundation in the laws of nature at all. " Itaque 
recte respondit ille," (we may say with Bacon,*) " qui cum suspensa 
tabula in templo ei monstraretur eorum, qui vota solverant, quod 
naufragii periculo elapsi sint, atque interrogando premeretur, anne 
tum quidem Deorum numen agnosceret, qusesivit denuo. At uhi sunt 
illi depicti qui post vota nuncupata perieruntl Eadem ratio est fere 
omnis superstitionis, ut in Astrologicis, in Somniis, Ominibus, Neme- 
sibus, et hujusmodi ; in quibus, homines delectati hujusmodi vanitati- 
bus, advertunt eventus, ubi implentur ; ast ubi fallunt, licet multo fre- 
quentius, tamen negligunt, et praetereunt." And he proceeds to say, 
that independently of the love of the marvelous, or any other bias in 
the inclinations, there is a natural tendency in the intellect itself to this 
kind of fallacy ; since the mind is more moved by affirmative instances, 
although negative ones are of most use in philosophy : "Is tamen 
humane intellectui error est proprius et perpetuus, ut magis moveatur 
et excitetur Affirmativis, quam Negativis j cum rite et ordine aequum 
se utrique prasbere debeat ; quin contra, in omni Axiomate vero con- 
stituendo, major vis est instantiae negativae." 

But the greatest of all causes of non-observation is a preconceived 
opinion. This it is which, in all ages, has made the whole race of 
mankind, and every separate section of it, for the most part unobser- 
vant of all facts, however abundant, even when passing under their own 
eyes, which are contradictory to any first appearance, or any received 
tenet. It is worth while to recall occasionally to the oblivious memory 
of mankind, some of the striking instances in which opinions that the 
simplest experiment would have shown to be erroneous, continued to 
be entertained because nobody ever thought of trying that experiment. 
One of the most remarkable of these was exhibited in the Copernican 
controversy. The opponents of Copernicus argued that the earth did 
not move, because if it did, a stone let fall from the top of a high tower 
would not reach the ground at the foot of the tower, but at a little dis- 
tance from it, in a contrary direction to the earth's course; in the same 
manner (said they) as, if a ball is let drop from the mast-head while 
the ship is in full sail, it does not fall exactly at the foot of the mast, 
but nearer to the stern of the vessel. The Copernicans would hare 
silenced these objectors at once if they had tried dropping a ball from 
the mast-head, because they would have found that it does fall exactly 
at the foot, as the theory requires; but no; they admitted the spurious 
fact, and struggled vainly to make out a difference between the two 
cases. " The ball was no part of the ship — and the motion forward 
was not natural, either to the ship or to the ball. The stone, on the 
other hand, let fall from the top of the tower, was ^ part of the earth; 
and therefore, the diurnal and annual revolutions which were natural 
to the earth, were also natural to the stone ; the stone . would, there- 
fore, retain the same motion with the tower, and strike the ground pre- 
cisely at the bottom of it."t 

* Nov. Org., Aph. 46. t Playfaie's Dissertation, sect. 4. < • 



FALLACIES OF OBSERVATION. 479 

Other examples, scarcely less striking, are recorded ^y Mr. Whewell,* 
where imaginary laws of nature have continued to be received as real, 
merely because no one person had steadily looked at facts which almost 
every one had the opportunity of observing. "A vague and loose 
mode of looking at facts very easily obsei'vable, left men for a long 
time under the belief that a body ten times as heavy as another falls 
ten times as fast; that objects immersed in water are always magnified, 
without regard to the form of the surface ; that the magnet exerts an 
irresistible force ; that crystal is always found associated with ice ; and 
the like. These g,nd many other are examples how blind and careless 
man can be, even in observation of the plainest and commonest ap- 
pearances; and they show us that the mere faculties of perception, 
although constantly exercised upon innumerable objects, may long fail 
in leading to any exact knowledge." 

The influence of a preconceived theory is well exemplified in the 
superstitions of barbarians respecting the virtues Of medicaments, and 
of charms. The negroes, among whom coral, as of old among our- 
selves, is worn as an amulet, affirm, acccording to Dr. Paris, f that its 
color " is always affected by the state of health of the wearer, it becom- 
ing paler in disease." On a matter open to universal observation, a 
general proposition which has not the smallest vestige of truth, is 
received as a result of experience ; the preconceived opinion prevent- 
iiig all observation of such instances as do not accord with it. 

§ 4. For illustration of the first species of non-observation, that of 
Instances, what has now been stated may suffice. But there may also 
be non-observation of some material circumstances, in instances which 
have not been altogether overlooked — nay, which may be the very 
instances upon which the whole superstructure of a theory has been - 
founded. As, in the cases hitherto examined, a general proposition 
was too rashly adopted, on the evidence of particulars, true indeed, but 
insufficient to support it ; so in the cases to which we now turn, the 
particulars themselves have been imperfectly observed, and the singu- 
lar propositions upon which the generalization is grounded, or some at 
least of those singular propositions are false. 

Such, for instance, was one of the mistakes committed in the cele- 
brated phlogistic theory; a doctrine which accounted for combustion- 
by the extrication of a substance supposed to be contained in all com- 
bustible matter, and to which the name phlogiston was given. The 
hypothesis accorded tolerably well with superficial appearances : the 
ascent of flame naturally suggests the escape of a substance ; and the 
visible residuum of ashes, in bulk and weight, generally falls extremely 
short of the combustible material. The error was, non-observation of 
an important portion of the actual residue, namely, the gaseous pro- 
ducts of combustion. When these were at last noticed and brought 
into account, it appeared to be an universal law, that all substances 
gain instead of losing weight by undergoing combustion ; and, after 
the usual attempt to accommodate the old theory to the new fact by 
means of an arbitrary hypothesis (that phlogiston had the quality of 
positive levity instead of gravity), chemists were conducted to the true 

* Whewell's Phil, of the Inductive Sciences, ii., 203. 
f Pharmacologia, ■p. 21 — 



480 ^ FALLACIES. 

explanation, namely that instead of -a substance separated, there was 
OH the contrary a substance absorbed^ 

Many of the absurd practices which have been deemed to possess 
medicinal efficacy, have been indebted for their reputation to non- 
observance of some accompanying circumstance which was the real 
agent in the cures ascribed to them. Thus, of the sympathetic powder 
of Sir Kenelm Digby : " Whenever any wound had been inflicted, 
this powder was applied to the weapon that had inflicted it, which 
was, moreover, covered with ointment, and dressed two or three times 
a day. The wound itself, in the meantime, was directed to be brought 
together, and carefully bound up with clean linen rags, but ahovc all, 
to he let alone for seven days, at the end of which period the bandages 
were removed, when the wound was generally found perfectly united. 
The triumph of the cure was decreed to the mysterious agency of the 
sympathetic powder which had been so assiduously applied to the 
weapon, whereas it is hardly necessary to observe that the promptness 
of the cure depended upon the total exclusion of air from the wound, 
and upon the sanative operations of nature not having received any 
disturbance from the officious interference of art. The result, beyond 
all doubt, furnished the first hint which led surgeons to the improved 
practice of healing wounds by what is technically called the first inten- 
tionP* "In all records," adds Dr. Paris, *' of extraordinary cures 
performed by mysterious agents, there is a great desire to conceal the 
remedies and other curative means which were simultaneously admin- 
istered with them : thus Oribasius commends in high terms a necklace 
of Pgeony root for the cure of epilepsy ; but we learn that he always 
took care to accompany its use with copious evacuations, although he 
assigns to them no share of credit in the cure. In later times we have 
a good specimen of this species of deception, presented to us in a work 
on Scrofula by Mr. Morley, written, as we are informed, for the sole 
purpose of restoring the much injured character and use of the Ver- 
vain ; in which the author directs the root of this plant to be tied vnth 
a yard of white satin riband around the neck, where it is to remain 
until the patient is cured ; but mark — during this interval he calls to 
his aid the most active medicines in the materia medica !"t 

In other cases the cures really produced by rest, regimen, and 
amusement, have been ascribed to the medicinal, or occasionally to 
the supernatural, means which were put in requisition. *' The cele- 
brated John Wesley, while he commemorates the triumph of sulphur 
and supplication over his bodily infirmity, forgets to appreciate the 
resuscitating influence of four months repose from his apostolic labors ; 
and such is the disposition of the human mind to place confidence in 
the operation of mysterious agents, that we find him more disposed to 
attribute his cure to a brown paper plaster of e^'^ and brimstone, than 
to Dr. Fothergill's salutary prescription of country air, rest, asses' milk, 
and horse exercise."| 

* In the following example, the circumstance overlooked was of a 
somewhat different character. " When the yellow fever raged in 
America, the practitioners trusted exclusively to the copious use of 
mercm-y ; at first this plan was deemed so universally efficacious, that, 
in the enthiLsiasm of the moment, it was triumphantly proclaimed that 

* Pharmacologia, pp. 23-4. f Ibid., p. 28. t Ibid., p. 62. 



FALLACIES OF OBSERVATION. 481 

death never took place after the mercury had evinced its effect upon 
the system : all this was very true, but it furnished no proof of the 
efficacy of that metal, since the disease in its aggravated form M^as so 
rapid in its career, that it swept away its victims long before the sys- 
tem could be brought under mercurial influence, while in its milder 
shape it passed off equally well without any assistance from art."* 

In these examples the circumstance overlooked was, cognizable by 
the senses. In other cases, it is one the knowledge of which could 
only be an'ived at by reasoning ; but the fallacy may still be classed 
under the head to which, for want of a more appropriate name, we 
have given the appellation Fallacies of Non-observation. It is not the 
nature of the faculties which ought to have been employed, but the non- 
employment of them, which constitutes this natural Order of Fallacies. 
Wherever the error is negative, not positive ; wherever it consists 
specially in overlooking, in being ignorant or unmindful of some fact 
which, if known and attended to, would have made a difference in the 
conclusion arrived at ; the en'or is properly placed in the Class which 
we are considering. In this Class, there is not, as in all other falla- 
cies there is, a positive mis-estimate of evidence actually had. The 
conclusion would be just, if the portion which is seen of the case were 
the whole of it ; but there is another portion overlooked, which vi- 
tiates the result. 

For instance, there is a remarkable doctrine which has occasionally 
found a vent in the public speeches of unwise legislators, but which 
only in one instance that I am aware of has received the sanction of a 
philosopher, namely M. Victor Cousin, who, in his preface to the G-orgias 
of Plato, contending that punishment must have some other and higher 
justification than the prevention of crime, makes use of this argument 
- — that if punishment were only for the sake of example, it would be 
indifferent whether we punished the innocent or the guilty, since the 
pTiiiishment, considered as an example, is equally efficacious in either 
case. Now we must, in order to go along with M. Cousin, suppose, 
that the person who feels himself under temptation, observing some- 
Body punished, concludes himself to be in danger of being punished 
likewise, and is terrified accordingly. But it is forgotten that if the ' 
person punished is supposed to be innocent, or even if there be any 
doubt of his guilt, the spectator will reflect that his own danger, what- 
ever it may be, is not contingent upon his guiltiness, but threatens him 
equally if he remains innocent, and how therefore is he deterred from 
guilt by the apprehension of such punishment? M. Cousin supposes 
that men will be dissuaded from guilt by whatever renders the condi- 
tion of the guilty more perilous, forgetting that the condition of the 
innocent (also one of the elements in the calculation) is, in the case 
supposed, made perilous in precisely an equal degi^ee. This is a fal- 
lacy of overlooking; or of non-observation, within the intent of our 
classification. 

Fallacies of this description are the gi^eat stumbling-block to just . 
views in political economy. The economical workings of society afford 
innumerable cases in which the effects of a cause consist of two sets 
of phenomena : the one immediate, concenti'ated, obvious to vulgar 
eyes, and passing, in common apprehension, for the whole effect ; the 

* Pharmacologia, pp. 61-62. 

3P 



482 , . FALLACIES. 

Other widely diffused, or lying deeper under the surface, and which is 
exactly contrary to the former. Take, for instance, the vulgar notion, 
so plausible at the first glance, of the encouragement given to industry 
by lavish expenditure. A, who spends his whole income, and even 
his capital, in expensive living, is supposed to give great employment to 
labor. B, who lives upon a small portion, and invests the remainder in 
the funds, is thought to give little or no employment. For everybody 
sees the gains which are made by A's tradesmen, servants, and othersi 
while his money is spending. B's savings,, on the contrary, pass into the 
hands of the person whose stoclv he piirchased, who with it pays a debt 
he owed to some banker, who lends it again to some merchant or manu- 
facturer ; and the capital, being laid out in hiring spinners and weavers, 
or carriers and the crews of merchant vessels, not only gives immediate 
employment to as much industry at once as A employs during the whole 
of his career, but coming back with increase by the sale of the goods 
which have been manufactured or imported, form a fund for the em- 
ployment of the same and perhaps a greater quantity of labor in per- 
petuity. But the careless observer does not see, and therefore does 
not consider, what becomes of B's money ; he does see what is done 
with A's : he observes the amount of industry which A's profusion 
feeds ; he observes not the far greater quantity which it prevents from 
being fed : and thence the prejudice, universal to the time of Adam 
Smith, and even yet only exploded among persons more than com- 
monly instructed, that prodigality encourages industry, and parsimony 
is a discouragement to it. 

The common argument against free-trade is a fallacy of the same 
nature. The purchaser of British silk encourages British industry; 
the purchaser of Lyons silk encourages only French; the former con- 
duct is patriotism, the latter ought to be interdicted by law. The 
circumstance is overlooked, that the purclmser of any foreign com- 
modity of necessity causes, directly or indirectly, the export of an 
equivalent value of some English article (beyond what would other- 
wise be exported), either to the same foreign country or to some 
other > which fact, although from the complication of the circumstances 
it cannot always be verified by specific observation, no observation can 
possibly be brought to contradict, while the evidence of reasoning upon 
which it rests is absolutely irrefragable/ The fallacy is, therefore, the 
same as in the preceding case, that of seeing a part only of the phe- 
nomena, and imagining that part to be the whole ; and may be ranked 
among Fallacies of Non-observation. 

§ 5. To complete the examination of the second of our five classes, 
we have now to speak of Mal-observation ; in which the eiTor does 
not lie in the fact that something is unseen, but that something seen is 
eeen wrong. 

Perception being infallible evidence of whatever is really perceived, 
the error now under consideration can be committed no otherwise 
than by mistaking for perception what is in fact inferepce. We have 
formerly shown how intimately the two are blended in almost every- 
thing which is called observation, and still more in every Description.* 
What is actually on any occasion perceived by our senses being so 

* Supra, p. 383. 



FALLACIES OF OBSERVATION. 483 

minute in amount, and generally so unimportant a portion of the state 
of facts which we wish to ascertain or to communicate, it would be 
absurd to say that either in our observations, or in conveying their 
result to others, we ought not to mingle inference with fact ; all that 
can be 'said is, that when we do so we ought to be aware of what we 
are doing, and to know what part of the assertion rests upon conscious- 
ness, and is therefore indisputable, what part upon inference, and is 
therefore questionable. 

One of the most celebrated examples of an universal error produced 
by mistaking an inference for the direct evidence of the senses, was 
the resistance made, on the ground of common sense, to the Copernican 
system. People fancied they saw the sun rise and set, the stars revolve 
in circles round the pole. We now know that they saw no such thing: 
what they really saw were a set of appearances, equally reconcila- 
ble with the theory they held and with a totally different one. It 
seems strange that such an instance as this, of the testimony of the 
senses pleaded with the most entire conviction in favor of something 
which was a mere inference of the judgment, and, as it turned out, 
a false inference, should not have opened the eyes of the bigots 
of common sense, and inspired them with a more modest disti-ust 
of the competency of mere ignorance to judge the conclusions of 
science. 

In proportion to any person's deficiency of knowledge and mental 
cultivation, is generally his inability to discriminate between his infer- 
ences and the perceptions on which they were grounded. Many a 
marvelous tale, many a scandalous anecdote, owes its origin to this 
incapacity. The narrator relates, not what he saw or heard, but the 
impression which he derived from what he saw or heard, and of which 
perhaps the greater part consisted of inference, though the whole is 
related not as inference, but as matter-of-fact. The difficulty of in- 
ducing witnesses to restrain within any moderate limits the intermix- 
ture of their inferences with the narrative of their perceptions, is well 
known to experienced cross-examiners ; and still more is this the case 
when ignorant persons attempt to describe any natural phenomenon. 
"The simplest nan-ative," says Dugald Stewart,* "of the most illiterate 
observer involves more or less of hypothesis ; nay, in general, it wiU 
be found that, in proportion to his ignorance, the^ greater is the number 
of conjectural principles involved in his statements. A village pothe- 
cary (and, if possible, in a still greater degree, an experienced nurse) 
is seldom able to describe the plainest case, without employing a phra- 
seology of which every word is a theory ; whereas a simple and, gen- 
uine specification of the phenomena which mark a particular disease, 
a specification unsophisticated by fancy, or by preconceived opinions, 
may be regarded as unequivocal evidence of a mind trained by long 
and successful study to the most difficult of all arts, that of the faithful 
interpretation of nature.''t 

* Elements of the Philosophy of the Mind, vol. ii., ch. 4, sect. 5. 

t The following anecdote, related by Dr. Paris {Pharmacologia, pp. 76-7), is an amusing 
instance of an inference mistaken for a direct perception. " Shortly after Sir Humphry 
Davy had succeeded in decomposing the fixed alkalies, a portion of potassium" (a sub- 
stance so light as to swim upon water) " was placed in the hand of one of our most dis- 
tinguished chemists, with a query as to its nature. The philosopher observing its aspect 
and splendor did not hesitate in pronouncing it to be metallic, and uniting at once the idea 
of weight with that of metal, the evidence of Ms senses was even insufficient to dissever 



484 FALLACIES. 

The universality of the confusion between perceptions and the infer- 
ences drawn from them, and the rarity of the power to discriminate 
the one from the other, ceases to surprise us when we consider that in 
the far gi*eater number of instances the actual perceptions of our senses 
are of no importance or interest to us except as marks from which we 
infer something beyond them. It is not the color and superficial exten- 
sion perceived by the eye that are important to us, but the object, of 
which those visible appearances testify the presence ; and where the 
sensation itself is indifferent, as it generally is, we have no motive to 
attend particularly to it, but acquire a habit of passing it over without 
distinct consciousness, and going on at once to the inference. So that 
to know what the sensation actually was, is a study in itself, to which 
the painter, for example, has to train himself by special and long con- 
tinued discipline and application. In things further removed from the 
dominion of the outward senses, no one who has not great experience 
in psychological analysis is competent to break this intense association: 
and when such analytic habits do not exist in the requisite degree, it is 
hardly possible to mention any of the habitual judgments of mankind 
on subjects of a high degree of abstraction, from the being of God and 
the immortality of the soul down to the multiplication table, which are 
not, or have not been, considered as- matter of direct intuition. In 
saying this I do not seek to prejudge the question of transcendental 
metaphysics, how far a certain number of these habitual judgments are 
really intuitive, or otherwise. I only point out the strength of the 
tendency to ascribe an intuitive character to judgments which are mere 
inferences, and often false ones. *No one can doubt that many a de- 
luded visionary has actually believed that he was directly inspired from 
heaven, and that the Almighty had conversed with him face to face; 
which yet was only, on his part, a conclusion drawn from appearances 
to his senses or feelings in his internal consciousness which were alto- 
gether an insufficient foundation for any such belief \ The caution, 
therefore, which is needful against this class of errors, could not with 
any propriety have been foregone ; though to determine whether, on 
any of the great questions of metaphysics, such errors are actually 
committed, belongs not to this place, but, as I have so often said, to a 
different science. 

ideas so inseparably associated in his mind, and, balancing the specimen on his fingers, he 
exclaimed, ' it is certainly metallic, and very ponderous J " He mistook his jvdgvient of the 
ponderosity of the substance for a sensation of it. 



FALLACIES OP GENERALIZATION. 485 

CHAPTER V. 

FALLACIES OF GENERALIZATION. 

§ 1. The class of Fallacies of which we are now to speak, is the 
most extensive of all ; embracing a greater number and variety of 
unfounded inferences than any of the other classes, and which it is even 
more difficult to reduce to sub- classes or species. If the attempt made 
in the preceding Books to define the principles of well-grounded gener- 
alization has been successful, all generalizations not conformable to 
those principles might, in a certain sense, be brought under the present 
class: when however the rules are known and kept in view, but a 
casual lapse committed in the application of them, this is a blunder, 
not a fallacy. To entitle an error of generalization to the latter epithet, 
it must be committed on principle; there must lie in it some erroneous 
general conception of the inductive process ; the legitimate mode of 
drawing conclusions from observation and experiment must be funda- 
mentally misconceived. 

Without attempting anything so chimerical as an exhaustive classifi- 
cation of all the misconceptions which can exist on the subject, let us 
content ourselves with noting, among the cautions which might be 
suggested, a few of the most useful and needful. 

§ 2. In the first place, there are certain kinds of generalization which, 
if the principles already laid down be coiTect, inust be groundless : ' 
experience cannot afford the necessary conditions for establishing them 
by a correct induction. Such, for instance, are all inferences from the 
order of nature existing on the earth, or in the solar system, to that 
which may exist in remote parts of the universe; where the phenom- 
ena, for aught we know, may be entirely different, or may succeed one 
another according to different laws, or even according to no fixed law 
at all. Such, again, in matters dependent on causation, are all universal 
nec^atives, all propositions that assert impossibility. The non-existence 
of any given phenomenon, however uniformly experience may as yet 
have testified to the fact, proves at most that no cause, adequate to its 
production, has yet manifested itself; but that no such causes exist in 
nature can only be inferred if we commit the absurdity of supposing 
that we know all tl?.e forces in nature. The supposition would at least 
be premature while our acquaintance wdth some even of those which 
we do loiow is so extremely recent. And however much our knowl- 
edge of nature may hereafter be extended, it is not easy to see how 
tliat knowledge could ever be complete, or how, if it were, we could' 
ever be assured of its being so. 

The only laws of nature which afford sufficient warrant for attribut- 
ino° impossibility, are first, those of number and extension, which are 
paramount to the laws of the succession of phenomena, and not ex- 
posed to the agency of counteracting causes ; and secondly, the univer- 
sal law of causality itself. That no variation in any effect or consequent 
will take place while the whole of the antecedents remain the same, 
may be affirmed with full assurance. But, that the addition of some 
new antecedent might not entirely alter and subveit the accustomed 



486 FALLACIES. 

consequent, or that antecedents competent to do this do not exist in 
nature, we are in no case empowered positively to conclude. 

§ 3. It is next to be remarked that all generalizations which profess, 
like the theories of Thales, Democritus, and others of the early Greek 
philosophers, to resolve all things into some one element, or, like m^ny 
modern theories, to resolve phenomena radically different into the 
same, are necessarily false. By radically different phenomena I mean 
impressions on our senses which differ in quality, and not merely in 
degree. On this subject what appeared necessary was said in the 
chapter on the Limits to the Explanation of Laws of Nature; but as 
the fallacy is even in our own times a common one, I shall touch upon 
it somewhat further in this place. 

When we say that the force which holds the planets in their orbits 
is resolved into gravity, or that the force which make substances com- 
bine chemically is resolved into electricity, we assert in the one case 
what is, and in the other case what might, and probably will ultimately 
be a legitimate result of induction. In both these cases, motion is 
resolved into motion. The assertion is, that a case of motion, which 
was supposed to be special, and to follow a distinct law of its own, 
conforms to and is included in the general law which regulates another 
class of motions. But, from these and similar generalizations, counte- 
nance and currency has been given to attempts to resolve not motion 
into motion, but heat into motion, light into motion, sensation itself into 
motion (as in Hartley's doctrine of vibrations) ; states of consciousness 
into states of the nervous system, as in the ruder forms of the materi- 
alist philosophy; vital phenomena into mechanical or chemical pro- 
cesses, as in some schools of physiology. 

Now I am far from pretending that it may not be capable of proof, 
or that it would not be a very important addition to our knowledge if 
proved, that certain motions in the particles of bodies are among the 
conditions of the -pvoduction of heat or light; that certain assignable 
physical modifications of the nerves may be among the conditions not 
only of our sensations or emotions, but even of our thoughts; that cer- 
tain mechanical and chemical conditions may, in the order of nature, be 
sufficient to determine to action the physiological laws of life. All I 
insist upon, in common with every sober thinker since modern science 
has been definitively constituted, is, that it shall not be supposed that by 
proving these things one step would be made towards a real explanation 
of heat, light, or sensation; or that the generic peculiarity of those 
phenomena can be in the least degree evaded by any such discovei'ies, 
however well established. Let it be shown, for instance, that the 
most complex series of physical causes and effects succeed one another 
in the eye and in the brain to produce a sensation of color ; rays falling 
upon the eye, refracted, converging, crossing one another, making an 
inverted image on the retina, and after this a motion — let it be a 
vibration or a rush of nervous fluid, or whatever else you are pleased to 
suppose, along the optic nerve — a propagation of this motion to the 
brain itself, and as many more different motions as you choose; still, 
at the end of these motions, there is something which is not a motion, 
there is a feeling or sensation of color. Whatever number of motions 
we may be able to interpolate, and whether they be real or imaginary, 
wc shall still find, at the end of the seiies, a motion antecedent and a color 



FALLACIES OF GENERALIZATION. 487 

consequent. The mode in wliich any one of the motions produces the 
next, might possibly be susceptible of explanation by some general 
law of motion previously known; but the mode in which the last mo- 
tion produces the sensation of color, cannot be explained by any law 
of motion; it is the law of color; which is, and must always remain a 
peculiar thing. Where our consciousness recognizes between two 
phenomena an inherent distinction ; where we are sensible of a differ- 
ence which is not merely of degree, and feel that no adding one of the 
phenomena to itself would produce the other; any theory which 
attempts to. bring either under the laws of the other must be false; 
though a theory which merely treats the, one as a cause or condition of 
the other, may possibly be true. 

§ 4. Among the remaining forms of erroneous generalization, sev- 
eral of those most worthy of and most requiring notice have fallen under 
our examination in former places, v/here, in investigating the rules of 
correct induction, we have had occasion to advert to the distinction 
between it and some common mode of the incorrect. In this number 
is what I have formerly called the natural Induction of uninquiring 
minds, the Induction of the ancients, which proceeds per enuincratlo- 
nem simplicem : " This, that, and the other A are B, I cannot think of 
any A which is not B, therefore every A is B." As a final condem- 
nation of this rude and slovenly mode of generalization, I will quote 
Bacon's emphatic denunciation of it; the most important part, as I have 
more than once ventured to assert, pf the permanent service rendered 
by him to philosophy. " Inductio quae procedit per enumerationem 
simplicem, res puerilis est, et precario concludit," (concludes only hy 
your leave, or provisionally,) " et periculo exponitur ab instantia con- 
tradictoria, et plerumque secundum pauciora quam par est, et ex his 
tantummodo quce prccsto sunt pronunciat. At Inductio quae ad inven- 
tionem et demonstrationem Scientiarum et Artium erit utilis, Naturam 
separare debet, per rejectiones et exclusiones debitas ; ac deinde post 
negativas tot quot sufficiunt, super affirmativas concludere." 

I have already said that the mode of Simple Enumeration is still the 
common and received method of Induction in whatever relates to man 
and society. Of this a very few instances, more by way of memento 
than of instruction, may suffice. What, for example, is to be thought 
of all the " common-sense" maxims for which the following may serve 
as the universal formula : " Whatsoever has never been, will never 
be." As for example : negroes have never been as civilized as whites 
sometimes are, therefore it is impossible they should be so. Women, 
. as a class, have not hitherto equaled men as a class in intellectual 
energy and comprehensiveness, therefore they are necessarily inferior. 
Society cannot prosper without this or the other institution ; e. g., in 
Aristotle's time, without slavery ; in later times, without an established 
priesthood, without artificial distinctions of ranks, &c. One working 
man in a thousand, educated, while the nine hundred and ninety-nine 
remain uneducated, has usually aimed at raising himself out of his 
class, therefore education makes people dissatisfied with their condi- 
tion in life. Bookish men, taken from speculative pursuits and set to 
work on something they know nothing about, have generally been 
found or thought to do it ill ; therefore philosophers are unfit for busi- 
ness, &c., &c. All these are inductions by simple enumeration. 



488 ~ FALLACIES. - ' 

E-easons having some reference to the canons of scientific investigation 
may have been given or iattempted to be given for several of these 
propositions; but to the multitude of those w^ho parrot them, the 
enumeratio simplex, ex Ms tantummodo quce prcesto sunt pronuncians, 
is the sole evidence. Their fallacy consists in this, that they are induc- 
tions without elimination ; there has been no real comparison of in- 
stances, nor even ascertainment of the material circumstances in any 
given instance. There is also the further en^or, of forgetting that such 
generalizations, even if v^ell established, cannot be ultimate truths, but 
must be the results of other law^s much more elementary ; and there- 
fore could at most be admitted as empirical law^s, holding good v^ithin 
the limits of space and time by which the particular observations* that 
suggested the generalization were bounded. 

This error of placing mere empirical laws, and laws in which there 
is no direct evidence of causation, on the same footing of certainty as 
laws of cause an effect, and error which is at the root of perhaps the 
greater number of bad inductions, is exemplified only in its grossest 
form in the kind of generalizations to which we have now referred. 
These, indeed, do not possess even the degree of evidence which per- 
tains to a Well-ascertained empirical law ; but admit of refutation oii 
the empirical ground itself, without ascending to causal laws. A little 
reflection, indeed, will show that mere negations can only form the 
ground of the lowest and least valuable kind of empirical law. A 
phenomenon has never been noticed; this only proves that the condi- 
tions of that phenomenon have not yet occurred in human experience, 
but does not prove that they may not occur to-mon-ow. There is a 
higher kind of empirical law than this, namely, when a phenomenon 
which is observed presents within the limits of observation a series of 
gradations, in which a regularity, or something like a mathematical 
law, is perceptible: from which, therefore, something may be ration- 
ally presumed as to those terms of the- series which are beyond the 
limits of observation. But in negation there are no gradations, and no 
series : the generalizations, therefore, which deny the possibility of any 
given condition of Man and Society merely because it has never yet 
been witnessed, cannot possess this higher degree of validity even as 
empirical laws. What is more, the minuter examination which that 
higher order of empirical laws presupposes, being applied to- the sub- 
ject matter of these, not only does not confirm but actually refutes 
them. For in reality the past history of Man and Society, instead of 
exhibiting them as immovable, unchangeable, incapable of ever pre- 
senting new phenomena, shows them on the contrary to be, in many 
most important particulars, not only changeable, but actually undergo- 
ing a progressive change. The empirical law, therefore, best expres- 
sive, in most cases, of the genuine result of observation, would be, not 
that such and such a phenomenon will continue unchanged, but that it 
will continue to change in some particular manner. 

Accordingly, while almost all generalizations relating to Man and 
Society, antecedent to the last fifty years, have erred in the gross way 
which we have attempted to characterize, namely, by implicitly as- 
suming that human nature and society will for ever revolve in the 
same orbit, and exhibit essentially the same phenomena ; which is also 
the vulgar error of practicalism and common sense in our own day, 
especially in Great Britain ; the more thinking minds of the present 



FALLACIES OF GENERALIZATION. 489 

age, having applied a more minute analysis to the past records of our 
race, have for the most part adopted the contrary opinion, that the 
human species is in a state of necessary progression, and that from the 
terms of the series which are past we may infer with certainty those 
which are yet to come. Of this doctrine, considered as a philosophical 
tenet, we shall have occasion to speak fully in the concluding Book. 
If not, in all its forms, free from error, it is at least always free from 
the gross and stupid error which we previously exemplified. But, in all 
except the most eminently philosophical minds, it is infected with pre- 
cisely the same ki7id of fallacy as that is. For we must remember that 
even this other and better generalization, the progressive change in the 
condition ^ of the human species, is, after all, but an empirical law : to 
which, moreover, it is not difficult to point out exceedingly large excep- 
tions ; and even if these could be got rid of, either by disputing the facts 
or by explaining and limiting the theory, the general objection remains 
valid against the supposed law, as applicable to any other than what, in 
our third Book, were termed Adjacent Cases. , For not only is it no ulti- 
mate, but not even a causal law. Changes do indeed take place in 
human affairs, but every one of those changes depends upon determi- 
nate causes ; the '* progressibility of the species^' is not a cause, but' a 
summary expression for the general result of all the causes. So soon 
as, by a quite different sort of induction, it shall be ascertained what 
causes have produced these successive changes from the beginning of 
history in so far as they have really taken place, and by what causes of a 
^ contrary tendency they have been occasionally checked or entirely coun- 
teracted, we shall then be prepared to predict the future with reason- 
able foresight : we shall be in possession of the real law of the future ; 
a,nd shall be able to declare upon what circumstances the continuance 
of the same onv^ard movement will eventually depend. But this it is 
the error of many of the more advanced thinkers, in the present age, 
to overlook ; and to imagine that the empirical law collected from a 
mere comparison of the condition of our species at different past times, 
is a real law, is the law of its changes, not only past but also to come. 
The truth is, that the causes upon which the phenomena of the moral 
world depend, are in every age, and almost in every country, com- 
bined in some different proportion ; so that it is scarcely to be expect- 
ed that the general result of them all should conform very closely, in 
its details at least, to any uniformly progi-essive series. And all 
generalizations which affirm that mankind have a tendency to gi^ow 
better or worse, richer or poorer, more- cultivated or more barbarous, 
that population increases faster than subsistence, or subsistence than 
population, that inequality of fortunes has a tendency to increa,se or to 
break down, and the like, propositions of considerable value as empiri- 
cal laws within certain (but generally rather narrow) limits, are in 
reality true or false according to times and circumstances. 

What we have said of empirical generalizations from times past to 
times still to come, holds equally true of similar generalizations from 
present times to times past ; when men whose acquaintance with moral 
and social facts is confined to their own age, take the men and the 
things of that age for the type of men "and things in general, and apply 
without scruple to the interpretation of the events of history, the em- 
pirical laws which represent sufficiently for daily guidance the com- 
mon phenomena of human nature at that time and in that particular 



490 - FALLACIES. 

State of society. If examples are wanted, almost every historical work, 
until a very recent period, abounded in them. The same may be said 
of those who generalize empirically from the people of their own 
country to the people of other countries, as if human beings felt, 
judged, and acted, everywhere in the same manner. 

§ 5. In the foregoing instances, the distinction is confounded between 
empirical laws, which express merely the customary order of the suc- 
cession of effects, and the laws of causation on which the effects depend. 
There may, however^ be incorrect generalization when this mistake 
is not committed ; w^ien the investigation takes its proper direction, 
that of causes, and the result erroneously obtained purports to be a 
really causal law. 

The most vulgar form of this fallacy is that which is commonly called 
fost hoc, ergo propter hoc, or cwrn hoc, ergo proptter hoc. As when it is 
inferred that England owes her industrial preeminence to her restric- 
tions on commerce : as when the old school of financiers, and I am 
sorry to add, Coleridge, maintained that the national debt was one of 
•the causes of the national prosperity: as when the excellence of the 
Church, of the Houses of "Lords and Commons, of the procedure of 
the law courts, &c., are inferred from the mere fact that the country 
has prospered under them. In these and similar cases, if it can be 
rendered probable by other evidence that the supposed causes have 
some tendency to produce the effect ascribed to them, the fact of its 
having been produced, though only in one instance, is of some value 
as a verification by specific experience : but in itself it goes scarcely 
any way at all towards establishing such a tendency, since, admitting 
the effect, a hundred other antecedents could show an equally strong 
title of that kind to be considered as the cause. 

In these examples we see bad generalization a posteriori, or empir- 
icism properly so called : causation inferred from casual conjunction, 
without either due elimination, or any presumption arising from known 
properties of the supposed agent. But bad generalization a jiriori is 
fully as common ; which is properly called false theory ; conclusions 
drawn, by way of deduction, from properties of some one agent which 
is known or supposed to be present, all other coexisting agents being 
overlooked. As the former is the error of sheer ignorance, so the 
latter is especially that of instructed minds ; and is mainly committed 
in attempting to explain complicated phenomena by a simpler theory 
than their nature admits of. As when one school of physicians sought 
for the universal principle of all disease in " lentor and morbid viscid- 
ity of the blood," and imputing most bodily derangements to mechan- 
ical obstructions, thought to cure them by mechanical remedies ;* while 
another,' the chemical school,, " acknowledged no source of disease but 
the presence of some hostile- acid or alkali, or some deranged con- 

* " Thus Fourcroy," says Df. Paris, " explained the operation of mercury by its specific 
gravity,, and the advocates of this doctrine favored the general introduction of the prepara- 
tions of iron, especially in schirrus of the spleen or liver, upon the same hypothetical prin- 
ciple ; fof, say they, whatever is most forcible in removing the obstruction must be the 
most proper instrument of 'cure ; such is steel, which, besides the attenuating power with 
•which it is furnished, has stilj a greater force in this case from the gravity of its particles, 
which, being ^even times specifically heavier. than any vegetable, acts in proportion with 
a stronger impulse, and therefore is a more powerful dcoljstruent. This may be taken as a 
specimen of the style in which these mechanical physicians reasoned and practised." 
l^harmacolosia, pp. 38-9. - 



FALLACIES OF GENERALIZATION. 491 

dition in the chemical composition of the fluid or solid parts," and 
conceived, therefore, that " all remedies must act by producing chem- 
ical changes in the body. We find Tournefort busily engaged in test- 
ing every vegetable juice, in order to discover in it some traces of an 
acid or alkaline ingredient, w^hich might confer upon it medicinal ac- 
tivity. The fatal errors into v\^hich such an hypothesis was liable to 
betray the practitioner, receive an awful illustration in the history of 
the memorable fever that raged at Leyden in the year 1699, and which 
consigned two-thirds of the population of that city to an untimely 
grave ; an event which in a great measure depended upon the Pro- 
fessor Sylvius de la Boe, who having just embraced the chemical doc- 
trines of Van Helmont, assigned the orighi of the distemper to a pre- 
vailing acid, and declared that its cure could alone be effected by the 
copious administration of absorbent and testaceous medicines."* John 
Brown, the author of the famous Brunonian Theory, " generalized dis- 
eases, and brought all within the compass of two grand classes, those 
of increased and diminished excitement;" and maintained " that every 
agent which could operate on the human body was a stimulant, having 
an identity of action, and differing only in the degree of its force ; so 
that according to his views the lancet and the brandy bottle were but 
the opposite extremes of one and the same class, "f 

These aberrations in medical theory have their exact parallels in 
politics. All the doctrines which ascribe absolute goodness to partic- 
ular forms of government, particular social arrangements, and even to 
particular modes of education, without reference to the state of civiliza- 
tion and the various distinguishing characters of the society for which 
they are intended, are open to the same objection — that of assuming 
one class of influencing circumstances to be the paramount rulers of 
phenomena which depend in an equal or greater degree upon many 
others. But on these considerations it is the less necessary that we 
should now dwell, as they will occupy our attention very largely iri 
the concluding Book. 

§ 6"., The last of the modes of erroneous generalization to which I 
shall advert, is that to which we may give the name of False Analogies. 
This Fallacy stands distinguished from those already treated of by the 
peculiarity, that it does not even simulate a complete and conclusive 
induction, but consists in the misapplication of an argument which is 
at best only admissible as an inconclusive presumption, where real 
proof is unattainable. 

An argument from analogy, is an inference that what is true in a cer- 
tain case is true in a case known to be somewhat similar, but not known 
to be exactly parallel, that is, to be similar in all the material circum- 
stances. An object has the property B : another object is not known to 
have that property, but resembles the first in a property A, not known to 
be connected with B; and the conclusion to which the analogy points, 
is that this object has the property B also. As, for example, that the 
planets are inhabited because the earth is. The planets resemble the 
earth in describing elliptical orbits round the sun, in being attracted 
by it and by one another, in being spherical, revolving upon their axes, 
&c. ; but it is not known that any of these properties, or all of them 

* Pharmacologia, pp. 39, 40. f Ibid., p. 43. 



492 FALLACIES. 

together, are the conditions upon which the possession of inhabitants 
is dependent, or are even marks of those conditions. Nevertheless, 
so long as we do not know what the conditions are, they may be con- 
nected by some law of nature with those common properties; and to 
the extent of that possibility the planets are more likely to be inhabited, 
than if they did not resemble the earth at all. This non-assignable 
and generally small increase of probability, beyond what would other- 
wise exist, is all the evidence which a conclusion can derive from 
analogy. For if we have any the slightest reason to suppose any real 
connexion between the two properties A and B, the argument is no 
longer one of analogy. If it had been ascertained (I purposely put 
an absurd supposition) that there was any connexion, by causation, 
between the fact of revolving round an axis and the existence of ani- 
mated beings, or if there were any reasonable ground for even suspect- 
ing such a connexion, a probability would arise of the existence of 
inhabitants in the planets, which might be of any degree of strength, 
up to a complete induction ; but we should then infer the fact from the 
ascertained or presumed law of causation, and not from the analogy of 
the earth. 

The name analogy, however, is sometimes employed by extension, 
to denote those arguments of an inductive character, but not amount- 
ing to a real induction, which are employed to strengthen the argument 
drawn from a simple resemblance. Though A, the property common 
to the two cases, cannot be shown to be the cause or effect of B, the 
analogical reasoner will endeavor, if he can, to show that there is some 
less close degree of connexion between them ; that A is one of a set 
of conditions from which, when all united, B would result ; or is an 
occasional effect of some cause which has been known also to produce 
B; and the like. Any of which things, if shown, would render the 
existence of B by so much more probable, than if there had not been 
even that amount of known connexion between B and A. 

Now an error, or fallacy, of analogy may occur in two ways. Some- 
times it consists in employing an argument of either of the above kinds 
with correctness indeed, but overrating its probative force. This very 
common aberration is sometimes supposed to be particularly incident 
to persons distinguished fo,r their imagination ; but in reality it is the 
characteristic intellectual vice of those whose imaginations are barren, 
either from want of exercise, natural defect, or the narrowness of their 
range of ideas. To such minds, objects present themselves clothed in 
but few properties ; and as, therefore, few analogies betv/een one ob- 
ject and another occur to them, they almost invariably overrate the 
degi'ee of importance of those few : while one whose fancy takes a 
wider range, perceives and remembers so many analogies tending to 
conflicting conclusions, that he is not so likely to lay undue stress upon 
any of them. We always find that those are the greatest slaves to 
metaphorical language who have but one set of metaphors. 

But this is only one of the modes of error in the employment of 
arguments of analogy. There is another, more properly deserving the 
name of fallacy; namely, when resemblance in one point is inferred 
from resemblance in another point, although there is not only no 
evidence to connect the two circumstances by way of causation, but 
the evidence tends positively to disconnect them. This is properly the 
Fallacy of False Analogies. 



FALLACIES OF GENERALIZATION. 493 

As a first instance, we may cite that favorite argument in defence 
of absolute power, drawn from the analogy of paternal government in 
a family, which government is not, and by universal admission ought 
not to be, controlled hy (though it sometimes ought to be controlled 

for) the children. Paternal government, in a family, works well; 
therefore, says the argument, despotic government in a state will work 
well : implying that the beneficial working of parental government 
depends, in the family, upon the only point which it has in common 
with political despotism, namely, irresponsibility. Whereas it does not 
depend upon that, but upon two other attributes of parental govern- 
ment, the aftection of the parent for the children, and the superiority of 
the parent in wisdom and experience ; neither of which properties can 
be reckoned upon, or are at all likely to exist, between a political 
despot and his subjects ; and when either of these circumstances fails, 
even in the family, and the influence of the irresponsibility is allowed 
to work uncorrected, the result is anything but good government. 
This, therefore, is a false analogy. 

Another example is the not uncommon dictum, that bodies politic 
have youth, maturity, old age, and death, like bodies natural : that 
after a certain duration of prosperity, they tend spontaneously to decay. 
This also is a false analogy, because the decay of the vital powers in 
an animated body can be distinctly traced to the natural progress of 
those very changes of structure which, in their earlier stages, constitute 
its growth to maturity; while in the body politic the progress of those 
changes cannot, generally speaking, have any effect but the still further 
continuance of growth : it is the stoppage of that progress, and the 
commencement of retrogression, that alone would constitute decay. 
Bodies politic die, but it is of disease, or violent death : they have no 
old age. 

The following sentence from Hooker's Ecclesiastical Polity is an 
instance of a false analogy from physical bodies to what are called 
bodies politic. "As there could be in natural bodies no motion of any- 
thing unless there were some which moveth all things, and continueth 
immovable ; even so in politic societies there must be some unpunish- 
able, or else no man shall suffer punishment," There is a double 
fallacy here, for not only the analogy, but the premise from which it is 
drawn, is untenable. The notion that there must be something im- 

, movable which moves all others, is the old scholastic error of a j^rijiium 
mobile. 

Some of the false analogies upon which systems of physics were 
confidently. gi'ounded in the time of the Greek philosophers, are such 
as we now call fanciful; not that the resemblances are not often real, 
but that it is long since any one has been inclined to draw from them 
the inferences which were then drawn. Such, for instance, are the 
curious speculations of the Pythagoreans on the subject of numbers. 
Finding that the distances of the planets bore or seemed to bear to one 
another a proportion not varying much from that of the divisions of the 
monochord, they inferred from it the existence of an inaudible music, 
that of the spheres ; as if the music of a harp had depended solely on 
the numerical proportions, and not on the material, nor even on the ex- 
istence of any material, any strings at all. It has been similarly ima- 
gined that certain combinations of numbers, which were found to pre- 
vail in some natural phenomena, must run through the whole of nature : 



494 FALLACIES. 

as that there must be four elements, because there are four possible 
combinations of hot and cold, wet and dry: that there must be seven 
planets, because there were seven metals, and even because there were 
seven days of the week. Kepler himself thought that there could be 
only six planets because there were c>nly five regular solids. With these 
we may class the reasonings, so common in the speculations of the 
ancients, founded upon a supposed perfection in nature ; meaning by 
nature the customary order of events as they take place of themselves 
without human interference. This also is a rude guess at an analogy 
supposed to pervade all phenomena, however dissimilar. Since what 
was thought to be perfection appeared to obtain in some phenomena, 
it was inferred to obtain in all. " We always suppose that which is 
better to take place in nature, if it be possible," says Aristotle : and 
the vaguest and most heterogeneous qualities being confounded to- 
gether under the notion of being better, there was no limit to the wild- 
ness of the inferences. Thus, because the heavenly bodies were " per- 
fect," they must move in circles, and uniformly. For *' they" (the 
Pythagoreans) "would not allow," says Geminus,* *' of any such disor- 
der among divine and eternal things, as that they should sometimes 
move quicker and sometimes slower, and sometimes stand still ; for no 
one would tolerate such anomaly in the movements even of a man 
who was decent and orderly. The occasions of life, however, are 
often reasons for men going quicker or slower, but in the incorrupt- 
ible nature of the stars, it is not possible that any cause can be alleged 
of quickness or slowness." It is seeking an argument of analogy very 
far to suppose that the stars must observe the rules of decorum in gait 
and carriage, prescribed for themselves by the long-bearded philos- 
ophers satirized by Lucian. 

As late as the Copernican controversy it was urged as an argument 
in favor of the true theory of the solar system, that " it placed the fire, 
the noblest element, in the centre of the universe."! This was a rem- 
nant of the notion that the order of nature must be perfect, and that 
perfection consisted in conformity to rules of precedency in, dignity, 
either real or conventional. Again, reverting to numbers : certain 
numbers were _^?er/ec^, therefore those numbers must obtain in the 
great phenomena of nature. Six was a perfect number, that is, equal 
to the sum of all its factors ; an additional reason why there must be 
exactly six planets. The Pythagoreans, on the other hand, attributed 
perfection to the number ten ; but agreed in thinking that the perfect 
number must be somehow realized in the heavens ; and knowing only 
of nine heavenly bodies to make up the enumeration, they asserted 
" that there was an anticlitlion or counter-earth, on the other side of the 
sun, invisible to us. "J Even Huygens was persuaded that when the 
number of the heavenly bodies had reached twelve, it could not admit 
of any further increase. Creative power could not go beyond that 
sacred number. 

Some curious instances of false analogy are to be found in the argu- 
ments of the Stoics to prove the equality of all crimes, and the equal 
wretchedness of all who had not realized their idea of perfect virtue. 
Cicero, towards the end of his Fourth Book J)e Finibus, states some 

* I quote from Mr. Whewell's Hist, of the Ind. Sc, i. 165. 
t Ibid., i., 365. t Ibid., 70. 



FALLACIES OF GENERALIZATION. 495 

of these as follows. *' Ut, inquit, in fidibus plurimis, si nulla earum ita 
contenta numeris sit, ut concentum servare possit, omnes asque incon- 
tentae sint ; sic peccata, quia discrepant, aeque discrepant : paria sunt 
igitur." To which Cicero himself aptly answers, " aeque contingit om- 
nibus fidibus, ut incontentas sint; illud non continuo, ut Eeque incon- 
tentcG." The Stoic resumes: " Ut enim, inquit, gubernator seque 
peccat, si palearum navem evertit, et si auri ; item aeque peccat qui 
parentem, et qui servum, injuria verberat ;" assuming, that because 
the magnitude of the interest at stake makes no difference in the mere 
defect of skill, it can make none in the moral defect : a false analogy. 
Again, " Q,uis ignorat, si plur'es ex alto emergere velint, propius fore eos 
quidem ad respirandum, qui ad summam jam aquam aj)propinquant, 
sed nihilo magis respirare posse, quam eos, qui sunt in profundo ] 
Nihil ergo adjuvat procedere, et progredi in virtute, quominus miserri- 
mus sit, antequam ad earn pervenerit, quoniam in aqua nihil adjuvat : 
et quoniam Catuli, qui jam despecturi sunt, c£eci aeque, et ii qui mode 
nati ; Platonem quoque necesse est, quoniam nondum videbat sapien- 
tiam, aeque caecum animo, ac Phalarim fuisse." Cicero, in his own 
person, combats these false analogies by other analogies tending to 
an opposite conclusion. " Ista similia non sunt, Cato : . . . . Ilia sunt 
similia ; hebes acies est cuipiam oculorum : corpore alius languescit : 
hi curatione adhibita levaptur in dies : alter valet plus quotidie : alter 
videt. Hi similes sunt omnibus, qui virtuti student ; levantur vitiis, 
levantur eiToribus." 

§ 7. In these and all other arguments drawn fi'om remote analogies, 
and from metaphors, which are cases of analogy, it is apparent (espe- 
cially when we consider the extreme facility of raising up contrary anal- 
ogies and conflicting metaphors), that so far from the metaphor or 
analogy proving anything, the applicability of the metaphor is the very 
thing to be made out. It has to be shown that iii the two cases asserted 
to be analogous, the same law is really operating ; that between the 
known resemblance and the inferred one there is some connexion by 
means of causation. Cicero and Cato might have bandied ojjposite 
analogies forever : it rested with each of them to prove by just induc- 
tion, or at least to render probable, that the case resembled the one set , 
of analogous cases and not the other, in the circumstances upon which 
the disputed question really hinged. Metaphors, for the most part, 
therefore, assume the proposition which they are brought to prove : 
their use is, to aid the apprehension of it ; to make clearly and vividly 
comprehended what it is that the person who employs the metaphor is 
proposing to make out; and sometimes also, by what media he proposes 
to do so. For an apt metaphor, though it cannot prove, often suggests 
the proof. 

For instance, when Mr. Carlyle, rebuking the Byronic vein, says 
that " strength does not manifest itself in spasms, but in stout bearing 
of burdens;" the metaphor proves nothing, it is no argument, only an 
allusion to an argument ; in no other way however could so much of 
argument be sb completely suggested in so few words. In fact, this 
admirable expression suggests a whole train of reasoning, which it 
would take many sentences to w^rite out at length. As thus : Motions 
which are violent but brief, which lead to.no end, and are not under 
the conti'ol of the will, are, in the physical body, more incident to a 



496 ' FALLACIES. 

weak than to a strong constitution. If this be owing to a cause which 
equally operates in what relates to the mind, the same conclusion will 
hold there likewise. But such is really the fact. For the body's 
liability to these sudden and uncontrollable motions arises from irrita- 
bility, that is, unusual susceptibility of being moved out of its ordinary 
course by transient influences : which may equally be said of the mind. 
And this susceptibility, whether of mind or body, must arise from a 
weakness of the forces which maintain and carry on the ordinary ac- 
tion of the system. All this is conveyed in Mr. Carlyle's short sen- 
tence. And since the causes are alike in the body and in the mind, the 
analogy is a just one, and the maxim holds of the one as much as of 
the other. 

Thus we see that the metaphor, although no proof but a statement 
of the thing to be proved, states it in terms which, by suggesting a 
parallel case, put the mind upon the track of the real proof The 
hearer says, " Strength does not manifest itself in spasms — very true ; 
and for what reason 1" Then in discovering the reason, he finds it pre- 
cisely as applicable to the mind as it is to the body. This mode, there- 
fore, of conveying an argument, independently of its rhetorical advan- 
tages, has a logical value ; since it not only suggests the grounds of 
the conclusion, but points out another case in which those grounds 
have been found, or at least deemed to be, sufficient. 

On the other hand, when Bacon, who is equally conspicuous in the 
use and abuse of figurative illustration, says that the stream of time 
has brought down to us only the least valuable part of the writings of 
the ancients, as a river carries froth and straws floating on its surface, 
while more weighty objects sink to the bottom; this, even if the asser- 
tion illustrated by it were true, would be no good illustration, there 
being no parity of cause. The levity by vvhich substances float on a 
stream, and the levity which is synonymous with worthlessness, have 
nothing in common except the name ; and (to show how little value 
there is in the metaphor) we need only change the word into buoyancy, 
to turn the semblance of argument involved in Bacon's illustration 
directly against himself 

A -metaphor, then, is not to be considered as an argument, but as 
an assertion that an argument exists ; that a parity subsists between 
the case from which the metaphor is drawn and that to which it is 
applied. This parity may exist though the two cases be apparently 
very remote from one another: the only resemblance existing between 
them may be a resemblance of relations, an analogy in Ferguson's and 
Archbishop Whately's sense. As in the instance quoted from Mr. 
Carlyle: there is no resemblance between convulsions of the body and 
fits of passion in the mind, considered in themselves; the resemblance 
is' between the relation which convulsions of the body bear to its ordi- 
nary motions, and that which fits of passion in the mind bear to its 
steadier feelings. Thus, where the real difference between the two 
cases is the widest; where the metaphor seems the most far-fetched, 
the analogy the most remote ; and where, consequently, a limited and 
literal understanding would be most, apt to shut itself up within its 
intrenchment of prose, and refuse admittance to the metaphor, under 
an idea that cases so very unlike can throw no light upon each other; 
it is often in those very cases that the argument which the metaphor 
involves and suggests is the most conclusive. 



FALLACIES OF GENERALIZATION. 497 

§ 8. To terminate the subject of Fallacies of Generalization, it re- 
mains to be said, that the most fertile source of them is bad classifica- 
tion; bringing together in one group, and under one name, things 
which have no common properties, or none but such as are too unim- 
portant to allow general propositions of any considerable value to be 
made respecting the class. The misleading effect is greatest, when a 
word which in common use expresses some definite fact, is extended 
by slight links of connexion to cases in which that fact does not exist, 
but some other or others only slightly resembling it. Thus Bacon,* 
in speaking of the Idola or Fallacies arising from notions temere et 
incBqualiter a. rebus abstractce, exemplifies them by the notion of Humi- 
dum or Wet, so familiar in the physics of antiquity and of the middle 
ages. " Invenietur verbum istud, Humidum, nihil aliud quam nota 
confusa diversarum actionum, quae nullam constantiam aut reductionem 
patiuntur. Significat enim, et quod circa aliud corpus facile se cir- 
cumfundit ; et quod in se est indeterminabile, nee consistere potest; 
et quod facile cedit undique ; et quod facile se dividit et dispergit ; et 
quod facile se unit et colligit ; et quod facile fluit, et in motu ponitur ; 
et quod alteri corpori facile adhaeret, idque madefacit ; et quod facile 
reducitur in liquidum, sive coUiquatur, cum antea consisteret. Itaque 
quum ad hujus nominis praedicationem et impositionem ventum sit ; 
si alia accipias, flamma humida est ; si alia accipias, aer humidus non 
est ; si alia, pulvis minutus humidus est ; si alia, vitrum humidum est : 
ut facile appareat, istam notionem ex aqua tantum, et communibus et 
vulgaribus liquoribus, absque ulla debita verificatione, temere abstrac- 
tam esse." 

Bacon himself is not exempt from a similar accusation when inquir- 
ing into the nature of heat ; where he occasionally proceeds like one 
who, seeking for the cause of hardness, after examining that quality in 
iron, flint, and diamond, should expect to find that it is something 
which can be traced also in hard water, a hard knot, and a hard 
heart. 

The word Ktv-quLg in the Greek philosophy, and the words Genera- 
tion and Corruption both then and long afterwards, denoted such a 
multitude of heterogeneous phenomena, that any attempt at philo- 
sophizing in which those words were used was almost as necessarily 
abortive as if the word Jiard had been taken to denote a class including 
all the things mentioned above. KivrjOLg, for instance, which properly 
signified motion, was taken to denote not only all emotion but even all 
change : dXXoLCJOLg being recognized as one of the modes of KLvrjacg. 
The effect was, to connect with every form of d?^,XoiG)aLg or change, 
ideas drawn from motion in the proper and literal sense, and which 
had no real connexion with any other kind of nivrjOK; than that. Aris- 
totle and Plato labored under a continual embarrassment from this 
misuse of terms. But if we proceed further in this direction we shall 
encroach upon the Fallacy of Ambiguity, which belongs to a different 
class, the last in order of our classification, Fallacies of Confusion. 

* Nov. Org., Aph. 60. 



311 



498 FALLACIES. 



CHAPTER VI. 

FALLACIES OF RATIOCINATION. 



§ 1. We have now, in our progi^ess through the classes of Fallacies, 
arrived at those to which, in the common books of logic, the appellation 
is in general exclusively appropriated; those which have their seat in 
the ratiocinative or deductive part of the investigation of truth. On 
these fallacies it is- the less necessary for us to insist at any length, as 
they have been so admirably treated in a work familiar to almost all, 
in this country at least, who feel any interest in these speculations, 
Archbishop Whately's Logic. Against the more obvious forms of this 
class of fallacies, the rules of the syllogism are a complete protection. 
Not (as we have so often said) that the ratiocination cannot be good, 
unless it be in the form of a syllogism ; but that, by showing it in that 
form, we are sure to discover if it be bad, or at least if it contain any 
fallacy of this class. 

§ 2. Among Fallacies of Ratiocination we ought, perhaps, to include 
the errors committed in processes which have the appearance only, not 
the reality, of an inference from premisses ; the fallacies connected with 
the conversion and gequipollency of propositions. I believe errors of 
this description to be far more frequently committed than is generally 
supposed, or than their extreme obviousness might seem to admit of. 
For example, the simple conversion of an universal affirmative propo- 
sition, All A are B therefore all B are A, I take to be a very common 
form of error: though committed, like many other fallacies, oftener in 
the silence of thought than in express words, for it can scarcely be 
clearly enunciated without being detected. And so with another form 
of fallacy, not substantially different from the preceding ; the erroneous 
conversion of an hypothetical proposition. The proper converse of an 
hypothetical proposition is this : If the consequent be false, the ante- 
cedent is false ; but this, If the consequent be true, the antecedent is 
true, by no means holds good, but is an error corresponding to the 
simple conversion of an universal affirmative. Yet hardly anything is 
more common than for people, in their private thoughts, to draw this 
inference. As when the conclusion is accepted, which it so often is, 
for proof of the premisses. That the premisses cannot be true if the 
conclusion is false, is the unexceptionable foundation of the legitimate 
mode of reasoning called a reductio ad absurdum. But men continu- 
ally think and express themselves as if they also believed that the 
premisses cannot be false if the conclusion is true. The truth, or sup- 
posed truth, of the inferences which follow from a doctrine, often ena- 
bles it to find acceptance in spite of gross absurdities in it. How many 
systems of philosophy, which had scarcely any intrinsic recommenda- 
tion, have been received by thoughtful men because they were sup- 
posed to lend additional support to religion, morality, some favorite 
view of politics, or some other cherished persuasion % not merely be- 
cause their wishes were thereby enlisted on its side, but because its 
leading to what they deemed sound conclusions appeared to them a 
Btrong presumption in favor of its truth : though the presumption, when 
viewed in its true light, amounted only to the absence of that particular 



FALLACIES OF RATIOCINATION. 499 

kind of evidence of falsehood, which would have resulted from its lead- 
ing by correct inference to something already recognized as false. 

Again, the very frequent error in conduct, of mistaking reverse of 
wrong for right, is the practical form of a logical error with respect to 
the Opposition of Propositions. It is committed for want of the habit 
of distinguishing the contrary of a proposition from the contradictory 
of it, and of attending to the logical canon, that contrary propositions, 
though they cannot both be true, may both be false. If the error 
were to express itself in words it would run distinctly counter to this 
canon. It generally, however, does not so express itself, and to com- 
pel it to do so is the most effectual method of detecting and exposing it. 

§ 3. Among Fallacies of Ratiocination are to be ranked, in the first 
place, all the cases of vicious syllogism laid down in the books. These 
generally resolve themselves into having more than three terms to the 
syllogism, either avowedly, or in the covert mode of an undisti^ibuted 
middle term or an illicit process of one of the two extremes. It is 
not, indeed, very easy fully to convict an argument of falling under 
any one of these vicious cases in particular; for the reason already 
quoted from Archbishop Whately, that the premisses are seldom for- 
mally set out : if they were, the fallacy would impose upon nobody ; 
and while they are not, it is almost always to a certain degree optional 
in what manner the suppressed link shall be filled up. The rules of 
the syllogism are rules for compelling a person to be aware of the 
whole of what he must undertake to defend if he persists in maintain- 
ing his conclusion. He has it almost always in his power to make his 
syllogism good by introducing a false premiss ; and hence it is scarcely 
ever possible decidedly to affirm that any argument involves a bad 
syllogism : but this detracts nothing fi-om the value of the syllogistic 
rules, since it is by them that a reasoner is compelled distinctly to make 
his election what premisses he is prepared to maintain. The election 
made, there is generally so little difficulty in seeing whether the con- 
clusion follows from the premisses set out, that we might without much 
logical impropriety have merged this fourth class of fallacies in the 
fifth, or Fallacies of Confusion. 

§ 4. Perhaps, however, the commonest, and certainly the most dan- 
gerous fallacies of this class, are those which do not lie in a single 
syllogism, but slip in between one syllogism and another in a chain of 
argument, and are committed by changing the premisses. A proposi- 
tion is proved, or an acknowledged truth laid down, in the first part of 
an argumentation, and in the second a further argument is founded not 
upon the same proposition, but upon some other, resembling it suffi- 
ciently to be mistaken for it. Instances of this fallacy will be found 
in almost all the argumentative discourses of unprecise thinkei-s ; and 
we need only here advert to one of the obscurer forms of it, recognized 
by the schoolmen as the fallacy a clicto secundum quid ad dictuvi sim- 
pliciter. This is committed when, in the premisses, a proposition is 
asserted with a qualification, and the qualification lost sight of in the 
conclusion ; or oftener, when a limitation or condition, though not as- 
serted, is necessary to the ti'uth of the proposition, but is forgotten 
when that proposition comes to be employed as a premiss. Many of 
the bad arguments in vogue belong to this class of eiTor. The premiss 



500 FALLACIES. 

is some admitted truth, some common maxim, the reasons or evidence 
for which have been forgotten, or are not thought of at the time, but 
if they had been thought of would have shown the necessity of so 
limiting the premiss, that it would no longer have supported the con- 
clusion drawn from it. 

Of this nature is the fallacy in what is called, by Adam Smith and 
others, the Mercantile Theory in Political Economy. That theory sets 
out from the common maxim, that whatever brings in money enriches ; 
or that every one is rich in proportion to the quantity of money he 
obtains. From this it is concluded that the value of any branch of 
trade, or of the trade of the country altogether, consists in the balance 
of money it brings in ; that any trade which carries more money out 
of the country than it draws into it is a losing trade ; that therefore 
money should be attracted into the country, and kept there, by pro- 
hibitions and bounties ; and a train of similar corollaries. All for want 
of reflecting that if the riches of an individual are in proportion to the 
quantity of money he can command, it is because that is the measure 
of his power of purchasing money's worth ; and is therefore subject 
to the proviso that he is not debarred from employing his money in 
such purchases. The premiss, therefore, is only true secundum quid; 
but the theory assumes it to be true absolutely, and infers that increase 
of money is increase of riches, even when produced by means subver- 
sive of the condition under which alone money is riches. 

A second instance is, the argument by which it used to be contended, 
before the commutation of tithe, that tithes fell upon the landlord, and 
were a deduction from rent ; because the rent of tithe-free land was 
always higher than that of land of the same quality and the same ad- 
vantages of situation, subject to tithe. Whether it be true that a tithe 
falls on rent or no, a treatise on Logic is not the place to examine : 
but it is certain that this is no proof of it. Whether the proposition 
be true or false, tithe-free land must, by the necessity of the case, pay 
a higher rent. For if tithes do not fall on rent, it must be because 
they fall on the consumer ; because they raise the price of corn. But 
if corn be raised in price, the farmer of tithe-free as well as the farmer 
of tithed land gets the benefit. To the latter the rise is but a com- 
pensation for the tithe he pays ; to the first, who pays none, it is clear 
gain, and therefore enables him, and if there be freedom of competi- 
tion forces him, to pay so much the more rent to his landlord. This 
is the refutation of the fallacy. The question remains, to what class 
of fallacies it belongs. The premiss is, that the owner of tithed land 
receives less rent than the owner of tithe-free land ; the conclusion is, 
that therefore he receives less than he himself would receive if tithe 
were abolished. But the premiss is only true conditionally; the owner 
of tithed land receives less than what the owner of tithe-free land is 
enabled to receive wJien other lands are tithed; while the conclusion 
is applied to a state of circumstances in which that condition fails, and 
in which, by consequence, the premiss would not be true. The fallacy, 
therefore, is a dicto secundum quid ad dictum simpliciter. 

A third example is the opposition sometimes made to legitimate in- 
terferences of government in the economical affairs of society, grounded 
upon a misapplication of the maxim, that an individual is a better 
judge than the government of what is for his own pecuniary interest. 
This objection was urged to Mr. Wakefield's system of colonization, 



FALLACIES OF RATIOCINATION. 501 

one of the greatest practical improvements in public affairs which have 
been made in our time. Mr. Wakefield's principle, as most people 
are now aware, is the artificial concentration of the settlers, by fixing 
such a price upon imoccupied land as may preserve the most desirable 
proportion between the quantity of land in culture, and the laboring 
population. Against this it was argued, that if individuals found it for 
their advantage to occupy extensive tracts of land, they, being better 
judges of their own interest than the legislature (which can only pro- 
ceed on general rules), ought not to be restrained from doing so. But 
in this argument it was forgotten that the fact of a man's taking a large 
tract of land is evidence only that it is his interest to take as much as 
other people, but not that it might not be for his interest to content 
himself with less, if he could be assured that other people would do 
so too ; an assurance which nothing but a government regulation can 
give. If all other people took much, and he only a little, he would 
reap none of the advantages derived from the concentration of the 
population and the consequent possibility of procuring labor for hire, 
but would have placed himself, without equivalent, in a situation of 
voluntary inferiority. The proposition, therefore, that the quantity of 
land which people will take when left to themselves is that which it 
is most for their interest to take, is true only secundum quid: it is only 
their interest while they have no guarantee for the conduct of one 
another. Bat the argument disregards the limitation, and takes the 
proposition for true simpliciter. 

One of the conditions oftenest dropped, when w^hat would otherwise 
be a true proposition is employed as a premiss for proving others, is 
the condition of tiine. It is a principle of political economy that prices, 
profits, wages, &c. "always find their level;" but this is often inter- 
preted as if it meant that they are always, or generally, at their level ; 
while the truth is, as Coleridge epigrammatically expresses it, that 
they are B\wn.js jiiiding their level, "which might be taken as a para- 
phrase or ironical definition of a storm." 

Under the same head of fallacy [a dicta secundum quid ad dictum 
simpliciter) might be placed all the errors which are vulgarly called 
misapplications of abstract truths : that is, where a principle, true (as 
the common expression is) in the abstract, that is, all modifying causes 
being supposed absent, is reasoned upon as if it were true absolutely, 
and no modifying circumstances could ever by possibility exist. This 
very common form of error it is not requisite that we should exemplify 
here, as it will be particularly treated of hereafter in its application to 
the subjects on which it is most frequent and most fatal, those of poli- 
tics and society. 



602 FALLACIES. 



CHAPTER VII. 

FALLACIES OF CONFUSION. 



§ 1. Under this fifth and last class we find it convenient to arrange 
all those fallacies, in which the source of error is not so much a false 
estimate of the probative force of known evidence, as an indistinct, in- 
definite, and fluctuating conception of what the evidence is. 

At the head of these stands that multitudinous body of fallacious 
reasonings in which the source of error is the ambiguity of terms : when 
something which is true if a word be used in a particular sense, is rea- 
soned upon as if it were true in another sense. In such a case there 
is not a mal-estimation of evidence, because there is not properly any 
evidence to the point at all ; there is evidence, but to a different point, 
which, from a confused apprehension of the' meaning of the terms used, 
is supposed to be the same. This error will naturally be oftener com- 
mitted in our ratiocinations than in our direct inductions, because in 
the former vy^e are deciphering our own or other people's notes, while 
in the latter we have the things themselves present, either to our senses 
or to our memory. Except, indeed, when the induction is not from 
individual cases to a generality, but from generalities to a still higher 
generalization ; in that case the fallacy of ambiguity may affect the in- 
ductive process as well as the ratiocinative. It occurs in ratiocination 
in two ways : when the middle term is ambiguous, or when one of the 
terms of the syllogism is taken in one sense in the premisses, and in 
another sense in the conclusion. 

Some good exemplifications of this fallacy are given by Archbishop 
Whately. " One case," says he, " which may be regarded as coming 
under the head of Ambiguous Middle, is what is called Fallacia 
FigurcB Dictionis, the fallacy built on the grammatical structure of 
language, from men's usually taking for granted that paronymous 
words [i. e. those belonging to each other, as the substantive, adjec- 
tive, verb, &c., of the same root) have a precisely correspondent 
meaning, which is by no means universally the case. Such a fallacy 
could not indeed be even exhibited in strict logical form, which would 
preclude even the attempt at it, since it has two middle terms in sound 
as well as sense ; but nothing is more common in practice than to vary 
continually the terms employed, with a view to grammatical conve- 
nience ; nor is there anything unfair in such a practice, as long as the 
meaning is preserved unaltered ;€.§.' murder should be punished 
with death; this man is a murderer, therefore he deserves to die,' &c. 
Here we proceed on the assumption (in this case just) that to commit 
murder, and to be a murderer, to deserve death, and to be one who 
ought to die, are, respectively, equivalent expressions ; and it would 
frequently prove a heavy inconvenience to be debarred this kind of 
liberty; but the abuse of it gives rise to the Fallacy in question : e.g. 
projectors are unfit to be trusted ; this man has formed a project, there- 
fore he is unfit to be trusted : here the sophist proceeds on the 
hypothesis that he who forms a project must be a projector: whereas 
the bad sense that commonly attaches to the latter word, is not at all 
implied in the former. This fallacy may often be considered as lying 



FALLACIES OF CONFUSION. 503 

not in the middle, but in one of the terms of the conclusion ; so that 
the conclusion drawn shall not be, in reality, at all warranted by the 
premisses, though it will appear to be so, by means of the grammatical 
affinity of the words ; e. g. to be acquainted with the guilty is a jpre- 
sumption of guilt; this man is so acquainted, therefore we m^j presume 
that he is guilty: this argument proceeds on the supposition of an 
exact coiTespondence between presume and presum2)tion, which, how- 
ever, does not really exist; for 'presumption' is commonly used to 
express a kind of slight suspicion; whereas 'to presume' amounts to 
absolute belief There are innumerable instances of a non-corres- 
pondence in paronymous words, similar to that above instanced; as 
between art and artful, design ^ud^ designing, faith lAXni faithful, &c., 
and the more slight the variation of meaning, the more likely is the 
fallacy to be successful ; for when the words have become so widely 
removed in sense as ' pity' and ' pitiful,' every one would perceive 
such a fallacy, nor could it be employed but in jest.* 

" The present Fallacy," continues the Archbishop, " is nearly allied 
to, or rather, perhaps, may be regarded as a branch of, that founded 
on etymology ; viz., when a term is used, at one time in its customary, 
and at another in its etymological sense. Perhaps no example of 
this can be found that is more extensively and mischievously employed 
than in the case of the word representative: assuming that its right 
meaning must correspond exactly with the strict and original sense of 
the verb ' represent,' the-sophist persuades the multitude, that a member 
of the House of Commons is bound to be guided in all points by the 
opinion of his constituents ; and, in short, to be merely their spokes- 
man: whereas law and custom, which in this case may be considered 
as fixing the meaning of the term, require no such thing, but enjoin the 
representative to act according to the best of his own judgment, and on 
his own responsibility." 

The following are instances, of great practical importance, in which 
arguments are habitually founded upon a verbal ambiguity. 

The mercantile public are frequently led into this fallacy by the 
phrase " scarcity of money." In the language of commerce "money" 
has two meanings : currency, or the circulating medium ; and capital 
seeking investment, especially investment on loan. In this last sense 
the word is used when the "money market" is spoken of, and when 
the " value of money" is said to be high or low, the rate of interest 
being meant. The consequence of this ambiguity is, that as soon as 
scarcity of money in the latter of these senses begins to be felt, as 
soon as there is difficulty of obtaining loans, and the rate of interest is 
high, it is concluded that this must arise from causes acting upon the 
quantity of money in the other and more popular sense ; that the 
circulating medium must have diminished in quantity, or ought to be 
increased. I am aware that, independently of the double meaning of 
the tenn, there are in the facts themselves some peculiarities, giving an 
apparent support to this error ; but the ambiguity of the language 

* An example of this fallacy is the popular error that strong drink must be a cause of 
strength. There is here fallacy within fallacy; for granting that the words " strong" and 
" strength" were not (as they are) applied in a totally different sense to fermented liquors 
and to the human body, there would still be involved the error of supposing that an effect 
must be like its cause ; that the conditions of a phenomenon are likely to resemble the 
phenomenon itself ; which we have already treated of as an a priori fallacy of the first 
rank. 



504 FALLACIES. 

Stands upon the very threshold of the subject, and intercepts all at- 
tempts to throw light upon it. 

Another ambiguous expression which continually meets us in the 
political controversies of the present time, especially in those which 
relate to organic changes, is the phrase "influence of property;" 
which is sometimes used for the influence of respect for superior in- 
telligence, or gratitude for the kind offices which persons of large 
property have it so much in their power to bestow ; at other times for 
thf! influence of fear ; fear of the worse sort of power, which large 
property also gives to its possessor, the power of doing mischief to 
dependents. To confound these two, is the standing fallacy of ambi- 
guity brought against those who seek to purify our electoral system 
from corruption and intimidation. ** The influence of property is 
beneficial :" granted, if the former species of influence and that alone 
be meant; but conclusions are thence drawn in condemnation of 
expedients which (like secret voting, for example) would deprive 
property of some of its influences, though only of the latter and bad 
kind. Persuasive influence, acting through the conscience of the 
voter, and carrying his heart and mind with it, is beneficial — there- 
fore we are to infer that coercive influence, which compels him to 
forget that he is a moral agent, or to act in opposition to his moral 
convictions, ought not to be placed under restraint. 

Another word which is often turned into an instrument of the fallacy 
of ambiguity is Theory. In its most proper acceptation, theory means 
the completed result of philosophical induction from experience. In 
that sense, there are erroneous as well as true theories, for induction 
may be incorrectly performed, but theory of some sort is the necessary 
result of knowing anything of a subject, and having put one's knowl- 
edge into the form of general propositions for the guidance of practice. 
In another and more vulgar sense, theory means any mere fiction of 
the imagination, endeavoring to conceive how a thing may possibly 
have been produced, instead of examining how it was produced. In 
this sense only are theory, and theorists, unsafe guides ; but because 
of this, ridicule or discredit is attempted to be attached to theory in its 
proper sense, that is, to legitimate generalization, the end and aim of 
all philosophy; and a conclusion is represented as worthless, just 
because that has been done, which if done correctly constitutes the 
highest worth that a principle for the guidance of practice can possess, 
namely, to comprehend in a few words the real law on which a phe- 
nomenon depends, or some property or relation which is universally 
true of it. 

" The Church" is sometimes understood to mean the clergy alone, 
sometimes the whole body of believers, or at least of communicants. 
The declamations respecting the inviolability of church property are 
indebted for the greater part of their apparent force to this ambiguity. 
The clergy, being called the church, are supposed to be the real owners 
of what is called church property; whereas they are in truth only the 
managing membei's of a much larger body of proprietors, and enjoy 
on their own part a mere usufinct, not extending beyond a life interest. 

The following is a favorite argument of Plato. No one desires evil, 
knowing it to be so : to do wrong is evil ; therefore no one desires to 
do wi'ong knowing that which he desires, but only in consequence of 
ignorance. In this syllogism the ambiguous word is the middle term. 



FALLACIES OF CONFUSION. 505 

Evil, the double meaning of which is too obvious to need explanation : 
yet on this foundation Plato constructs his principal ethical doctrine, 
in which he was followed by most of the philosophical sects among 
the later Greeks ; that virtue is a branch of intelligence, and is to be 
produced, therefore, mainly by intellectual cultivation. All the inquiries 
into the summum bonum in the philosophical schools were infected with 
the same fallacy ; the ambiguous word being, as before. Evil, or its 
contrary correlative. Good, which sometimes meant what is good for 
oneself, at other times what is good for other people. That nothing 
which is a cause of evil on the whole to other people, can be really 
good for the agent himself, is indeed a possible tenet, and always a 
favorite one with moralists, although in the present age the question 
has rather been, not whether the proposition is true, but how society 
and education can be so ordered as to make it true. At all events, it 
is not proved merely by the fact that a thing beneficial to the world, 
and a thing beneficial to a person himself, are both in common parlance 
called good. That is no valid argument, but a fallacy of ambiguity. 

Of such stuff, however, were the ethical speculations of the ancients 
principally composed, especially in the declining period of the Greek 
philosophic mind. The following is a stoical argument taken from 
Cicero De Finibus, book the third : " Quod est bonum, omne laudabile 
est. Quod autem laudabile est, omne honestum est. Bonum igitur 
quod est, honestum est." Here the ambiguous word is laudabile, 
which in the minor premiss means anything which mankind are accus- 
tomed, on good grounds, to admire or value; as beauty, for instance, 
or good fortune : but in the major, it denotes exclusively moral qualities. 
In much the same manner the Stoics were led to all their absurdest 
paradoxes ; as that the virtuous man is alone free, alone beautiful, 
alone a king, &c. Whoever has virtue has Good (because it has been 
previously determined not to call anything else good) ; but again, Good 
necessarily includes freedom, beauty, and even royalty, all of these 
being good things ; therefore whoever has virtue has all these. 

The following is an argument of Descartes to prove, in his d priori 
manner, the being of God. The conception, says he, of an infinite 
Being proves the real existence of such a being. For if there is not 
really any such being, / must have made the conception ; but if I 
could make it, I can also unmake it; which evidently is not true; 
therefore, there must be externally to myself, an archetype, from which 
the conception was derived. The ambiguity in this case is in the pro- 
noun I, by which, in one place, is to be understood my will, in another 
the laws of my nature. If the conception, existing as it does in my 
mind, had no original without, the conclusion would unquestionably 
follow that /made it : that is, the laws of my nature must have spon- 
taneously evolved it; but that my will made it, would not follow. 
Now w^hen Descartes afterwards adds that I cannot unmake the con- 
ception, he means that I cannot get rid of it by an act of my will : 
which is true, but is not the proposition required. That what some 
of the laws of my nature have produced, other laws, or those same 
laws in other circumstances, might not subsequently efface, he would 
have found it difficult to establish. 

Analogous to this are some of the ambiguities in the free-will con- 
troversy ; which, as they will come under special consideration in the 
concluding Book, I only mention memorice causd. In that discussion, 
3S 



606 FALLACIES. 

too, the word I is often shifted from one meaning to another, at one 
time standing for my vohtions, at another time for the actions which are 
the consequences of them, or the mental dispositions from which they 
proceed. The latter ambiguity is exemplified in an argument of Cole- 
ridge (in his Aids to Reflection), in support of the freedom of the will. 
It is not true, he says, that man is governed by motives ; ** the man 
makes the motive, not the motive the man;" the proof being that 
*' what is a strong motive to one man is no motive at all to another." 
The premiss is true, but only amounts to this, that different persons 
have different degrees of susceptibility to the same motive ; as they 
have also to the same intoxicating liquid, which however does not prove 
that they are free to be drunk or not drunk, whatever quantity they raay 
drink. What is proved is, that certain mental conditions in the man 
himself, must cooperate, in the production of the act, with the external 
inducement : but those mental conditions also are the effect of causes ; 
and there is nothing in the argument to prove that they can arise with- 
out a cause — that a spontaneous determination of the man's will, with- 
out any cause at all, ever takes place, as the free-will doctrine supposes. 

The double use, in the free-will controversy, of the word Necessity, 
which sometimes stands only for Certainty, at other times for Compul- 
sion ; sometimes for what cannot be prevented, at other times only for 
what we have reason to be assured will not ; has been pointed out 
by Archbishop Whately, and we shall have occasion hereafter to pur- 
sue it to some of its ulterior consequences. 

A most important ambiguity, both in common and in metaphysical 
language, is thus pointed out by Archbishop Whately in the Appendix 
to his Logic: ''■Same (as well as One, Identical, ■and other words de- 
rived from them) is used frequently in a sense very different from its 
primary one, as applicable to a single object ; being employed to de- 
note great similarity. When several objects are undistinguishably 
alike, one single description will apply equally to any of them : and 
thence they are said to be all of one and the same nature, appearance,, 
&c. As, e.g., when we say, ' this house is built of the savie stone with 
such another,' we only mean that the stones are undistinguishable in 
their qualities ; not that the one building was pulled down, and the 
other constructed with the materials. Whereas sameness.^ in the pri- 
mary sense, does not even necessarily imply similarity ; for if we say 
of any man that he is greatly altered since such a time, we understand, 
and indeed imply by the very expression, that he is one person, though 
different in several qualities. It is worth observing also, that Same, in 
the secondary sense, admits, according to popular usage, of degi-ees : 
we speak of two things being nearly the same, but not entirely : per- 
sonal identity does not admit of degrees. Nothing, perhaps, has con- 
tributed more to the error of Realism than inattention to this ambiguity. 
When several persons are said to have one and the same opinion, 
thought, or idea, men, overlooking the true, simple statement of the 
case, which is, that they are all thinking alike, look for something more 
abstruse and mystical, and imagine there must be some One Thing, in 
the primary sense, though not an individual, which is present at once 
in the mind of each of these persons ; and thence readily sprung Plato's 
theory of Ideas, each of which was, according to him, one real, eternal 
object, existing entire and complete in each of the individual objects 
that are known by one name." 



FALLACIES OF CONFUSION. 507 

It is, indeed, not a matter of inference but of authentic history, that 
Plato's doctrine of Ideas, and the AiistoteUan doctrine (essentially the 
same as the Platonic) of substantial forms and second substances, grew 
up in the precise way here pointed out ; from the supposed necessity 
of finding, in things which were said to have the sarne nature, or the 
same qualities, something which was the same in the very sense in which 
a man is the same as himself. All the idle speculations respecting to 
6v, TO ev, TO OfioLOV, and similar abstractions, so common in the ancient 
and in some modern schools of philosophy, sprung from the same 
source. The Aristotelian logicians had, however, seen one case of the 
ambiguity, and provided against it, with their peculiar felicity in the 
invention of technical language, when they distinguished things which 
differed both specie and numero from those which differed numero 
tantum, that is, which were exactly alike (in some particular respect at 
least) but were distinct individuals. An extension of this distinction 
to the two meanings of the word Same, namely, things which are the 
same specie tantum, and a thing which is the same numero as well as 
specie, would have prevented the confusion which has been a source of 
so much darkness and such an abundance of positive error in the higher 
philosophy. 

One of the most singular examples of the lengths to which a philos- 
opher of eminence may be led away by an ambiguity of language, is 
afforded by this very case. I refer to the famous argument by which 
Bishop Berkeley flattered himself that he had for ever put an end to 
" skepticism, atheism, and irreligion." It is briefly as follows. 1 
thought of a thing yesterday ; I ceased to think of it ; I think of it again 
to-day. I had, therefore, in my mind yesterday an idea of the object ; 
I have also an idea of it to-day : this idea is evidently not another, but 
the very same idea. Yet an intervening time elapsed in which I had 
it not. Where was the idea during this interval ] It must have been 
somewhere; it did not cease to exist; otherwise the idea I had yester- 
day could not be the same idea; no more than a man I see alive to-day 
can be the same whom I saw yesterday, if the man has died in the 
meanwhile. Now an idea cannot be conceived to exist anywhere 
except in a mind ; and hence here must exist an Universal Mind, in 
which all ideas have their permanent residence, during the intervals of 
their conscious presence in our own minds. 

That Berkeley here confounded sameness numero with sameness 
specie, that is, with exact resemblance, and assumed the former when 
there was only the latter, hardly needs be more particularly pointed 
out. He could never have broached this sti*ange theory if he had 
understood, that when we say we have the same thought to-day which 
we had yesterday, we do not mean the same individual thought, but a 
thought exactly similar : as we say that we have the same illness which 
we had last year, meaning only the same sort of illness. 

In one remarkable instance the scientific world was divided into two 
fiiriously hostile parties by an ambiguity of language affecting a branch 
of science which, more completely than most others, enjoys the advan- 
tage of a precise and well-defined terminology. I refer to the famous 
dispute respecting the vis viva, the history of which is given at large in 
Professor Playfair's Dissertation. The question was whether theybrce 
of a moving body was proportional (its mass being given) to its velocity 
simply, or to the square of its velocity : and the ambiguity was in the 



508 FALLACIES. 

word Force. " One of the effects," says Playfair, " produced by a 
moving body is proportional to the square of the velocity, while another 
is proportional to the velocity simply :" from whence clearer thinkers 
were subsequently led to establish a double measure of the efficiency 
of a moving power, one being called vis viva, and the other momentum. 
About the facts, both parties were from the first agreed : the only ques- 
tion was, with which of the two effects the term Jbrce should be, or 
could most conveniently be, associated. But the disputants were by 
no means aware that this was all ; they thought that force was one thing, 
the production of effects another : and the question, by which set of 
effects the force which produced both the one and the other should be 
measured, was supposed to be a question not of terminology but of fact. 

The ambiguity of the word Infinite is- the real fallacy in the amusing 
logical puzzle of Achilles and the Tortoise, a puzzle which has been 
too hard for the ingenuity or patience of many philosophers, and among 
others of Dr. Thomas Brown, who considered the sophism as insoluble; 
as a sound argument, though leading to a palpable falsehood: not seeing 
that such an admission would be a reductio ad absurdum of the reason- 
ing faculty itself. The fallacy, as Hobbes hinted, lies in the tacit as- 
sumption that whatever is infinitely divisible is infinite ; but the follow- 
ing solution (to the invention of which I have no claim) is more precise 
and satisfactory. 

The argument is^ let Achilles run ten times as fast as the tortoise, 
yet if the tortoise has the start, Achilles will never overtake him. For 
suppose them to be at first separated by an interval of a thousand feet : 
when Achilles has run these thousand feet, the tortoise will have got 
on a hundred ; when Achilles has run those hundred, the tortoise will 
have run ten, and so on for ever ; therefore Achilles may run for ever 
without overtaking the tortoise. 

Now, the " for ever" in the conclusion, means, for any length of time 
that can be supposed ; but in the premisses " ever" does not mean any 
length of time : it means any number of subdivisions of time. It means 
that we may divide a thousand feet by ten, and that quotient again by 
ten, and so on as often as we please ; that there never needs be an end 
to the subdivisions of the distance, nor consequently to those of the 
time in which it is performed. But an unlimited number of subdivi- 
sions may be made of that which is itself limited. The argument 
proves no other infinity of duration than may be embraced within five 
minutes. As long as the five minutes are not expired, what remains 
of them may be divided by ten, and again by ten, as often as we like, 
which is perfectly compatible with their being only five minutes alto- 
gether. It proves, in short, that to pass through this finite space re- 
quires a time which is infinitely divisible, but not an infinite time ; the 
confounding of which distinction Hobbes had already seen to be the 
gist of the fallacy. 

The following ambiguities of the word right (in .addition to the ob- 
vious and familiar one of a right and the adjective right) are abstracted 
from a forgotten paper of my own, in a periodical work : — 

"Speaking morally, you are said to ha,ve a right to do a thing, if all 
persons are morally bound not to hinder you from doing it. But, in 
another sense, to have a right to do a thing, is the opposite of having 
no right to do it, viz., of being under a moral obligation to forbear 
from doing it. In this sense, to say that you have a right to do a 



FALLACIES OF CONFUSION. 509 

tiling, means that you may do it without any breach of duty on your 
part ; that other persons not only ought not to hinder you, but have no 
cause to think the worse of you for doing it. This is a perfectly dis- 
tinct proposition from the preceding. The right which you have by 
virtue of a duty incumbent upon other persons, is obviously quite a differ- 
ent thing from a right consisting in the absence of any duty incumbent 
upon yourself Yet the two things are perpetually confounded. Thus 
a man will say he has a right to publish his opinions ; which may be 
true in this sense, that it would be a breach of duty in any other per- 
son to interfere and prevent the publication: but he assumes there- 
upon, that in publishing his opinions, he himself violates no duty; 
which may either be true or false, depending, as it does, upon his 
having taken due pains to satisfy himself, first, that the opinions are 
true, and next, that their publication in this manner, and at this par- 
ticular juncture, will probably be beneficial to the interests of truth on 
the whole. 

" The second ambiguity is that of confounding a right of any kind, 
with a right to enforce that right by resisting or punishing a violation 
of it. Men will say, for example, that they have a right to a good 
government, which is undeniably true, it being the moral duty of their 
governors to govern them well. But in granting this, you are sup- 
posed to have admitted their right or liberty to turn out their govern- 
ors, and perhaps to punish them, for having failed in the performance 
of this duty ; which, far from being the same thing, is by no means 
universally true, but depends upon an immense number of varying cir- 
cumstances, and is altogether one of the knottiest questions in practical 
ethics." This example is (like others which have been cited) a case 
of fallacy within fallacy ; it involves not only the second of the two 
ambiguities pointed out, but the first likewise. 

One not unusual form of the Fallacy of Ambiguous Terms, is known 
technically as the Fallacy of Composition and Division: when the 
same term is collective in the premisses, distributive in the conclusion, 
or vice versd,: or when the middle term is collective in one premiss, 
distributive in the other. As if one were to say (I quote from Arch- 
bishop Whately) "All the angles of a triangle are equal to two right 
angles: ABC is an angle of a triangle; therefore ABC is equal to 

two right angles There is no fallacy," continues the Archbishop, 

" more common, or more likely to deceive, than the one now before 
us. The form in which it is most usually employed is to establish 
some truth, separately, concerning each single member of a certain 
class, and thence to infer the same of the whole collectively J ^ As in 
the argument one often hears, sometimes from persons worthy of better 
things, to prove that the world could do without great men. If Co- 
lumbus (it is said) had never lived, America would still have been dis- 
covered, at most only a few years later ; if Newton had never lived, 
some other person would have discovered the law of gravitation ; and 
so forth. Most true ; these things would have been done, but in all 
probabilit}^ not until some one had again been found with the qualities 
of a Columbus or a Newton. Because any one great man might have 
had his place supplied by the help of others, the argument concludes 
that all great men could have been dispensed with. The term "gi^eat 
men" is distributive in the premisses and collective in the conclusion. 

"Such also," says Archbishop Whately, "is the fallacy which prob- 



510 FALLACIES. 

ably operates on most adventurers in lotteries; e.g., 'the gaining of a 
high prize is no uncommon occurrence ; and what is no uncommon 
occurrence may reasonably be expected ; therefore the gaining of a 
high prize may reasonably be expected :' the conclusion when applied 
to the individual (as in practice it is) must be understood in the sense 
of 'reasonably expected hy a certain individual;^ therefore for the 
major premiss to be true, the middle term must be understood to mean, 
'no uncommon occurrence to some one particular ^GT&on;'' whereas 
for the minor (which has been placed first) to be true, you must 
understand it of 'no uncommon occurrence to some one or other ;^ 
thus you will have the Fallacy of Composition." 

" This is a Fallacy with which men are extremely apt to deceive 
themselves ; for when a multitude of particulars are presented to the 
mind, many are too weak or too indolent to take a comprehensive view 
of them; but confine their attention to each single point, by turns; and 
then decide, infer, and act accordingly : e. g., the imprudent spend- 
thrift, finding that he is able to afford this, or that, or the other expense, 
forgets that all of them together will ruin him." The debauchee de- 
stroys his health by successive acts of intemperance, because no one of 
those acts would be of itself sufficient to do him any serious harm. A sick 
person reasons with himself, " one, and another, and another, of my 
symptoms, do not prove that I have a fatal disease;" and practically 
concludes that all taken together do not prove it. 

§ 2. We have now suflniciently exemplified one of the principal 
Genera in this Order of Fallacies ; where, the source of error being 
the ambiguity of terms, the premisses are verbally what is required to 
support the conclusion, but not really so. In the second great Fallacy 
of Confusion they are neither verbally nor really sufficient, though, 
from their multiplicity and confused arrangement, and still often er 
from defect of memory, they are not seen to be what they are-. The 
fallacy I mean is that of Petitio Principii, or begging the question ; 
including that more complex and not uncommon variety of it, which 
is termed Reasoning in a Circle. 

Petitio Principii, as defined by Archbishop Whately, is the fallacy 
"in which the premiss either appears manifestly to be the same as the 
conclusion, or is actually proved from the conclusion, or is such as 
would naturally and properly so be proved." By the last clause I 
presume is meant, that it is not susceptible of any other proof; for 
otherwise, there would be no fallacy. To deduce from a proposition, 
propositions from which it would itself more naturally be deduced, is 
often an allowable deviation fi'om the usual didactic order ; or at most, 
what, by an adaptation of a phrase familiar to mathematicians, may be 
called a logical inelegance. 

The employment of a proposition to prove that upon which it is, 
itself dependent for proof, by no means implies the degree of mental 
imbecility which might at first be supposed. The difficulty of com- 
prehending how this fallacy could possibly be committed, disappears 
when we reflect that all persons, even philosophers, hold a gi-eat num- 
ber of opinions without exactly recollecting how they came by them. 
Believing that they have at some foi-mer time verified them by sufficient 
evidence, but having forgotten what the evidence was, they may easily 
be betrayed into deducing from them the very propositions which are 



FALLACIES OF CONFUSION. 511 

alone capable of serving as premisses for their establishment. An 
example is given by Archbishop Whately : " As if one should attempt 
to prove the being of a God from the authority of Holy Writ ;" w^hich 
might easily happen to one w^ith w^hom both propositions, as funda- 
mental tenets of his religion, stand upon the same ground of familiar 
and traditional belief. 

Arguing in a circle, however, is a stronger case of the fallacy, and 
implies more than the mere passive reception of a premiss by one v\^ho 
does not remember how it is to be proved. It implies an actual 
attempt to prove two propositions reciprocally from one another ; and 
is seldom resorted to, at least in express terms, by any person in his 
own speculations, but is committed by those who, being hard pressed 
by an adversary, are forced into giving reasons for an opinion of which, 
when they began to argue, they had not sufficiently considered the 
grounds. As in the following example from Archbishop Whately : 
" Some mechanicians attempt to prove (what they ought to lay dovm 
as a probable but doubtful hypothesis*) that every particle of matter 
gravitates equally: 'why]' 'because tliose bodies which contain more 
particles ever gravitate more strongly, i. e. are heavier:' 'but (it may 
be urged), those which are heaviest are not always more bulky;' 'no, 
but they contain more particles, though more closely condensed :' 
* how do you know that V ' because they are heavier :' * how does that 
prove \tV 'because all particles of matter gravitating equally, that 
mass which is specifically the heavier must needs have the more of 
them in the same space.' " It appears to me that the fallacious 
reasoner, in his private thoughts, would not be likely to proceed beyond 
the first step.f He would acquiesce in the sufficiency of the reason 
first given, " bodies which contain more particles are heavier." It is 
when he finds this questioned, and is called upon to prove it, without 
knowing how, that he tries to establish his premiss by supposing 
proved what he is attempting to prove by it. The most effectual way, 
in fact, of exposing a Petitio Principii, when cu'cumstances allow of 
it, is by challenging the reasoner to prove his premisses ; which if he 
attempts to do, he is necessarily driven into arguing in a circle. 

It is not uncommon, however, for thinkers, and those not. of the low- 
est description, to be led, even in their own thoughts, not indeed into 
formally proving each of two propositions from the other, but into ad- 
mitting propositions which can only be so proved. In the preceding 
example the two together form a complete and consistent, though hy- 
pothetical, explanation of the facts concerned. And the tendency to 
mistake mutual coherency for truth ; to trust one's safety to a strong 
chain although it has no point of support ; is at the bottom of much 
which, when reduced to the stiict forms of argumentation, can exhibit 
itself no otherwise than as reasoning in a circle. All experience bears 
testimony to the enthralling effect of neat concatenation in a system of 

* No longer even a probable hypothesis, but (since the establishment of the atomic 
theoiy) opposed to all probability ; it being now certain that the integrant particles of dif- 
ferent substances gravitate unequally. It is true that these particles, though real minima 
for the purposes of chemical combination, may not be the ultimate particles of the sub- 
stance ; and this doubt alone renders the hyyothesis admissible, even as an hypothesis. 

t I have found, however, an argument of this exact type in a Bridgewater Treatise : — 
" Ice and silver, under the same volume, contain veiy unequal portions of matter, the sil- 
ver being ten times as heavy as the ice. The vacuities in the ice, therefore, must be very 
much greater than those in the silver." 



512 FALLACIES. 

docti'ines, and the difficulty with which men admit the persuasion that 
anything which holds so well together can possibly fall. 

Since every case where a conclusion which can only be proved from 
certain premisses is used for the proof of those premisses, is a case of 
petitio principii, that fallacy includes a very great proportion of all in- 
correct reasoning. It is necessary, for completing our view of the 
fallacy, to exemplify some of the disguises under which it is accustomed 
to mask itself, and to escape exposure. 

A proposition would not be admitted by any person in his senses as 
a corollary from itself, unless it were expressed in language which 
made it §.eem different. One of the commonest modes of so expressing 
it, is to present the proposition itself, in abstract terms, as a proof of 
the same proposition expressed in concrete language. This is a very 
frequent mode not only of pretended proof, but of pretended explana- 
tion ; and is parodied by Moliere when he makes one of his absurd 
physicians say, "I'opium endormit parcequ'il a une vertu soporifique," 
or, in the amusing doggerel quoted by Mr. Whewell — 

Mihi demand atur 

A doctissimo doctore, 
Quare opium facit dormire ; 

Et ego respondeo, 

Quia est m eo 

Virtus dormitiva, 
Cujus natura est sensus assopire. 

The words Nature and Essence are grand instruments of this mode 
of begging the question. As in the well-known argument of the scho- 
lastic theologians, that the mind thinks always, because the essence of 
the mind is to think. Locke had to point out, that if by essence is 
here meant some property which must manifest itself by actual exer- 
cise at all times, the premiss is a direct assumption of the conclusion ; 
while if it only means that to think is the distinctive property of a 
mind, there is no connexion between the premiss and the conclusion, 
since it is not necessary that a distinctive property should be perpet- 
ually in action. 

The following is one of the modes in which these abstract terms, 
Nature and Essence, are used as instruments of this fallacy. Some 
particular properties of a thing are selected, more or less arbitrarily, 
to be termed its nature or essence ; and when this has been done, these 
properties are supposed to be invested with a kind of indefeasible- 
ness ; to have become paramount to all the other properties of the 
thing, and incapable of being prevailed over or counteracted by them. 
As when Aristotle, in a passage which we have already cited from Mr. 
Whewell, '* decides that there is no void on such arguments as this : 
in a void there could be no difference of up and down; for as in 
nothing there are no differences, so there are none in a privation or 
negation ; but a void is merely a privation or negation of matter ; 
therefore, in a void, bodies could not move up and down, which it is 
in their nature to do."* In other words; It is the nature of bodies to 
move up and down, ergo any physical fact which supposes them not 
so to move, cannot be authentic. This mode of reasoning, by which 
a bad generalization is made to overrule all facts which contradict it, 
is petitio principii in one of its most palpable forms. 

* Whewell's History of the Inductive Sciences, i., 4t. 



FALLACIES OF CONFUSION. 513 

None of the modes of assuming what should be proved are in more 
frequent use than what are termed by Bentham '* question-begging 
appellatives ;" names which beg the question under the guise of stating 
it. The most potent of these are such as have a laudatory or vitupe- 
rative character. For instance, in politics, the word Innovation. The 
dictionary meaning of this term being merely " a change to something 
new," it is difficult for the defenders even of the most salutary im- 
provement to deny that it is an inaovation ; yet the word having ac- 
quired in common usage a vituperative connotation in addition to its 
dictionary meaning, the admission is always consti-ued as a large con- 
cession to the disadvantage of the thing proposed. 

The following passage from the argument in refutation of the Epi- 
cureans, in the second book of Cicero De Flnibus, affords a fine exam- 
ple of this sort of fallacy. " Et quidem illud ipsum nonnimium probo 
(et tantum patior) philosophum loqui de cupiditatibus finiendis. An 
potest cupiditas finiri 1 tollenda est, atque extrahenda radicitus. Quis 
est enim, in quo sit cupiditas, quin recte cupidus dici possit ] Ergo et 
avarus erit, sed finite : adulter, verum habebit modum : et luxuriosus 
eodem mode, Qualis ista philosophia est, quae non interitum afferat 
pravitatis, sed sit contenta mediocritate vitiorum f The question was 
whether certain desires, when kept within definite bounds, are vices 
or not ; and the argument decides the point by applying to them a 
word {cupiditas) which hnplies vice. It is shown, however, in the 
remarks which follow, that Cicero did not intend this as a serious 
argument, but as a criticism on what he deemed an inappropriate 
expression. '* Rem ipsam prorsus probo : elegantiam desidero. Ap- 
pellet haec desidcria naturce.; cupiditatis nomen ser\^et alio," &c. But 
many persons, both ancient and modern, have employed this, or some- 
thing equivalent to it, as a real and conclusive argument. We may 
remark that the passage respecting cupiditas and cupidus is also an 
example of another fallacy already noticed, that of Paronymous Terms. 

Many more of the arguments of the ancient moralists, and especially 
of the Stoics, fall within the definition of Petitio Principii. In the De 
Finihus, for example, which I continue to quote as being probably the 
best extant exemplification at once of the doctrines and the methods of 
the schools of Greek philosophy existing at that time ; what are we to 
think of the arguments of Cato in the third book, derived from common 
notions : That if virtue were not happiness, it could not be a thing to 
hoast of: That if death or pain were evils, it would be impossible not 
to fear them, and it could not, therefore, be laudable to despise them, 
&c. In one way of viewing these arguments, they may be regarded 
as appeals to the authority of the general sentiment of mankind, which 
had stamped its approval upon certain actions and characters by the 
phrases referred to ; but that such could have been the meaning in- 
tended is very unlikely, considering the contempt of the ancient philo- 
sophers for vulgar opinion. In any other sense they are clear cases of 
Petitio Principii, since the word laudable, and the idea of boasting, 
imply principles of conduct ; and practical maxims can only be proved 
from speculative truths, namely, from the properties of the subject 
matter, and cannot, therefore, be employed to prove those properties. 
As well might it be argued that a government is good because we 
ought to support it, or that there is a God because it is our duty to 
pray to him. 
3 T 



514 FALLACIES. 

It is assumed by all the disputants in the Ve Finihus as the founda- 
tion of the inquiry into the summum honum, that " sapiens semper 
beatus est." The idea that wisdom could be consistent with unhap- 
piness, was always rejected as inadmissible : the reason assigned by 
one of the interlocutors, near the beginning of the third book, being, 
that if the wise could be unhappy, there was not much use in pursuing 
wisdom. But by unhappiness they did not mean pain or suffering ; to 
that, it was granted that the wisest person was liable in common with 
others : he was happy, because in possessing wisdom he had the most 
valuable of possessions, the most to be sought and prized of all things, 
and to possess the most valuable thing was to be the most happy. By 
laying it down, therefore, at the commencement of the inquiry, that the 
sage must be happy, the disputed question respecting the summum 
honum was in fact begged ; with the further assumption, that pain and 
suffering, so far as they can coexist with wisdom, are not unhappiness, 
and are no evil. 

The following are additional instances of Petitio Principii, under 
more or less of disguise. 

Plato, in the Sophistes, attempts to prove that things may exist which 
are incorporeal, by the argument that justice and wisdom are incorpo- 
real, and justice and wisdom must be something. Here, if by some- 
thing be meant, as PHto did in fact mean, a thing capable of existing 
in and by itself, and not as. a quality of some other thing, he begs the 
question in asserting that justice and wisdom must be something : if 
he means anything else, his conclusion is not proved. This fallacy 
might also be classed under ambiguous middleterm ; something, in the 
one premiss, meaning some substance, in the other, merely some object 
of thought, whether substance or attribute. 

It was formerly an argument employed in proof of what is now no 
longer a popular doctrine, the infinite divisibility of matter, that every 
portion of matter, however small, must at least have an upper and an 
under surface. Those who used this argument did not see that it 
assumed the very point in dispute, the impossibility of arriving at a 
minimum of thickness; for if there be a minimum, its upper and under 
surface will of course be one : it will be itself a surface and no more. 
The argument owes its very considerable plausibility to this, that the 
premiss does actually seem more obvious than the conclusion, although 
really identical with it. As expressed in the premiss, the proposition 
appeals directly and in concrete language to the incapacity of the 
human imagination for conceiving a minimum. Viewed in this light, 
it becomes a case of the a priori fallacy or natural prejudice, that 
whatever cannot be conceived cannot exist. Every Fallacy of Confu- 
sion (it is almost unnecessary to repeat) will, if cleared up, become a 
fallacy of some other sort; and it will be found of deductive or ratio- 
cinative fallacies generally, that when they mislead there is mostly, as 
in this case, a latent fallacy of some other description lurking under 
them, by virtue of which chiefly it is that the verbal juggle which is 
the outside or body of this kind of fallacy, passes undetected. 

Euler's Algebra, a book otherwise of great merit, but full, to over- 
flowing, of logical errors in respect to the foundation of the science, 
contains the following argument to prove that minus multiplied by minus 
giwea2^ius, a doctrine the opprobrium of all mathematicians who are not 
philosophers, and which Euler had not a glimpse of the true method of 



FALLACIES OF CONFUSION. 515 

proving. He says, minus multiplied by minus cannot ^ve minus; for 
minus multiplied by plus gives minus, and minus multiplied by minus 
cannot give the same product as minus multiplied by plus. Now one 
is obliged to ask, why minus multiplied by minus must give any pro- 
duct at all] and if it does, why its product cannot be the same as that 
of minus multiplied by pins'? for this would seem, at the first glance, 
not more absurd than that minus by minus should give the same as 
plus by plus, the proposition which Euler prefers to it. The premiss 
requires proof, as much as the conclusion : nor can it be proved, except 
by that more comprehensive view of the nature of multiplication, and 
of algebraic processes in general, which would also supply a far better 
proof of the mysterious doctrine which Euler is here endeavoring to 
demonstrate. 

A very striking instance of reasoning in a circle is that of some ethical 
philosophers, who first take for their standard of moral truth what, being 
the general, they deem to be the natural or instinctive, sentiments and 
perceptions of mankind, and then explain away the numerous instances 
of divergence from their assumed standard by representing them as 
cases in which the perceptions are unhealthy. Some particular mode 
of conduct or feeling is affirmed to be unnatural; whyl because it is 
abhorrent to the universal and natural sentiments of mankind. Find- 
ing no such sentiment in yourself, you question the fact; and the 
answer is (if your antagonist is polite) that you are an exception, a 
peculiar case. But neither (say you) do I find in the people of some 
other country, or of some former age, any such^feeling of abhorrence ; 
**aye, but their feelings were sophisticated and unhealthy." 

One of the most notable specimens of reasoning in a circle is the 
doctrine of Hobbes, Rousseau, and others, which rests the obligations 
by which human beings are bound as members of society, upon a sup- 
posed social compact. I wave the consideration of the fictitious nature 
of the compact itself; but wlien a philosopher (as Hobbes does through 
the whole Leviathan) elaborately deduces the obligation of obeying 
the sovereign, not fi.'om the necessity or utility of doing so, but from a 
promise supposed to have been made by our ancestors, on renouncing 
savage life and agreeing to establish a political society, it is impossible 
not to retort by the question, why are we bound to keep a promise 
made for us by others 1 or why bound to keep a promise at all % No 
satisfactoiy ground can be assigned for the obligation, except tlie mis- 
chievous consequences of the absence of faith and mutual confidence 
among mankind. We are, therefore, brought round to the interests of 
society, as the ultimate ground of the obligation of a promise ; and yet 
those interests are not admitted to be a sufficient justification for the 
existence of govenmient and law. Without a promise it is thought 
that we should not be bound to that without which the existence of 
society would be impossible, namely, to yield a general obedience to 
the laws therein established ; and so necessary is the promise deemed, 
that if none has actually been made, some additional safety is supposed 
to be given to the foundations of society by feigning one. 

§ 3. Two principal subdivisions of the class of Fallacies of Con- 
fusion having been disposed of; there remains a third, in which the 
confusion is not, as in the Fallacy of Ambiguity, in misconceiving the 
import of the premisses, nor, as in Petitio Fri?icipii, in forgetting what 



516 FALLACIES. 

the premisses are, but in mistaking the conclusion which is to be proved: 
This is the fallacy of Ignoratio Elenchi, in the widest sense of the 
phrase ; also called by Archbishop Whately the fallacy of Irrelevant 
Conclusion. His examples and remarks are highly worthy of citation, 

" Various kinds of propositions are, according to the occasion, sub- 
stituted for the one of which proof is required; sometimes the par- 
ticular for the universal ; sometimes aproposition with different terms; 
and various are the contrivances employed to effect and to conceal this 
substitution, and to make the conclusion which the sophist has drawn, 
answer practically the same purpose as the one he ought to have 
established. We say, 'practically the same purpose,' because it will 
very often happen that some emotion will be excited, some sentiment 
impressed on the mind (by a dextrous employment of this fallacy), 
such as shall bring men into the disjyosition requisite for your purpose ; 
though they may not have assented to, or even stated distinctly in their 
own minds, the proposition which it was your business to establish. 
Thus if a sophist has to defend one who has been guilty of some. 
serious offence, which he wishes to extenuate, though he is unable dis- 
tinctly to prove that it is not such, yet if he can succeed in making the 
audience laugh at some casual matter, he has gained practically the 
same point. So also if any one has pointed out the extenuating cir- 
cumstances in some particular case of offence, so as to show that it 
differs widely from the generality of the same class, the sophist, if he 
find himself unable to disprove these circumstances, may do away the 
force of them, by simply referring the action to that very class, which 
no one can deny that it belongs to, and the very name of which will 
excite a feeling of disgust sufficient to counteract the extenuation ; 
e. g., let it be a case of peculation, and that many mitigating circum- 
stances have been brought forward which cannot be denied ; the 
sophistical opponent will reply, ' Well, but after all, the man is a 
rogue, and there is an end of it ;' now in reality this was (by hypoth- 
esis) never the question ; and the mere assertion of what was never 
denied, ought not, in fairness, to be regarded as decisive : but, prac- 
tically, the odiousness of the word, arising in great measure from the 
association of those very circumstances which belong to most of the 
class, but which we have supposed to be absent in this particular in- 
stance, excites precisely that feeling of disgust, which in effect destroys 
the force of the defence. In like manner, we may refer to this head 
all cases of improper appeal to the passions, and everything else which 
is mentioned by Aristotle as extraneous to the matter in hand (e^w 
rov rrpdyfjiaTog). 

" A good instance of the employment and exposure of this fallacy 
occurs in Thucydides, in the speeches of Cleon and Diodotus con- 
cerning the Mitylenaeans : the former (over and above his appeal to 
the angry passions of his audience) urges the justice of putting the re- 
volters to death; which, as the latter remarked, was nothing to the 
purpose, since the Athenians were not sitting in judgment, but in de- 
liberation, of which the proper end is expedience/. 

" It is evident that ignoratio elenchi may be employed as well for 
the apparent refutation of your opponent's proposition, as for the ap- 
parent establishment of your- own ; for it is substantially the same 
thing, to prove what was not denied or to disprove what was not 
asserted : the latter practice is not less common, and it is more offen- 



FALLACIES OF CONFUSION. 517 

sive, because it frequently amounts to a personal affront, in attributing 
to a person opinions, &c., which he perhaps holds in abhorrence. 
Thus, when in a discussion one party vindicates, on the ground of 
general expediency, a particular instance of resistance to govern- 
ment in a case of intolerable oppression, the opponent may gravely 
maintain, that 'we ought not to do evil that good may come;' a 
proposition which of course had never been denied, the point in dis- 
pute being, ' whether resistance in this particular case ivere doing evil 
or not.' " 

The works of controversial writers are seldom free from this fallacy. 
They join issue on the wrong point, or do not join issue at all. ' The 
attempts, for instance, to disprove the population doctrines of Malthus, 
have been mostly cases of ignoratio elencJii. Malthus has been sup- 
posed to be refuted if it could be shown that in some countries or ages 
population has been nearly stationary ; as if he had asserted that popu- 
lation always increases in a given ratio, or had not expressly declared 
that it increases only in so far as it is not restrained by prudence, or 
kept down by poverty and disease. Or, perhaps, a great collection of 
facts is produced to prove that in some one country the people are 
better off with a dense population than they are in another country 
with a thin one ; or that the people have become more numerous and 
better off at the same time. As if the assertion were that a dense popu- 
lation could not possibly be well off: as if it were not part of the very 
doctrine, and essential to it, that, where there is a more abundant cap- 
ital there may be a greater population without any increase of poverty, 
or even with a diminution of it. 

The favorite argument against Berkeley's theory of the non-existence 
of matter, and the most popularly effective, next to a " grin"* — an^ 
argument, moreover, which is not confined to " coxcombs," nor to 
men like Samuel Johnson, of practical understanding, without any 
particular turn for metaphysical speculation, but is the stock argument 
of the Scotch school of metaphysicians, is a palpable ignoratio elenchi. 
The argument is perhaps as frequently expressed by gesture as by 
wor<ls, and one of its commonest forms consists in knocking a stick 
against the ground. This short and eas^ confutation overlooks the 
fact, that in denying matter, Berkeley did not deny anything to which 
our senses bear witness, and therefore cannot be answered by any 
appeal to. them. His skepticism related to the supposed substratum, 
or hidden cause of the appearances perceived by our senses : the evi- 
dence of which, whatever may be its conclusiveness, is certainly not 
the evidence of sense. And it will always remain a signal proof of 
the want of metaphysical profundity of Reid, Stewart, and, I am sorry 
to add, of Brown, that they should have persisted in asserting that 
Berkeley, if he believed his own doctrine, was bound to walk into the 
kennel, or run his head against a post. As if men who do not recog- 
nize an occult cause of their sensations could not possibly believe that 
a fixed order subsists among the sensations themselves. Such a want 
of comprehension of the distinction between a thing and its sensible 
manifestation, or, in transcendental language, between the noumenon 
and the phenomenon, would be impossible to even the dullest disciple 
of Kant or Coleridge. 

* And coxcombs vanquish Berkeley with a grin. — (Pope.) 



518 FALLACIES. 

It would be easy to add a greater number of examples of this fallacy, 
as well as of the others which I have attempted to characterize. But 
a more copious exemplification does not seem to be necessary ; and 
the intelligent reader will have little difficulty in adding to the cata- 
logue from his own reading and experience. We shall therefore here 
close our exposition of the general principles of logic, and proceed 
at once to the supplemental inquiry which is necessary to complete 
our design. - - 



BOOK VI. 

ON THE LOGIC OF THE MORAL SCIENCES. 



" Une propriety fondamentale que je dois faire remarquer des ce moment dans ce que 
i'ai appele la philosophie positive, et qui doit sans doute lui meriter plus que toute autre 
I'attention generale, puisqu'elle est aujourd'hui la plus importante pour la pratique, c'est 
qu'elle pent 6tre consideree comme la seule base solide de la reorganisation sociale qui doit 
terminer I'etat de crise dans lequel se trouvent depuis si long-temps les nations les plus 

civilisees Tant que les intelligences individuelles n'auront pas adhere par un assenti- 

ment unanime a un certain nombre d'idees generales capablesde former une doctrine sociale 
commune, on ne peut se dissimuler que I'etat des nations restera,de toute necessite, essen- 
tiellement revolutionnaire, malgre tous les palliatifs poliliques qui pourront 6tre adoptes, et 
ne, comportera reellement que des institutions provisoires. II est egaiement certain que si 
cette reunion des esprits dans une meme communion de principes peut une fois etre 
obtenue, les institutions convenables en decouleront necessairement, sans donner lieu a 
aucune secousse grave, le plus grand desordre etant deja dissipe par ce seul fait." — Comte, 
Cours de Philosophie Positive, Ire lecjon. 



CHAPTER I. 

INTRODUCTORY REMARKS. 



§ 1. Principles of Evidence and Theories of Method are not to be 
constructed d priori. The laws of our rational faculty, like those of 
every other natural agency, are only learnt by seeing the agent at 
work. The earlier achievements of science were made without the 
conscious observance of any Scientific Method ; and we should never 
have known by what process truth is to be ascertained, if we had not 
previously ascertained many truths. But it was only the easier pro- 
blems which could be thus resolved : natural sagacity, when it tried its 
strength against the more difficult ones, either failed altogether, or if 
it succeeded here and there in obtaining a solution, had no sure means 
of convincing others that its solution was correct. In scientific in- 
vestigation, as in all other works of human skill, the way of attaining 
the end is seen as it were instinctively by superior minds in some 
comparatively simple case, and is then, by judicious generalization, 
adapted to the variety of complex cases. We learn to do a thing in 
difficult circumstances, by attending to the manner in which we have 
spontaneously done the same thing in easy ones. 

This truth is exemplified by the history of the various branches of 
knowledge which have successively, in the ascending order of their 
complication, assumed the character of sciences ; and will doubtless 
receive fresh confirmation from those, of which the final scientific con- 
stitution is yet to come, and which are still abandoned to the uncer- 
tainties of vague and popular discussion. Although several other sci- 
ences have emerged from this state at a comparatively recent date 



520 LOGIC OF THE MORAL SCIENCES. 

none now remain in it except those whicli relate to man himself, the 
most complex and most difficult subject of study on which the human 
mind can be engaged. 

Concerning the physical nature of man, as an organized being: — al- 
though there is still much uncertainty and much controversy, which 
can only be terminated by the general acknowledgment and employ- 
ment of stricter rules of induction than are commonly recognized — 
there is, however, a considerable body of truths which all who have 
attended to the subject consider to be fully established ; nor is there 
now any radical imperfection in the method observed in this depart- 
ment of science by its most distinguished modern teachers. But the 
laws of Mind, and, in even a gi'eater degree, those of Society, are so 
far from having attained a similar state of even partial recognition, 
that it is still a controversy whether they are capable of becoming siib- 
jects of science, in the strict sense of the term; and among those who 
are agreed on this point there reigns the most irreconcilable diversity 
on almost every othet". Here, therefore, if anywhere, the principles 
laid down in the preceding Books may be expected to be useful. 

If on matters so much the most important with which human intel- 
lect can occupy itself, a more general agi'eement is ever to exist among 
thinkers ; if what has been pronounced " the proper study of mankind" 
is not destined to remain the only subject which Philosophy cannot 
succeed in rescuing from Empiricism ; the same processes through 
which the laws of simpler phenomena have by general acknowledg- 
ment been placed beyond dispute, must be consciously and deliberately 
applied to those more difficult inquiries. If there are some subjects 
on which the results obtained have finally received the unanimous as- 
sent of all who have attended to the proof, and others on which man- 
kind have not yet been equally successful ; on which the most sagacious 
minds have occupied themselves from the earliest date, with every 
assistance except that of a tried scientific method, and have never suc- 
ceeded in establishing any considerable body of truths, so as to be 
beyond denial or doubt ; it is by generalizing the methods success- 
fully followed in the former inquiries, and applying them to the latter, 
that we may hope to remove this blot upon the face of science. The re- 
maining chapters are an attempt to facilitate this most desirable object. 

§ 2. In attempting this, I am not unmindful how little can be done 
towards it in a mere Treatise on Logic, or how vague and unsatis- 
factory all precepts of Method must necessarily appear, when not prac- 
tically exemplified in the establishment of a body of doctrine. Doubt- 
less, the most effectual way of showing how the sciences of Ethics and 
Politics may be constructed, would be to construct them : a task which, 
it needs scarcely be said, I am not about to undertake. But even if 
there were no other examples, the memorable one of Bacon would be 
sufficient to demonstrate, that it is sometimes both possible and useful 
to point out the way, though without being oneself prepared to adven- 
ture far into it. And if more were to be attempted, this at least is not 
a proper place for the attempt. 

In substance, whatever can be done in a work like this, for the Logic 
of the Moral Sciences, has been or ought to have been accomplished 
in the five preceding Books ; to which the present can be only a kind 
of supplement or appendix, since the methods of investigation applica- 



LIBERTY AND NECESSITY. 521 

ble to moral and social science must have been described by implica- 
tion, if I have succeeded in enumerating and characterizing those of 
science in general. It only remains to examine which of those 
methods are more especially suited to the various branches of moral 
inquiry ; under w^hat peculiar facilities or difficulties they are there 
employed ; how far the unsatisfactory state of those inquiries is owing 
to a wrong choice of methods, how far to want of skill in the applica- 
tion of right ones ; and what degree of ultimate success may be at- 
tained or hoped for, by a better choice or more careful ernployment of 
logical processes appropriate to the case. In other words, whether 
moral sciences exist, or can exist ; to what degi'ee of perfection they 
a.re susceptible of being carried; and by what selection or adaptation 
,of the methods brought to view in the previous part of this work, that 
degree of perfection is attainable. 

At the threshold of this inquiry we are met by an objection, which, 
if not removed, would be fatal to the attempt to treat human conduct 
as a subject of science. Are the actions of man, like all other natural 
events, subject to invariable laws 1 Does that constancy of causation, 
which is the foundation of every scientific theory of successive phe- 
nomena, really obtain among them 1 This is often denied ; and 
for the sake of systematic completeness, if not from any very urgent 
practical necessity, the question should receive a deliberate answer in 
this place. We shall devote to the subject a chapter apart. 



CHAPTER 11. 

OF LIBERTY AND NECESSITY, 



"^ § 1. The question, whether the law of causality applies in the same 
strict sense to human actions as to other phenomena, is the celebrated 
controversy concerning the freedom of the will; which, from at least as 
far back as the time of Pelagius, has divided both the philosophical 
and the religious world. The affirmative opinion is commonly called 
the doctrine of Necessity, as asserting human volitions and actions to 
be necessary and inevitable. The negative maintains that the will is 
not determined, like other phenomena, by antecedents, but determines 
itself; that our volitions are not, properly speaking, the effects of 
causes, or at least have no causes which they uniformly and implicitly 
obey. 

I have already made it sufficiently appear that the former of these 
opinions is that which I consider the true one; but the misleading 
terms in which it is often expressed, and the indistinct manner in which 
it is usually apprehended, have both obstructed its reception, and per- 
verted its influence when received. The metaphysical theory of free 
will, as held by philosophers (for the practical feehng of it, common in 
a greater or less degree to all mankind, is in no way inconsistent with 
the contrary theory), was invented because the supposed alternative of 
admitting human actions to be necessary, was deemed inconsistent with 
every one's instinctive consciousness, as well as humiliating to the pride 
3U 



522 LOGIC OF THE MORAL SCIENCES. 

and even degi-ading to the moral nature of man. Nor do I deny that 
the doctrine, as sometimes held, is open to these imputations; for the 
misapprehension in which I shall be able to show that they originate, 
unfortunately is not confined to the opponents of the doctrine, but par- 
ticipated in by many, perhaps we might say by most of its supporters. 

§ 2. Correctly conceived, the doctrine called Philosophical Neces- 
sity is simply this : that, given the motives which are present to an 
individual's mind, and given likewise tho character and disposition of 
the individual, the manner in which he will act may be unerringly 
inferred ; that if we knew the person thoroughly, and knew all the 
inducements which are acting upon him, we could foretell his conduct 
with as much certainty as we can predict any physical event. This 
proposition I take to be a mere interpretation of universal experience, 
a statement in words of what every one is internally convinced of. No 
one who believed that he knew thoroughly the circumstances of any 
case, and the characters of the different persons concerned, would hes- 
itate to foretell how all of them would act. Whatever degree of doubt 
he may in fact feel, arises from the uncertainty whether he really knowg 
the circumstances, or the character of some one or other of the persons, 
with the degree of accuracy required ; but by no means from thinking 
that if he did know these things, there could be any uncertainty what 
the conduct would be. Nor does this full assurance conflict in the 
smallest degree with what is called our feeling of freedom. We do 
not feel ourselves the less free, because those to whom we are intimately 
known are well assured how we shall will to act in a particular case. 
We often, on the contrary, regard the doubt what our conduct will be, 
as a mark of ignorance of our character, and sometimes even resent 
it as an imputation. It has never been admitted by the religious phi- 
losophers who advocated the free-will doctrine, that we must feel not 
free because God foreknows our actions. We may be free, apd yet 
another may have reason to be perfectly certain what use we shall 
make of our freedom. It is not, therefore, the doctrine that our voli- 
tions and actions are invariable consequents of our antecedent states 
of mind, that is either contradicted by our consciousness, or felt to be 
degrading. 

But the doctrine of causation, when considered as obtaining between 
our volitions and their antecedents, is almost universally conceived as 
involving more than this. Many do not believe, and very few prac- 
tically feel, that there is nothing in causation but invariable, certain, 
and unconditional sequence. There are few to whom mere constancy 
of succession appears a sufficiently stringent bond of union for so pe- 
culiar a relation as that of cause and effect. Even if the reason repu- 
diates, imagination retains, the feeling of some more intimate connex- 
ion, of some peculiar tie, or mysterious constraint exercised by the 
antecedent over the consequent. Now this it is which, considered as 
applying to the human will, conflicts with our consciousness, and re- 
volts our feelings. We are certain that, in the case of our volitions, 
there is not this mysterious constraint. We know that we are not 
compelled, as by a magical spell, to obey any particular motive. We 
feel, that if we wished to prove that we have the power of resisting 
the motive we could do so, (that wish being, it needs scarcely be ob- 
served, ^ new antecedent j) and it would be humiliating to our pride 



LIBERTY AND NECESSITY. 523 

and paralyzing to our desire of excellence if we thought otherwise. 
But neither is any such mysterious compulsion now supposed, by the 
best philosophical authorities, to be exercised by any cause over its 
effect. Those who think that causes draw their effects after them by a 
mystical tie, are right in believing that the relation between volitions 
and their antecedents is of another nature. But they should go 
further, and admit that this is also true of all other effects and their an- 
tecedents. If such a tie is considered to be involved in the word ne- 
cessity, the doctrine is not true of human actions ; but neither is it then 
true of inanimate objects. It would be more correct to say that mat- 
ter is not bound by necessity than that mind is so. 

That the free-will philosophers, being mostly of the school which 
rejects Hume's and Brown's analysis of Cause and Effect, should miss 
their way for want of the light which that analysis affords, cannot sur- 
prise us. The wonder is, that the necessarians, who usually admit that 
philosophical theory, should in practice equally lose sight of it. The 
very same misconception of the doctrine called Philosophical Neces- 
sity, which prevents the opposite party from recognizing its truth, I 
believe to exist more or less obscurely in the minds of most necessa- 
rians, however they may in words disavow it, I am much mistaken 
if they habitually feel that the necessity which they recognize in actions 
is but uniformity of order, and capability of being predicted. They 
have a feeling as if there were at bottom a stronger tie between the 
volitions and their causes : as if, when they asserted that" our will is 
governed by the balance of motives, they meant something more co- 
gent than if they had only said, that whoever knew the motives, and 
our habitual susceptibilities to them, could predict how we should will 
to act. They commit, in opposition to their own philosophical system, 
the very same mistake which their adversaries commit in obedience 
to theirs; and in consequence do really in some instances (I speak 
from personal experience) suffer those depressing consequences, which 
their opponents erroneously impute to the doctrine itself 

§ 3. I am inclined to think that this error is almost wholly an effect 
of the associations with a word ; and that it would be prevented by 
forbearing to employ, for the expression of the simple fact of causa- 
tion, so extremely inappropriate a term as Necessity. That word, in 
its other acceptations, involves much more than mere uniformity of 
sequence ; it implies irresistibleness. Applied to the will, it only 
means that the given cause will be followed by the effect, subject to 
all possibilities of counteraction by other causes : but in common use 
it stands for the operation of those causes exclusively, which are sup- 
posed too powerful to be counteracted at all. When we say that all 
human actions take place of necessity, we only mean that they will 
certainly happen if nothing prevents : — when we say that dying of 
want, to those who cannot get food, is a necessity, we mean that it will 
certainly happen whatever may be done to prevent it. The applica- 
tion of the same term to the agencies on which human actions depend, 
as is used to express those agencies of nature which are really uncon- 
trollable, cannot fail, when habitual, to create a feeling of uncontrolla- 
bleness in the former also. This however is a mere illusion. There 
are physical sequences which we call necessary, as death for want of 
food or air; there are others which are not said to be necessary, as 



524 LOGIC OF THE MORAL SCIENCES. 

death from poison, which an antidote, or the use of the stomach pump, 
will sometimes avert. It is apt to be forgotten by people's feelings, 
even if remembered by their understandings, that human actions are 
in this last predicament: they are never (except in some cases of 
mania) ruled by any one motive with such absolute sway, that there 
is no room for the influence of any other. The causes, therefore, on 
which action depends, are never uncontrollable; and any given effect 
is only necessary provided that the causes tending to produce it are 
not controlled. That whatever happens, could not have happened 
otherwise unless something had taken place which was capable of 
preventing it, no one surely needs hesitate to admit. But to call this 
by the name necessity is to use the term in a sense so different from 
its primitive and familiar meaning, from that which it bears in the 
common occasions of life, as to amount almost to a play upon words. 
The associations derived from the ordinary sense of the term will ad- 
here to it in spite of all we can do ; and though the doctrine of Neces- 
sity, as stated by most who hold it, is very remote from fatalism, it is 
probable that most necessarians are fatalists, more or less, in their 
feelings. 

A fatalist believes, or half believes (for nobody is a consistent fatal- 
ist) not only that whatever is about to happen, will be the infallible 
result of the causes which produce it (which is the true necessarian 
doctrine), but moreover that there is no use in struggling against it; 
that it will happen however we may strive to prevent it. Now, a 
necessarian, believing that our actions follow from our characters, and 
that our characters follow from our organization, our education, and 
our circumstances, is apt to be, with more or less of consciousness on 
his part, a fatalist as to his own actions, and to believe that his nature 
is such, or that his education and circumstances have so moulded his 
character, that nothing can now prevent him from feeling and acting 
in a particular way, or at least that no effort of his ownn can hinder it. 
In the words of the sect which in our own day has so perseveringly 
inculcated and so perversely misunderstood this great doctrine, his 
character is formed for him, and not Z»?/him; therefore his wishing ~ 
that it had been formed differently is of no use ; he has no power to 
alter it. But this is a grand error. He has, to a certain extent, a 
power to alter his character. Its being, in the ultimate resort, formed 
for him, is not inconsistent with its being, in part, formed hy him as 
one of the intermediate agents. His character is formed by his cir- 
cumstances (including among these his particular organization) ; but 
,his own desire to mould it in a particular way, is one of those circum- 
stances, and by no means one of the least influential. We cannot, 
indeed, directly will to be different from what we are. But neither did 
those who are supposed to have formed our characters, directly vdll 
that we should be what we are. Their will had no direct power 
except over their own actions. They made us what they did make 
us, by willing, not the end, but the requisite means : and we, when our 
habits are not too inveterate, can, by similarly willing the requisite 
means, make ourselves different. If they could place us under the 
influence of certain circumstances, we, in like manner, can place our- 
selves under the influence of other circumstances. We are exactly as 
capable of making our own character, ^/*^d;e will, as others are of mak- 
ing it for us. 



LIBERTY AND NECESSITY. 525 

Yes (answers the Ovvenite), but these words, " if we will," surrender 
the whole point : since the will to alter our own character is given us, 
not by any efforts of ours, but by circumstances which we cannot help; 
it comes to us either from external causes, or not at all Most ti'ue : 
if the Owenite stops here, he is in a position from which nothing can 
expel him. Our character is foraied by us as well as for us ; but the 
wish which induces us to attempt to form it is formed for us : and how "? 
not, in general, by our organization or education, but by our experi- 
ence ; experience of the painful consequences of the character we 
previously had : or by some strong feeling of admiration or aspiration, 
accidentally aroused. But to think that we have no power of altering 
our characters, and to think that we shall not use our power unless we 
have a motive, are very different things, and have a very different effect 
upon the mind. A person who does not wish to alter his character, 
cannot be the person who is supposed to feel discouraged or paralyzed 
by thinking himself unable to do it. The depressing effect of the fatalist 
doctrine can only be felt where there is a wish to do what that doctrine 
represents as impossible. It is of no consequence what we think foiTns 
our character when we have no desire of our ovra about forming it ; 
but it is of great consequence that we should not be prevented from 
forming such a desire by thinking the attainment impracticable, and 
that if we have the desire, we should know that the work is not so 
irrevocably done as to be incapable of being altered. 

And indeed, if we examine closely, we shall find that this feeling, of 
our being able to modify our own character if we wish, is itself the 
feeling of moral freedom which we are conscious of. A person feels 
morally free, who feels that his habits or his temptations are not his 
masters, but he theirs : who even in yielding to them knows that he 
could resist; that were he, for any reasouj desirous of altogether throw- 
ing them off, there would not be required for that purpose a stronger 
desire than he knows himself to be capable of feeling. It is of course 
necessary, to render our consciousness of freedom complete, that we 
should actually have made our character all we have hitherto wished 
to make it ; for if we have wished, and not attained, we have not power 
over our own character, we are not free. Oi' at least, we must feel 
that our wish, if not strong enough to alter our character, is strong 
enough to conquer our character when the two are brought into conflict 
in any particular case of conduct. 

The application of so improper a term as Necessity to the doctrine 
of cause and effect in the matter of human character, seems to me one 
of the most signal instances in philosophy of the abuse of terms, and its 
practical consequences one of the most striking examples of the power 
of language over oui' associations. The subject will never be generally 
understood, until that objectionable term is dropped. The free-will 
docti'ine, by keeping in view precisely that portion of the truth which 
the word Necessity puts out of sight, namely, the power of the mind to 
cooperate in the fonnation of its own character, has given to its adher- 
ents a practical feeling much nearer to the truth than has generally (I 
believe) existed in the minds of necessarians. The latter may have had 
a stronger sense of the importance of what human beings can do to 
shape the characters of one another ; but the free-will doctrine has, I 
believe, fostered, especially in the younger of its supporters, a much 
stronger spirit of self-culture. 



626 LOGIC OF THE MORAL S€IENCEa. 

§ 4. There is still one fact which requires to be noticed (in addition 
to the existence of a power of self-formation) before the doctrine of 
the causation of human actions can be freed from the confusion and 
misapprehensions which surround it in many minds. When the will 
is said to be determined by motives, a motive does not mean always, 
or solely, the anticipation of a pleasure or of a pain. I shall not here 
inquire whether it be true that, in the commencement, all our volun- 
tary actions are mere means consciously employed to obtain some pleas- 
ure, or avoid some pain. It is at least certain that we gradually, 
through the influence of association, come to desire the means without 
thinking of the end: the action itself becomes an object of desire, and 
is performed without reference to any motive beyond itself. Thus 
far, it may still be objected, that, the action having through association 
become pleasurable, we are, as much as before, moved to act by the 
anticipation of a pleasure, namely, the pleasure of the action itself. 
But granting this, the matter does not end here. As we proceed in 
the formation of habits, and become accustomed to will a particular 
act or a particular course of conduct because it is pleasurable, we at 
last continue to will it whether it is pleasurable or not. Although, 
from some change in us or in our circumstances, we have ceased to 
find any pleasure in the action, or to anticipate any pleasure as the 
consequence of it, we still continue to desire the action, and conse- 
quently to do it. In this manner it is that habits of hurtful indulgence 
continue to be practised although they have ceased to be pleasurable ; 
and in this manner also it is that the habit of willing to persevere in a 
prescribed course does not desert the moral hero, even when the re- 
ward, however real, which he doubtless receives from the conscious- 
ness of well-doing, is anything but an equivalent for the sufferings he 
undergoes, or the wishes which he may have to renounce. 

A habit of willing is commonly called a purpose; and among the 
causes of our volitions, and of the actions which flow from them, must 
be reckoned not only likings and aversions, but also purposes. It is 
only when our purposes have become independent of the feelings of 
pain or pleasure from which they originally took their rise, that we are 
said to have a confirmed character. "A character," says Novalis, " is 
a completely fashioned will :" and the will, once so fashioned, may be 
steady and constant, when the passive susceptibilities of pleasure and 
pain are greatly weakened, or naaterially changed. 

"With the corrections and explanations now given, the doctrine of 
the causation of our volitions by motives, and of motives by the desi- 
rable objects offered to us, combined with our particular susceptibilities 
of desire, may be considered, I hope, as sufficiently established; and 
J shall henceforth assume its truth without any further discussion. 



HUMAN NATURE A SUBJECT OF SCIENCE. 527 

CHAPTER III. 

THAT THERE IS, OR MAY BE, A SCIENCE OF HUMAN NATURE. 

§ 1. It is a common notion, or at least it is implied in many common 
modes of speech, that the thoughts, feelings, and actions of sentient 
beings are not a subject of science, in the same strict sense in which 
this is true of the objects of outward Nature. This notion seems to 
involve some confusion of ideas, which it is necessary to begin by 
clearing up. 

Any facts are fitted, in themselves, to be a subject of science, which 
follow one another according to constant laws ; although those laws 
may not have been discovered, nor even be discoverable by our exist- 
ing resources. Take, for instance, the most familiar class of meteor- 
ological phenomena, those of rain and sunshine. Scientific inquiry 
has not yet succeeded in ascertaining the order of antecedence and 
consequence among these phenomena, so as to be able, at least in our 
regions of the earth, to predict them with certainty, or even with any 
high degree of probability. Yet no one doubts that the phenomena 
depend upon laws, and that these must be derivative laws resulting 
from known ultimate laws, those of heat, vaporization, and elastic 
fluids. Nor can it be doubted that if we were acquainted with all the 
antecedent circumstances, we could, even from those more general 
laws, predict (saving difficulties of calculation) the state of the weather 
at any future time. Meteorology, therefore, not only has in itself 
every natural requisite for being, but actually is, a science ; although, 
from the difficulty of observing the facts upon which the phenomena 
depend (a difficulty inherent in the peculiar nature of those phe- 
nomena) the science is still very imperfect ; and were it perfect, might 
probably be of little avail in practice, since the data requisite for 
applying its principles to particular instances would rarely be pro- 
curable. 

A case may be conceived, of an intermediate character between the 
perfection of science, and this its extreme imperfection. It may hap- 
pen that the greater causes, those on which the principal part of a 
phenomenon depends, are within the reach of observation and 
measurement ; so that if no other causes intervened, a complete 
explanation could be given not only of the phenomenon in general, but 
of all the variations and modifications which it admitted of But inas- 
much as other, perhaps many other causes, separately insignificant in 
their effects, cooperate or conflict in many or in alb cases with those 
greater causes ; the effect, accordingly, presents more or less of aberra- 
tion from what would be produced by the greater causes alone. Now, 
if these minor causes are not so constantly accessible, or not accessible 
at all, to accurate observation ; the principal mass of the effect may 
still, as before, be accounted for, and even predicted ; but there will 
be variations and modifications which we are not competent to explain 
thoroughly, and our predictions will not be fulfilled accurately, but 
only approximately. 

It is thus, for example, with the theory of the tides. No one doubts 
that Tidology (as Mr. Whewell proposes to call it) is really a science. 



528 LOGIC OF THE MORAL SCIENCES. 

As much of the phenomena as depends upon the attraction of the sun 
and moon is completely understood, and may in any, even unknown, 
part of the earth's surface, be foretold with certainty; and the far 
greater part of the phenomena depends upon those causes. But cir- 
cumstances of a local or casual nature, such as the configuration of the ' 
bottom of the ocean, the degree of confinement from shores, the direc- 
tion of the wind, &c,, influence, in many or in all places, the height 
and time of the tide ; and a portion of these circumstances being either 
not accurately knowable, not precisely measurable, or at least not 
capable of being certainly foreseen, the tide in known places com- 
monly varies from the calculated result of general principles by some 
difference that we cannot explain, and in unknown ones may vary from 
it by a difference that we are not able to foresee or conjecture. Never- 
theless, not only is it certain that these variations depend upon causes, 
and follow their causes by laws of unerring uniformity ; not only, 
therefore, is tidology a science, like meteorology, but it is, what 
meteorology perhaps will never be, a science largely available in 
practice. General laws may be laid down respecting the tides, pre- 
dictions may be founded upon those laws, and the result will in the 
main, though often not with complete accuracy, correspond to the 
predictions. 

And this is what is or ought to be meant by those who speak of 
sciences which are not exact sciences. Astronomy was once a science, 
without being an exact science. It could not become exact until not 
only the general course of the planetary motions, but the perturbations 
-also, were accounted for, and referred to their causes. It has now be- 
come an exact science, because its phenomena have been brought under 
laws comprehending the whole of the causes by which the phenomena 
are influenced, whether in a great or only in a trifling degi'ee, whether 
in all or only in some cases, and assigning to each of those causes the 
share of effect which really belongs to it. But in tidology the only laws 
as yet accurately ascertained, are those of the causes which affect the 
phenomenon in all cases, and in a considerable degree ; while others 
which affect it in some cases only, or, if in all, only in a slight degree, 
have not yet been sufficiently ascertained and studied to enable us to 
lay down their laws ; still less to deduce the completed law of the phe- 
nomenon, by compounding the effects of the greater with those of the 
minor causes. Tidology, therefore, is not yet an exact science ; not 
from any inherent incapacity of being so, but from the difficulty of 
ascertaining with complete precision the real derivative uniformities. 
By combining, however, the exact laws of the greater causes, and of 
such of the minor ones as are sufficiently known, with such empirical 
laws or such approximate generalizations respecting the miscellaneous 
variations as can be obtained by specific observation, we can lay down 
general propositions which will be true in the main, and upon which, 
with allowance for the degree of their probable inaccuracy, we may 
safely gi*ound our expectations and our conduct. 

§ 2. The science of human nature is of this description. It falls far 
short of the standard of exactness now realized in Astronomy; but 
there is no reason that it should not be as much a science as Tidology 
is, or as Astronomy was when its calculations had only mastered the 
main phenomena, but not the perturbations. 



HUMAN NATURE A SUBJECT OF SCIENCE. 529 

The phenomena with which this science is conversant being the 
thoughts, feeUngs, and actions of human beings, it would have attained 
the ideal perfection of a science if it enabled us to foretell how an indi- 
vidual would think, feel, or act, throughout life, with the same certainty 
with which astronomy enables us to predict the places and the occulta- 
lions of the heavenly bodies. It needs scarcely be stated that nothing 
approaching to this can be done. The actions of individuals could not 
be predicted with scientific accuracy, were it only because we cannot 
foresee the whole of the circumstances in which those individuals will 
be placed. But further, even in any given combination of (present) 
circumstances, no assertion, which is both precise and universally true, 
can be made respecting the manner in which human beings will think, 
feel, or act. This is not, however, because every person's modes of 
thinking, feeling, and acting, do not depend upon causes ; nor can we 
doubt that if, in the case of any individual, our data could be complete, 
v/e even now know enough of the ultimate laws by which mental phe- 
nomena are determined to enable us to predict with tolerable certainty, 
if not with perfect precision, what, under any given set of circumstances, 
his conduct or sentiments would be. But the impressions and actions 
of human beings are not solely the result of their present circumstances, 
but the joint result of those circumstances and of the characters of the 
individuals : and the agencies which determine human character are so 
numerous and diversified (nothing which has happened to the person 
throughout life being without its portion of influence), that in the ag- 
gregate they are never in any two cases exactly similar. Hence, even 
if our science of human nature were theoretically perfect, that is, if we 
could calculate any character as we can calculate the orbit of any 
planet, Jro7n given data ; still as the data are never all given, nor ever 
precisely alike in different cases, we could neither make infallible pre- 
dictions, nor lay down universal propositions. 

Inasmuch, however, as many of those effects which it is of most im- 
portance to render amenable to human foresight and control, are de- 
termined, like the tides, in an incomparably greater degree by general 
causes, than by all partial causes taken together ; depending in the main 
on those circumstances and those qualities which are common to all 
mankind, or common at least to large bodies of them, and only in a 
small degree on the idiosyncracies of organization or the peculiar his- 
tory of individuals ; it is evidently possible, with regard to all such 
effects, to make predictions which will almost always be verified, and 
general propositions which are almost always true. And whenever it 
is sufficient to know how the great majority of the human race, or of 
some nation or class of persons, will think, feel, and act, these proposi- 
tions are equivalent to universal ones. For the purposes of political 
and social science this is sufficient. As we formerly remarked,* an 
approximate generalization is practically, in social inquiries, equivalent 
to an exact one ; that which is only probable when asserted of human 
beings taken individually, being certain when affirmed of the character 
and collective conduct of masses. 

It is no disparagement, therefore, to the science of Human Nature, 
that those of its general propositions which descend sufficiently into 
detail to serve as a foundation for predicting phenomena in the con- 

* Supra, p. 359. 

3X 



530 LOGIC OF THE MORAL SCIENCES. 

Crete, are for the most part only approximately true. But in order to 
give a genuinely scientific character to the study, it is indispensable 
that these approximate generalizations, which in themselves would 
amount only to the lowest kind of empirical laws^ should be connected 
deductively with the laws of nature from which they result ; should be 
resolved into the properties of the causes on which the phenomena 
depend. In other words, the science of Human Nature may be said 
to exist, in proportion as those approximate truths, which compose a 
practical knowledge of mankind, can be exhibited as corollaries from 
the universal laws of human nature on which they rest ; whereby the 
proper limits of those approximate truths would be shown, and we 
should be enabled to deduce others for any new state of circumstances, 
in anticipation of specific experience. 

The proposition now stated is the text on which the two succeeding 
chapters will furnish the comment. 



CHAPTER IV. 

OF THE LAWS OF MIND. 



§ 1. What the Mind is, as well as what Matter is, or any other 
question respecting Things in themselves, as distinguished from their 
sensible manifestations, it would be foreign to the purposes of this 
Treatise to consider. Here, as throughout our inquiry, we shall keep 
clear of all speculations respecting the Mind's own nature, and shall 
understand by the Laws of Mind, those of mental Phenomena; of the 
various feelings or states of consciousness of sentient beings. These, 
according to the classification we have uniformly followed, consist of 
Thoughts,' Emotions, Volitions, and Sensations : the last being as truly 
States of Mind as the three former. It is usual indeed to speak of 
Sensations as states of body, not of mind. But this is the common 
confusion of giving one and the same name to a phenomenon and to 
the proximate cause or conditions of the phenomenon. The immediate 
antecedent of a Sensation is a state of Body, but the sensation itself is 
a state of Mind. If the word Mind means anything, it means that which 
feels. If we allow ourselves to use language implying that the Body 
feels, there is no reason against being consistent in that language, and 
saying that the Body also thinks. 

The phenomena of Mind, then, are the various feelings of our 
nature, both those called physical, and those peculiarly designated as 
Mental : and by the Laws of Mind, I mean the laws according to which 
those feelings generate one another. 

§ 2. All states of mind are immediately caused either by other states 
of mind, or by states of body. When a state of mind is produced by 
a state of mind, I call the law concerned in the case, a law of Mind. 
When a state of mind is produced directly by a state of body, the law 
is a law of Body, and belongs to physical science. 

With regard to those states of mind which are called Sensations, all 
are agreed that these have for their immediate antecedents, states of 



LAWS OF MIND. 531 

Dody. Every sensation has for its proximate cause some affection of 
the portion of our frame called the nervous system ; whether this affec- 
tion originate in the action of some external object, or in some patho- 
logical condition of the nervous organization itself The laws of this 
portion of our nature — the varieties of our sensations, and the physi- 
cal conditions on which they proximately depend — manifestly fall 
under the province of Physiology. 

Whether any other portion of our mental states are similarly de- 
pendent on physical conditions, is one of those scientific questions 
respecting human nature which are still in abeyance. It is yet unde- 
cided whether our thoughts, emotions, and volitions are generated 
through the intervention of material mechanism ; whether we have 
organs of thought and of emotion, in the same sense in which we have 
organs of sensation. Many eminent physiologists hold the affirmative. 
These contend, that a thought (for example) is as much the result of 
nervous agency, as a sensation : that some particular state of our nervous 
system, in particular of that central portion of it called the brain, invaria- 
bly precedes, and is presupposed by, every state of our consciousness. 
According to this theory, one state of mind is never really produced by 
another : all are produced by states of body. When one thought seems to 
call up another by association, it is not really a thought which recalls a 
thought ; the association did not exist between the two thoughts, but 
between the two states of the brain or nerves which preceded the 
thoughts ; one of those states recalls the other, each being attended, in 
its passage, by the particular mental state which is consequent upon it. 
On this theory, the uniformities of succession among states of mind 
would be mere derivative uniformities, resulting from the laws of suc- 
cession of the bodily states which cause them. There would be no 
original mental laws, no Laws of Mind in the sense in which I use the 
term, at all ; but Mental Science would be a mere branch, though the 
highest and most recondite branch, of the Science of Physiology. 
This is what M. Comte must be understood to mean, when he claims 
the scientific cognizance of moral and intellectual phenomena exclu- 
sively for physiologists ; and not only denies to Psychology, or Mental 
Philosophy properly so called, the character of a science, but places it, 
in the chimerical nature of its objects and pretensions, almost on a par 
with Astrology. 

But, after all has been said which can be said, it remains incontest- 
able by M. Comte and by all others, that there do exist uniformities of 
succession among states of mind, and that these can be ascertained by 
observation and experiment. Moreover, even if it were rendered far 
more certain than I believe it as yet to be, that every mental state has 
a nervous state for its immediate antecedent and proximate cause ; yet 
evei-y one must admit that we are wholly ignorant of the characteristics 
of these nervous states ; we know not, nor can hope to know, in what 
respect one of them differs from another; and our only mode of study- 
ing their successions or coexistences must be by observing the succes- 
sions and coexistences of the mental states of which they are supposed 
to be the generators or causes. The successions, therefore, which ob- 
tain among mental phenomena, do not admit of being deduced from 
the physiological laws of our nervous organization ; and all real 
knowledge of them must continue, for a long time at least, if not for 
ever, to be sought in the direct study, by observation and expeiiment, 



532 LOGIC OF THE MORAL SCIENCES. 

of the mental successions themselves. Since therefore the order of our 
mental phenomena must be studied in those phenomena, and not in- 
ferred fi'om the laws of any phenomena more general, there is a dis- 
tinct and separate Science of Mind. The relations, indeed, of that 
science to the Science of Physiology must never he overlooked or un- 
dervalued. It must by no means be forgotten that the law^s of mind 
may be derivative law^s resulting from law^s of animal hfe, and that 
their truth, therefore, may ultimately depend upon physical conditions ; 
and the influence of physiological states or physiological changes in 
altering or counteracting the mental successions, is one of the most 
important departments of psychological study. 

§ 3. The subject, then, of Psychology, is the uniformities of succes- 
sion, the laws, whether ultimate or derivative, according to which one 
mental state succeeds another; is caused by, or at the least, is caused 
to follow, another. Of these laws, some are general, others more 
special. The following are examples of the most general laws. 

First : Whenever any state of consciousness has once been excited 
in us, no matter by what cause ; an inferior degree of the same state of 
consciousness, a state of consciousness resembling the former, but 
inferior in intensity, is capable of being reproduced in us, without 
the presence of any such cause as excited it at first. Thus, if we have ' 
once seen or touched an object, we can afterwards think of the object 
although it be absent from our sight or firom our touch. If we have 
been joyful or grieved at some event, we can think of, or remember, 
our past joy or grief, although no new event of a happy or a painful 
iiature has taken place. When a poet has put together a mental pic- 
ture of an imaginary object, a Castle of Indolence, a Una, or a Juliet, 
he can afterwards think of the ideal object he has created, without any 
fresh act of intellectual combination. This law is expressed by saying, 
in the language of Hume, that every mental impression has its idea. 

Secondly : These Ideas, or secondary mental states, are excited by 
our impressions, or by other ideas, according to certain laws which 
are called Laws of Association. Of these laws the first is, that simi- 
lar ideas tend to excite one another. The second is, that when two 
impressions have been frequently experienced (or even thought of) 
either simultaneously or in immediate succession, then whenever 
either of these impressions or the idea of it recurs, it tends to excite 
the idea of the other. The third law is, that greater intensity, in either 
or both of the impressions, is equivalent, in rendering them excitable 
by one another, to a greater frequency of conjunction. These are the 
laws of Ideas : upon which I shall not enlarge in this place, but 
refer the reader to works professedly psychological, in particular to 
Mr. Mill's Analysis of the Phenomena of the Human Mind, where the 
principal laws of association, both in themselves and in many of their 
applications, are copiously exemplified, and with a masterly hand. 

These simple or elementary Laws of Mind have long been ascer- 
tained by the ordinary methods of experimental inquiry ; nor could 
they have been ascertained in any other manner. But a certain num- 
ber of elementary laws having thus been obtained, it is a fair subject 
of scientific inquirj how far those laws can be made to go in explain- 
ing the actual phenomena. It is obvious that complex laws of thought 
and feeling not only n»ay, but must, be generated from these simple 



LAWS OF IMIND. 533 

laws. And it is to be remarked, that the case is not always one of 
Composition of Causes : the effect of concurring causes is not always 
precisely the sum of the effects of those causes when separate, nor even 
always an effect of the same kind with them. Reverting to the dis- 
tinction which occupies so prominent a place in the theory of induc- 
tion ; the laws of the phenomena of mind are sometimes analogous to 
mechanical, but sometimes also to chemical laws. When many im- 
pressions or ideas are operating in the mind together, there sometimes 
takes place a process of a similar kind to chemical combination. 
When impressions have been so often experienced in conjunction, that 
each of them calls up readily and instantaneously the ideas of the whole 
group, those ideas sometimes melt and coalesce into one another, and 
appear not several ideas but one ; in the same manner as when the 
seven prismatic colors are presented to the eye in rapid succession, 
the sensation produced is that of white. But as in this last case it is 
correct to say that the seven colors when they rapidly follow one 
another generate white, but not that they actually are white ; so it 
appears to me that the Complex Idea, formed by the blending together 
of several simpler ones, should, when it really appears simple, (that is 
when the separate elements are not consciously distinguishable in it,) 
be said to result from, or be generated by, the simple ideas, not to con- 
sist of them. Our idea of an orange really consuts of the simple ideas 
of a certain color, a certain form, a certain taste and smell, &c., be- 
cause we can by interrogating our consciousness, perceive all these ele- 
ments in the idea. But we cannot perceive, in so apparently simple a 
feeling as onr perception of the shape of an object by the eye, all that 
multitude of ideas derived from other senses, wdthout which it is well 
ascertained that no such visual perception would ever have had exist- 
ence ; nor, in our idea of Extension, can we discover those elementary 
ideas of resistance, derived from our muscular frame, in which Dr. 
Brown has rendered it highly probable that the idea originates. These 
therefore are cases of mental chemistry : in which it is proper to say 
that the simple ideas generate, rather than that they compose, the com- 
plex ones. 

With respect to all the other constituents of the mind, its beliefs, 
its abstruser conceptions, its sentiments, emotions, and volitions ; there 
are some (among whom are Hartley, and the author of the Analysis) 
who think that the whole of these are generated from simple ideas of 
sensation, by a chemistry similar to that which we have just exempli- 
fied. I am unable to satisfy myself that this conclusion is, in the pres- 
ent state of our knowledge, fully made out. In many cases I cannot 
even perceive, that the line of argument adopted has much tendency 
to establish it. The philosophers to whom I have referred have, in- 
deed, conclusively shown that there is such a thing as mental chemis- 
tiy ; that the heterogeneous nature of a feeling. A, considered in 
relation to B and C, is no conclusive argument against its being gener- 
ated from B and C. Having proved this, they proceed to show, that 
where A is found, B and C were, or may have been, present, and why 
therefore, they say, should not A have been generated from B and C ? 
But even if this evidence were carried to the highest degi'ee of com- 
pleteness which it admits of; if it were showni that certain groups of 
associated ideas not only might have been, but actually were, present 
whenever the more recondite mental feeling was experienced ; this 



534 LOGIC OP THE MORAL SCIENCES. 

would amount only to the Method of Agreement, and could not prove 
causation until confirmed by the more conclusive evidence of the 
Method of Difference. If the question be v^hether Belief is a mere 
case of close association of ideas, it would be necessary to examine 
experimentally if it be true that any ideas whatever, provided they are 
associated together with the required degree of closeness, are suffi- 
cient to give rise to belief. If the inquiry be into the origin of moral 
feelings, the feelings for example of moral reprobation, the first step 
must be to compare all the varieties of actions or states of mind which 
are ever morally disapproved, and see whether in all these cases it can 
be shown that the action or state of mind had become connected by 
association, in the disapproving mind, with some particular class of 
hateful or disgusting ideas ; and the method employed is, thus far, that 
of Agreement. But this is not enough. Supposing this proved, we 
must try further, by the Method of Difference, whether this particular 
kind of hateful or disgusting ideas, when it becomes associated v^ith an 
action previously indifferent, will render that action a subject of moral 
disapproval. If this question can be answered in the affirmative, it is 
shown to be a law of the human mind, that an association of that par- 
ticular description is the generating cause of moral reprobation. But 
these experiments have either never been tried, or never with the de- 
gree of precision indispensable for conclusiveness; and, considering 
the difficulty of accurate experimentation upon the human mind, it will 
probably be long before they are so. 

It is further to be remembered, that even if all which this theory of 
mental phenomena contends for could be proved, we should not be the 
more enabled to resolve the laws of the more complex feelings into 
those of the simpler ones. The generation of one class of mental 
phenomena from another, whenever it can be made out, is a highly 
interesting fact in psychological chemistry ; but it no more supersedes 
the necessity of an experimental study of the generated phenomenon, 
than a knowledge of the properties of oxygen and sulphur enables us 
to deduce those of sulphuric acid vnthout specific observation and ex- 
periment. Whatever, therefore, may be the final issue of the attempt 
to account for the origin of our judgments, our desires, or our volitions, 
from simpler mental phenomena, it is not the less imperative to ascer- 
tain the sequences of the complex phenomena themselves, by special 
tudy in conformity to the canons of Induction. Thus, in respect of 
Belief, the psychologist will always have to inquire, what beliefs we 
have intuitively, and according to what laws one belief produces 
another ; what are the laws in virtue of which one thing is recognized 
by the mind, either rightly or erroneously, as evidence of another 
thing. In regard to Desire, he will examine what objects we desire 
naturally, and by what causes we are made to desire things originally 
indifferent or even disagreeable to us ; and so forth. It may be re- 
marked, that the general laws of association prevail among these more 
intricate states of mind, in the same manner as among the simpler 
ones. A desire, an emotion, an idea of the higher order of abstrac- 
tion, even our judgments and volitions when they have become habitual, 
are called up by association, according to precisely the same laws as 
our simple ideas. 

§ 4. In the course of these inquiries it will be natural and necessary 



LAWS OF MIND. 535 

to examine, how far the production of one state of mind by another is 
influenced by any assignable state of body. The commonest observa- 
tion shows that different minds are susceptible in very different degrees 
to the action of the same psychological causes. The idea, for example, 
of a given desirable object, will excite in different minds very different 
degrees of intensity of desire. The same subject of meditation, pre- 
sented to different minds, will excite in them very unequal degrees of 
intellectual action. These differences of mental susceptibility in dif- 
ferent individuals may be, ^r*^, original and ultimate facts, ox, secondly , 
they may be consequences of the previous mental history of those in- 
dividuals, or, thirdly and lastly, they may depend upon varieties of 
physical organization. That the previous mental history of the indi- 
viduals must have some share in producing or in modifying the whole 
of their present mental character, is an inevitable consequence of the 
laws of mind ; but that differences of bodily structure also cooperate, 
is the assertion not only of phrenologists, but, to a greater or less 
extent, of all physiologists who lay any stress upon the magnitude of 
the hemispheres of the brain, indicated by the facial angle, as a meas- 
ure of natural intelligence, or upon temperament as a source of 
moral and emotional peculiarities. 

What portion of these assertions the physiological school of psychol- 
ogists, whether phrenologists or otherwise, have either succeeded in 
establishing, or shown ground for supposing it possible to establish 
hereafter, I would not undertake to say. Nor do I believe that the 
inquiry will be brought to a satisfactory issue, while it is abandoned, 
as unfortunately it has hitherto been, to physiologists who have no 
adequate knowledge of mental laws, or psychologists who have no 
sufficient acquaintance with physiology. 

It is certain that the natural differences which really exist in the 
mental predispositions or susceptibilities of different persons, are often 
not unconnected with diversities in their organic constitution. But it 
does not therefore follow that these organic differences must in all 
cases influence the mental phenomena directly and immediately. They 
may often affect them through the medium of their psychological 
causes. For example, the idea of some particular pleasure may excite 
in different persons, even independently of habit or education, very 
different strengths of desire, and this may be the effect of their dif- 
ferent degrees or kinds of nervous susceptibility; but these organic 
differences, we must remember, wdll render the pleasurable sensation 
itself more intense in one of these persons than in the other ; so that 
the idea of the pleasure will also be an intenser feeling, and will, by 
the operation of mere mental laws, excite an intenser desire, without 
its being necessary to suppose that the desire itself is directly influ- 
enced by the physical peculiarity. As in this, so in many cases, such 
differences in the kind or in the intensity of the physical sensations as 
must necessarily result from differences of bodily organization, will of 
themselves account for many differences not only in the degi'ee, but 
even in the kind, of the other mental phenomena. So true is this, that 
even different qualities of mind, different types of mental character, 
will naturally be produced by mere differences of intensity in the sen- 
sations generally. This truth is so well exemplified, and in so short a 
compass, in a very able essay on Dr. Priestley, mentioned in a former 
chapter, that I think it right to quote the passage : — 



536 LOGIC OF THE MOfiAL SCIENCES. 

" The sensations which form the elements . of all knowledge are 
received either simultaneously or successively; when several are 
received simultaneously, as the smell, the taste, the color, the foi-m, 
&c., of a fruit, their association together constitutes our idea of an 
ohject ; when received successively, their association makes up the 
idea of an event. Anything, then, which favors the associations of 
synchronous ideas, will tend to produce a knowledge of objects, a 
perception of qualities ; while anything which favors association in the 
successive order, will tend to produce a knowledge of events, of the 
order of occurrences, and of the connexion of cause and effect: in 
other words, in the one case a perceptive mind, with a discriminative 
feeling of the pleasurable and painful properties of things, a sense of 
the grand and the beautiful, will be the result : in the other, a mind 
attentive to the movements and phenomena, a ratiocinative and philo- 
sophic intellect. Now it is an acknowledged principle, that all sensa,- 
tions experienced during the presence of any vivid impression, become 
strongly associated with it, and with each other ; and does it not follow, 
that the synchronous feelings of a sensitive constitution (^'.e. the one 
which has vivid impressions) will be more intimately blended than in 
a differently formed mind 1 If this suggestion has any foundation in 
truth, it leads to an inference not unimportant; that where nature has 
endowed an individual with great original susceptibility, he will proba- 
bly be distinguished by fondness for natural history, a relish for the 
beautiful and great, and moral enthusiasm ; where there is but a 
mediocrity of sensibility, a love of science, of abstract truth, with a 
deficiency of taste and of fervor, is likely to be the result." 

We see from this example, that when the general laws of mind are 
more accurately known, and above all, more skillfully applied to the 
detailed explanation of mental peculiarities, they will account for many 
more of those peculiarities than is ordinarily supposed. I by no means 
seek to imply from this that they will account for all ; but that which 
remains to be othervdse accounted for is merely a residual phenomenon ; 
and the amount of the residue can only be determined by persons already 
familiar with the explanation of phenomena by psychological laws. 

On the other hand, it is equally clear that when physiologists, taking 
into account the whole animal creation, attempt, by a judicious appli- 
cation of the Method of Concomitant Variations, grounded chiefly on 
extreme cases, to establish a connexion between the strength of differ- 
ent mental propensities or capacities and the proportional or absolute 
magnitudes of different regions of the brain ; the evidences which are 
or may be produced in support of this pretension, ought to be taken 
into serious consideration by psychologists. Nor will this part of the 
science of mind be ever cleared up, until those evidences shall be not 
only sifted and analyzed, but, when necessary, added to and completed, 
by persons sufficiently versed in psychological laws to be capable of 
discriminating how much of each phenomenon such laws will suffice to 
explain. 

Even admitting the influence of cerebral conformation to be as great 
as is contended for, it would still be a question how far the cerebral 
development determined the propensity itself, and how far it only acted 
by modifying the nature and degree of the sensations on which the 
propensity may be psychologically dependent. And it is certain that, 
in human beings at least, differences in education and in outward cir- 



ETHOLOGY. 537 

cumstances, together with physical differences in the sensations produ- 
ced in different individuals by the same external or internal cause, are 
capable of accounting for a far greater portion of character than is 
supposed even by the most moderate phrenologists. There are, how- 
ever, many mental facts which do not seem to admit of this mode of 
explanation. Such, to take the strongest case, are the various instincts 
of animals, the portion of human nature which con-esponds to those 
instincts. No mode has been suggested, even by way of hypothesis, 
in which these can receive any satisfactory, or even plausible, expla- 
nation from psychological causes alone ; and they may probably be 
found to have as positive, and even perhaps as direct and immediate, a 
connexion with physical conditions of the brain and nerves, as any of 
our mere sensations hav-^i. 

How much further this remark might be extended, I do not pretend 
to determine. My object is not to establish the doctrines, but to dis- 
criminate the ti'ue Method, of mental science ; and this, so far as 
regards the establishment of the general and elementary laws, may be 
considered to be sufficiently accomplished. 



CHAPTER V. 

OP ETHOLOGY, OR THE SCIENCE OF THE FORMATION OF CHARACTER. 

§ 1. The Laws of Mind, as characterized in the preceding chapter, 
constitute the universal or abstract portion of the philosophy of human 
nature ; and all the various truths of common experience, constituting 
a practical knowledge of mankind, must, to the extent to which they 
are truths, be results or consequences of these. Such familiar maxims, 
when collected d posteriori from observation of life, occupy among the 
truths of the science the place of what, in our analysis of Induction, 
have BO often been spoken of under the title of Empirical Laws. 

An Empirical Law (it will be remembered) is an uniformity, whether 
of succession or of coexistence, which holds true in all instances within 
our limits of observation, but is not of a nature to afford any assurance 
that it would hold beyond those limits ; either because the consequent 
is not really the effect of the antecedent, but forms part along with it 
of a chain of effects, flowing from prior causes not yet ascertained ; or 
because there is ground to believe that the sequence (though a case of 
causation) is resolvable into simpler sequences, and, depending there- 
fore upon a concurrence of several natural agencies, is exposed to an 
unknown multitude of possibilities of counteraction. In other words, 
an empirical law is a generalization, of which, not content with finding 
it true, we are obliged to ask, why is it true 1 knowing that its truth is 
not absolute, but depends upon some more general conditions, and that 
it can only be relied on in so far as there is ground of assurance that 
those conditions are realized. 

Now, the observations concerning human affairs collected from com- 
mon experience, ai*e precisely of this nature. Even if they were uni- 
versally and exactly true within the bounds of experience, which they 
never are, still they are not the ultimate laws of human action : they 
3Y ^ 



538 LOGIC OF THE MORAL SCIENCES. 

are not the principles of human nature, but results of those principles 
under the circumstances in which mankind have happened to be placed. 
When the Psalmist " said in his wrath that all men are liars," he enun- 
ciated what in some ages and countries is borne out by ample experi- 
ence; but it is not a law of man's nature to lie ; though it is one of the 
consequences of the laws of his nature, that the habit of lying is nearly 
universal when certain external circumstances exist universally, espe- 
cially circumstances productive of habitual distrust and fear. When 
the character of the old is asserted to be cautious, and of the young 
impetuous, this, again, is but an empirical law; for it is not because of 
their youth that the young are impetuous, nor because of their age that 
the old are cautious. It is because the old, during their many years of 
life, have generally had much experience of its various evils, and having 
suffered or seen others suffer much from incautious exposure to them, 
have acquired associations favorable to circumspection : while the 
young, as well from the absence of similar experience as from the 
greater strength of the inclinations which tempt them into danger, 
expose themselves to it more readily. Here, then, is the explanation 
of the empirical law ; here are the conditions which ultimately deter- 
mine whether the law holds good or not. If an old man has not been 
oftener than most young men in contact with danger and difficulty, he 
will be equally incautious : if a youth has not stronger passions than an 
old man, he probably will be as little enterprising. The empirical law 
derives whatever truth it has, from the causal laws of which it is a 
consequence. If we know those laws, we know what are the limits to 
the derivative law : while, if we have not yet accounted for the empir- 
ical law — if it rests only upon observation — there is no safety in apply- 
ing it far beyond the limits of time, place, and circumstance, in which 
the observations were made. 

The really scientific truths, then, are not these empirical laws, but 
the causal laws which explain them. The empirical laws of those 
phenomena which depend on known causes, and of which a general 
theory can therefore be constructed, have, whatever may be their 
value in practice, no other function in science than that of verifying 
the conclusions of theory. Still more must this be the case when most 
of the empirical laws amount, even within the limits of observation, 
only to approximate generalizations. 

§ 2. This however is not, so much as is sometimes supposed, a pe- 
culiarity of the sciences called moral. It is only in the simplest 
branches of science that empirical laws are ever exactly true ; and 
not always in those. Astronomy, for example, is the simplest of all 
the sciences which explain, in the concrete, the actual course of natu- 
ral events. The causes, or forces, on which astronomical phenomena 
depend, are fewer in number than those which determine any other of 
the great phenomena of nature. Accordingly, as each effect results 
from the conflict of but few causes, a great degree of regularity and 
uniformity might be expected to exist among the effects ; and such is 
really the case : they have a fixed order, and return in cycles. But 
propositions which should express, with absolute con-ectness, all the 
successive positions of a planet until the cycle is completed, would be 
of almost unmanageable complexity, and could be obtained from the- 
ory alone. The generalizations which can be collected on the subject 



ETHOLOGY. 539 

from direct observation, even such as Kepler's law, are mere approx- 
imations : the planets, owing to their perturbations by one another, do 
not move in exact ellipses. Thus, even in astfonomy, perfect exact- 
ness in the mere empirical laws is not to be looked for; much less, 
then, in more complex subjects of inquiry. 

The same example shows how little can be infen'ed against the 
universality or even the simplicity of the ultimate laws, from the im- 
possibility of establishing any but approximate empirical laws of the 
effects. The laws of causation according to which a class of phenom- 
ena are produced may be very few and simple, and yet the effects 
themselves may be so various and complicated that it shall be impossi- 
ble to trace any regularity whatever, extending completely through 
them. For the phenomena in question may be of an eminently modi- 
fiable character ; insomuch that innumerable circumstances are capa- 
ble of influencing the effect, although they may all do it according to a 
very small number of laws. Suppose that all which passes in the mind 
of man is determined by a few simple laws : still, if those laws be such 
that there is not one of the facts surrounding a human being, or of the 
events which happen to him, that does not influence in some mode or 
degree his subsequent mental history, and if the circumstances of dif- 
ferent human beings are extremely different, it will be no wonder if 
very few propositions can be made respecting the details of their con- 
duct or feelings, which will be true of all mankind. 

Now, without deciding whether the ultimate laws of our mental nature 
are few or many, it is at least certain that they are of the above descrip- 
tion. It is certain that our mental states, and our mental capacities 
and susceptibilities, are modified, either for a time or permanently, by 
everything which happens to us in life. Considering, therefore, how 
much these modifying causes differ in the case of any two individuals, 
it would be unreasonable to expect that the empirical laws of the hu- 
man mind, the generalizations we make respecting the feelings or ac- 
tions of mankind without reference to the causes that determine them, 
should be anything but approximate generalizations. They are the 
common wisdom of common life, and as such are invaluable ; espe- 
cially as they are mostly to be applied to cases not very dissimilar to 
those from which they were collected. But if maxims of this sort, col- 
lected from Englishmen, come to be applied to Frenchmen, or col- 
■ected from the present day, are applied to past or future generations, 
they are apt to be very much at fault. Unless we have resolved the 
empirical law into the laws of the causes upon which it depends, and 
ascertained that those causes extend to the case which we have in 
view, there can be no reliance placed in our inferences. For every 
individual is surrounded by circumstances different from those of every 
other individual ; every nation or generation of mankind fi'om every 
other nation or generation : and none of these differences are vnthout 
their influence in forming a different type of character. There is, in- 
deed, also a certain general resemblance ; but peculiarities of circum- 
stances are continually constituting exceptions even to the propositions 
which are true in the great majority of cases. 

Although, however, there is scarcely any mode of feeling or conduct 
which is, in the absolute sense, common to all mankind ; and though 
the generalizations which assert that any given variety of conduct or 
feeling vnll be found universally (however nearly they may approxi- 



540 LOGIC OF THE MORAL SCIENCES. 

mate to trutli within given limits of observation), wiU4oe considered as 
scientific propositions by no one who is at all familiar with scientific 
investigation ; yet all modes of feeling and conduct met with among 
mankind have causes which produce them ; and in the propositions 
which assign those causes will be found the explanation of the empiri- 
cal laws, and the limiting principle of our reliance on them. Men do 
not all feel and act alike in the same circumstances ; but it is possible 
to determine what makes one man, in a given position, feel or act in 
one way, another in another ; how any given mode of feeling and con- 
duct, compatible with the general laws (physical and mental) of human 
nature, has been, or may be, formed. In other words, mankind have 
not one universal character, but there exist universal laws of the For- 
mation of Character. And since it is by these laws, combined with 
the facts of each particular case, that the whole of the phenomena of 
human action and feeling are produced, it is upon these that every 
rational attempt to construct the science of human nature in the con- 
crete, and for practical purposes, must proceed. 

§ 3. The laws then of the formation of character being the principal 
object of scientific inquiry into human nature, it remains to determine 
the method of investigation best fitted for ascertaining them. And the 
logical principles according to which this question is to be decided, 
must be those which preside over every other attempt to investigate 
the laws of very complex phenomena. For it is evident that both the 
character of any human being, and the aggregate of the circumstances 
by which that character has been formed, are facts of a high order of 
complexity. Now to such cases we have seen that the Deductive 
Method, setting out from general laws, and verifying their conse- 
quences by specific experience, is alone applicable. The grounds of 
this great logical doctrine have formerly been stated : and its truth 
will derive additional support from a brief examination of the speciali- 
ties of the present case. 

There are only two modes in which laws of nature can be ascer- 
tained : deductively, and experimentally : including under the denomi- 
nation of experimental inquiry, observation as well as artificial experi- 
ment. Are the laws of the formation of character susceptible of a 
satisfactory investigation by the method of experimentation ] Evi- 
dently not ; because even if we suppose unlimited power of varying 
the experiment, (which is abstractedly possible, though no one but an 
oriental despot either has that power, or if he had, would be disposed 
to exercise it,) a still more essential condition is wanting : the power of 
performing any of the experiments with scientific accuracy. 

The instances requisite for the prosecution of a directly experimental 
inquiry into the formation of character, would be a number of human 
beings to bring up and educate, from infancy to mature age. And to 
perform any one of these experiments with scientific propriety, it would 
be necessary to know and record every sensation or impression received 
by the young pupil from a period long before it could speak ; includ- 
ing its own notions respecting the sources of all those sensations and 
impressions. It is not only imposssble to do this completely, but even 
to do so much of it as should constitute a tolerable approximation. 
One apparently trivial circumstance which eluded our vigilance, might 
let in a train of impressions and associations sufficient to vitiate the ex- 



ETHOLOGY, 541 

periment as an authentic exhibition of the effects flowing from given 
causes. No one who has sufficiently reflected on education is igno- 
rant of this truth ; and whoever has not, will find it most instructively 
illustrated in the writings of Rousseau and Helvetius on that great 
subject. 

Under this impossibility of studying the laws of the formation of 
character by experiments purposely contrived to elucidate them, there 
remains the resource of simple observation. But if it be impossible to 
ascertain the influencing circumstances with any approach to complete- 
ness, even when we have the shaping of them ourselves, much more 
impossible is it when the cases are further removed from our observa- 
tion, and altogether out of our control. Consider the difficulty of the 
very first step — of ascertaining what actually is the character of the 
individual, in each particular case that we examine. There is hardly 
any person living, concerning some essential part of whose character 
there are not differences of opinion even among his intimate acquaint- 
ance : and a single action, or conduct continued only for a $hort time, 
goes a very little way indeed towards ascertaining it. We can only 
make our observations in a rough way, and en masse ; not attempting 
to ascertain completely, in any given instance, what character has been 
formed, and still less by what causes ; but only observing in what state 
of previous circumstances it is found that certain marked mental quali- 
tios or deficiencies oftenest exist. These conclusions, besides that they 
are mere approximate generalizations, deserve no reliance even as 
such, unless the instances are sufficiently numerous to eliminate not 
only chance, but every accidental circumstance in which a number of 
the cases examined may happen to have resembled one another. So 
numerous and vai'ious, moreover, are the circumstances which form 
individual character, that the consequence of any particular combina- 
tion is hardly ever some definite and strongly marked character, always 
found where that combination exists, and not otherwise. What is ob- 
tained, even after the most extensive and accurate observation, is mere- 
ly a comparative result ; as for example, that in a given number ojf 
Frenchmen, taken indiscriminately, there will be found more persons 
of a parficular mental tendency, and fewer of the contrary tendency, 
tlian among an equal number of Italians or English, similarly taken ; 
or thus : of a hundred Frenchmen and an equal number of Englishmen,, 
fairly selected, and aiTanged according to the degree in which they 
possess a particular quality, each number, 1, 2, 3, &c., of the one series, 
will surpass in that quality the corresponding number of the other. 
Since, therefore, the comparison is not one of kinds, but of ratios and 
degrees ; and since in proportion as the differences are slight, it re- 
quires a greater number of instances to eliminate chance ; it cannot 
often happen to any one to know a sufficient number of cases with the 
accuracy requisite for making the sor.t of comparison last mentioned ; 
less than which, however, would not constitute a real induction. Ac- 
cordingly there is hardly one cm-rent opinion respecting the characters 
of nations, classes, or descriptions of persons, which is universally ac- 
knowledged as indisputable.* 

* The most favorable cases for making such approximate generalizations are what may- 
be termed collective instances ; where we are fortunately enabled to see the whole class 
respecting which we are inquiring, in action at once ; and, from the qualities displayed by 
the collective body, are able to judge what must be the qualities of the majority of the ia- 



542 LOGIC OF THE MORAL SCIENCES. 

And finally, if we could even obtain by way of experiment a much 
more satisfactory assurance of these generalizations than is really possi 
ble, they would still be only empirical laws. They would show, indeed, 
that there was some connexion between the type of character formed, 
and the circumstances existing in the case ; but not what the precise 
connexion was, nor to which of the peculiarities of those circumstances 
the effect was really owing. They could only, therefore, be received 
as results of causation, requiring to be resolved into the general laws 
of the causes ; until the determination of which, we could not judge 
within what limits the derivative laws might serve as presumptions in 
cases yet unknovvm, or even be depended upon as permanent in the 
very cases from which they were collected. The French people had, 
or were supposed to have, a certain national character : but they drive 
out their royal family and aristocracy, alter their institutions, pass 
through a series of extraordinary events for half a century, and at the 
end of that time are found to be, in many respects, totally altered. 
The laboring classes are observed to be different from the higher in a 
long series of qualities ; but it becomes customary, perhaps, to give 
them an education more approximating to that of their superiors in 
station, and in the next age the differences, though still real, are no 
longer the same. 

But if the differences which you think you observe between French 
and English, or between persons of station and persons of no station, 
can be connected with more general laws ; if they be such as would 
naturally flow from the differences of government, former customs, and 
physical peculiarities in the two nations, and from the diversities of 
education, occupations, and social position in the different classes of 
society ; then, indeed, the coincidence of the two kinds of evidence 
justifies us in believing that we have both reasoned rightly and observed 
rightly. Our observation, though not sufficient as proof, is ample as 
veiification. And having ascertained not only the empirical laws but 
the causes of the peculiarities, we need be under no difficulty in judg- 
ing how far they may be expected to be permanent, or by what circum- 
stances they would be modified or destroyed. 

§ 4. Since then it is impossible to obtain really accurate propositions 
respecting the formation of character from observation and experi- 
ment alone, we are driven perforce to that which, even if it had not 
been the indispensable, would have been the most perfect mode of in- 
vestigation, and which it is one of the principal aims of philosophy to 
extend ; namely, that which tries its experiments not upon the complex 



dividuals composing it. Thus the character of a nation is shown in its acts as a nation : 
not so much in the acts of its government, for those are much influenced by other causes ; 
but in the current popular maxims, and other marks of the general direction of public 
opinion ; in the character of the men or writings that are held in permanent esteem or 
admiration ; in laws and institutions, so far as they are the work of the nation itself, or 
are acknowledged and supported by it; and so forth. But even here there is a large mar- 
gin of doubt and uncertainty. These things are liable to be influenced by many circum- 
stances : they are partly determined by the distinctive qualities of that nation or body of 
persons, but partly also by external causes which would influence any other body of per- 
sons in the same manner. In order, therefoi'^, to make the experiment really complete, we 
ought to be able to try it without variation upon other nations : to try how Englishmen 
would act or feel if placed in the same circumstances in which we have supposed French- 
men to be placed ; to apply, in short, the Method of Difference as well as that of Agree- 
ment. Now these experiments we cannot try, nor even approximate to. 



ETHOLOGY. 543 

facts, but upon the simple ones of which they are compounded ; and 
after ascertaining the laws of the causes, the composition of which 
gives rise to the complex phenomena, then considers whether these 
will not explain and account for the approximate generalizations which 
have been framed empirically respecting the sequences of those com- 
plex phenomena. The laws of the formation of character are, in short, 
derivative laws, resulting from the general laws of the mind ; and they 
are to be obtained by deducing them from those general laws ; by sup- 
posing any given set of circumstances, and then considering what, 
according to the laws of mind, will be the influence of those circum- 
stances on the formation of character. 

A science is thus formed, to which I would propose to give the 
name of Ethology, or the Science of Character ; from rjdog, a word 
more nearly corresponding to the term " character" as I here use it, 
than any other word in the same language. The name is perhaps 
etymologically applicable to the entire science of our mental and moral 
nature ; but if, as is usual and convenient, we employ the name Psy- 
chology for the science of the elementary laws of mind, Ethology will 
serve for the subordinate science which determines the kind of charac- 
ter produced, in conformity to those general laws, by any set of cir- 
cumstances, physical and moral. According to this definition, Ethology 
is the science which corresponds to the art of education ; in the widest 
sense of the tenn, including the formation of national character as well 
as individual. It would indeed be vain to expect (however completely 
the laws of the formation of character might be ascertained) that we 
could know so accurately the circumstances of any given case as to be 
able positively to predict the character that would be produced in that 
case. But we must remember that a degree of knowledge far short of 
the power of actual prediction, is often of great practical value. There 
may be great power of influencing phenomena, with a very imperfect 
knowledge of the causes by which they are in any given instance de- 
termined. It is enough that we know that certain means have a ten- 
dency to produce a given effect, and that others have a tendency to 
frustrate it. When the circumstances of an individual or of a nation 
are in any considerable degree under our control, we may, by our 
knowledge of tendencies, be enabled to shape those circumstances in 
a manner much more favorable to the ends we desire than the shape 
which they would of themselves assume. This is the limit of our 
power ; but within this limit the power is a most important one. 

The science of Ethology may be called the Exact Science of Human 
Nature ; for its truths are not, like the empirical laws which depend 
upon them, approximate generalizations, but real laws. It is, however, 
(as in all cases of complex phenomena,) necessary to the exactness of 
the propositions, that they should be hypothetical only, and affirm 
tendencies, not facts. They must not assert that something wdll always, 
or certainly, happen ; but only that such and such will be the effect of 
a given cause, so far as it operates uncounteracted. It is a scientific 
proposition, that cowardice tends to make men cruel; not that it 
always makes them so : that an interest on one side of a question 
tends to bias the judgment ; not that it invariably does so : that expe- 
rience tends to give wisdom ; not that such is always its effect. These 
propositions, being assertive only of tendencies, are not the less univer- 
sally true because the tendencies may be coimteracted. 



644 LOGIC OF THE MORAL SCIENCES. 

§ 5. Wliile on the one hand Psychology is altogether, or principally, 
a science of observation and experiment, Ethology, as I have conceived 
it, is, as I have already remarked, altogether deductive. The one 
ascertains the simple lavv^s of Mind in general, the other traces their 
operation in complex combinations of circumstances. Ethology stands 
to Psychology in a relation very similar to that in which the various 
branches of natural philosophy stand to mechanics. The principles of 
Ethology are properly the middle principles, the axiomata media (as 
Bacon would have said) of the scieuce of mind : as distinguished, on 
the one hand from the empirical laws resulting from simple observa- 
tion, and on the other from the highest generalizations. 

And this seems a very proper place for a logical remark, which, 
though of general application, is of peculiar importance in reference to 
the present subject. Bacon has judiciously observed that the axiomata 
media of every science principally constitute its value. The lowest 
generalizations, until explained by and resolved into the middle princi- 
ples of which they are the consequences, have only the imperfect 
accuracy of empirical laws; while the most general laws are too 
general, and include too few circumstances, to give sufficient indica- 
tion of what happens in individual cases, where the circumstances are 
almost always immensely numerous. In the importance, therefore, 
which Bacon assigns, in every science, to the middle principles, it is 
impossible not to agree with him. But I conceive him to have been 
radically wrong in his doctrine respecting the mode in which these 
axiomata media should be arrived at ; although there is no one propo- 
sition laid down in his works for which he has been so extravagantly 
eulogized. He enunciates as an universal rule, that induction should 
proceed from the lowest to the middle principles, and from those to the 
highest, never reversing that order, and consequently leaving no room 
for the discovery of new principles by way of deduction at all. It is 
not to be conceived that a man of Bacon's sagacity could have fallen 
into this mistake, if there had existed in his time, among the sciences 
which treat of successive phenomena, one single instance of a deduc- 
tive science, such as mechanics, astronomy, optics, acoustics, &c., now 
are. In those sciences it is evident that the higher and middle princi- 
ples are by no means derived from the lowest, but the reverse. In 
some of them the very highest generalizations were those earliest as- 
certained with any scientific exactness; as, for example (in mechanics), 
the laws of motion. Those general laws had not indeed at first the 
acknowledged universality which they acquired after having been suc- 
cessfully employed to explain many classes of phenomena to which 
they were not originally seen to be appHcable ; as when the laws of 
motion were employed in conjunction with other laws to explain de- 
ductively the celestial phenomena. Still, the fact remains, that the 
propositions which were afterwards recognized as the most general 
truths of the science, were, of all its accurate generalizations, those 
earliest arrived at. Bacon's greatest merit cannot, therefore, consist, 
as we are so often told that it did, in exploding the vicious method 
pursued by the ancients of flying to the highest generalizations first, 
and deducing the middle principles from them ; since this is neither a 
vicious nor an exploded, but the universally accredited method of 
modern science, and that to which it owes its greatest triumphs. The 
error of ancient speculation did not consist in making the largest 



ETHOLOGY. 545 

generalizations first, but in making them without the aid or warrant of 
rigorous inductive methods, and applying them deductively without 
the needful use of that important part of the Deductive Method termed 
Verification. 

The order in which truths of the various degrees of generality 
should be ascertained, cannot, I apprehend, be prescribed by any un- 
bending rule. I know of no maxim which can be laid down on the 
subject, but to obtain those first, in respect to which the conditions of 
a real induction can be first and most completely realized. Now, 
wherever our means of investigation can reach causes, without stopping 
at the empirical laws of the effects, the simplest cases, being those in 
which fewest causes are simultaneously concerned, will be most 
amenable to the inductive process; and these are the cases which 
elicit laws of the greatest comprehensiveness. In every science, there- 
fore, which has reached the stage at which it becomes a science of 
causes, it will be usual, as well as desirable, first to obtain the highest 
generalizations, and then deduce the more special ones from them. 
Nor can I discover any foundation for the Baconian maxim, so much 
extolled by subsequent writers, except this : That before we attempt 
to explain deductively from more general laws any new class of phe- 
nomena, it is desirable to have gone as far as is practicable in ascer- 
taining the empirical laws of those phenomena ; so as to compare the 
results of deduction, not with one individual instance after another, 
but with general propositions expressive of the points of agreement 
which have been found among many instances. For if Newton had 
been obliged to verify the theory of gravitation, not by deducing from 
it Kepler's laws, but by deducing all the observed planetary positions 
which had served Kepler to establish those laws, the Newtonian theory 
would probably never have emerged from the state of an hypothesis. 

The applicability of these remarks to the special case under con- 
sideration, cannot admit of question. The science of the formation of 
character is a science of causes. The subject is one to which those 
among the canons of induction, by which laws of causation are ascer- 
tained, can be rigorously applied. It is, therefore, both natural and 
advisable to ascertain the simplest, which are necessarily the most 
general, laws of causation first, and to deduce the middle principles 
from them. In other words. Ethology, the deductive science, is a sys- 
tem of corollaries from Psychology, the experimental science. 

§ 6. Of these, the earlier alone has been, as yet, really conceived or 
studied as a science : the other. Ethology, is still to be created. But 
all things are prepared for its creation. The empirical laws, destined 
to verify its deductions, have been afforded in abundance by every 
successive age of humanity ; and the premisses tor the deductions are 
now sufl^ciently complete. Exceptnig the degree of uncertainty which 
still exists as to the extent of the natural differe^ices of human minds, 
and the physical circumstances on which chese may be dependent, 
(considerations which are of secondary importance when we are con- 
sidering mankind in the average, or en masse,) I believe most compe- 
tent judges wiU agree that the generpi lavvs of the different constituent 
elements of human nature are nov sufficiently understood, to render 
it possible for a competent thinner to deduce from those laws the 
particular type of character w^nch would be formed, in mankind gen- 
3Z 



546 LOGIC OF THE MORAL SCIENCES. 

erally, by any assumed set of circumstances. A science of Ethology, 
founded upon the laws of Psychology, is therefore possible; though 
little has yet been done, and that little not at all systematically, towards 
forming it. The progress of this important but most imperfect science 
will depend upon a double process : first, that of deducing theoreti- 
cally the ethological consequences of particular circumstances of 
position, and comparing them with the recognized results of common 
experience ; and secondly, the reverse operation ; increased study of 
the various types of human nature that are to be found in the world, 
conducted by persons not only capable of analyzing and recording the 
circumstances in which these types severally prevail, but also suf- 
ficiently acquainted with psychological laws, to be able to explain and 
account for the characteristics of the type by the pecuHarities of the 
circumstances : the residuum, if any, being set down to the account of 
congenital predispositions. 

The experimental or a posteriori part of this process is carried on in 
our own day with much greater activity than heretofore. The great 
step, therefore, which remains to be taken in Ethology, is to deduce 
the requisite middle principles from the general laws of Psychology. 
The subject to be studied is, the origin and sources of all those qualities 
in human beings which are most interesting to us, either as facts to be 
produced, to be avoided, or merely to be understood : and the object 
is, to determine, from the general laws of mind, combined with the 
general position of our species in the universe, what actual or possible 
combinations of circumstances are capable of promoting or of pre- 
venting the production of those qualities. A science which possesses 
middle principles of this kind, arranged in the order, not of causes, 
but of the eftects which it is desirable to produce or to prevent, is 
duly prepared to be the foundation of the corresponding Art. And 
when Ethology shall be thus prepared, practical education will be the 
mere transformation of those principles into a parallel system of pre- 
cepts, and the adaptation of these to the sum total of the individual 
circumstances which exist in each particular case. 

It is hardly necessary again to repeat that, as in every other deduc- 
tive science, the work of verification a posteriori must proceed jpari 
passu with that of deduction a priori. The inference given by theory 
as to the type of character which would be formed by any given cir- 
cumstances, must be tested by specific experience of those circum- 
stances whenever obtainable ; and the whole conclusions of the science 
must undergo g, perpetual verification and correction from the general 
remarks afforded by common experience respecting human nature in 
our own age, and by history respecting times gone by. The conclusions 
of theory cannot be trusted, unless confirmed by observation; nor those 
of observation, unless they can be affiliated to the theory, by deducing 
them from the laws of human nature and from a close analysis of the 
circumstances of the particular situation. It is the accordance of 
these two kinds of evidence, separately taken — the consilience (as Mr. 
Whewell would express it) of a priori reasoning and specific experi- 
ence — which forms the on>y sofficient ground for the principles of any 
science so "immersed in matttr," dealing with so complex and so 
concrete phenomena, as Ethology, 



SOCIAL SCIENCE. 547 

CHAPTER VI. 

GENERAL CONSIDERATIONS ON THE SOCIAL SCffiNCE. 

§ 1. Next after the science of individual man, comes the science of 
man in society : of the actions of collective masses of mankind, and the 
various phenomena which constitute social life. •^ 

If the formation of individual character is already a complex sub- 
ject of study, this subject, it is evident, must be greatly more complex; 
because the number of concurrent causes, all exercising more or less 
influence on the total effect, is greater, in the proportion in which a 
nation, or the species at large, exposes a larger surface to the opera- 
tion of agents, psychological and physical, than any single individual. 
If it was necessary to prove, in opposition to an existing prejudice, that 
the simpler of the two is capable of being a subject of science ; the 
prejudice is likely to be yet stronger against the possibility of giving a 
scientific character to the study of Politics, and of the phenomena of 
Society. It is, accordingly, but of yesterday that the conception of a 
political or social science has existed, anywhere but in the mind of 
here and there an insulated thinker, generally very ill prepared for its 
realization : although the subject itself has of all others engaged the 
most general attention, and been a theme of interested and earnest dis- 
cussions almost from the beginning of recorded time. 

The condition indeed of politics, as a branch of knowledge, was 
until very lately, and has scarcely even yet ceased to be, that which 
Bacon animadverted upon, as the natural state of the sciences while 
their cultivation is abandoned to practitioners; not being carried on as 
a branch of speculative inquiry, but only with a view to the exigencies 
of daily practice, and t\iG fructif era experimentci, therefore, being aimed 
at, almost to the exclusion of the lucifera. Such Was medical science, 
before physiology and natural history began to be cultivated as 
branches of general knowledge. The only questions examined were, 
what diet is wholesome, or what medicine will cure some given dis- 
ease ; without any previous systematic inquiry into the laws of nutiition, 
and of the healthy and morbid action of the different organs, on which 
laws the effect of any diet or medicine must evidently depend. And in 
politics, the questions which engaged general attention were similar. 
Is such an enactment, or such a form of government, beneficial or the 
reverse — either universally, or to some particular community ] without 
inquiry into the general conditions by which the operation of legisla- 
tive measures, or the effects produced by forms of government, are 
determined. 

And even among the few who did carry their speculations to that 
gi-eater length, it is only at a still more recent date that social phe- 
nomena, properly so called, have begun to be looked upon as having 
any natural tendencies of their own. It is hardly an exaggeration to 
say that society has usually, both by practitioners in politics and by 
philosophical speculators on forms of government, from Plato to 
Bentham, been deemed to be whatever the men who compose it 
choose to make it. The only questions which people thought of pro- 
posing to themselves were, Would such and such a law or institution 



"S^^iS LOGIC OF THE MORAL SCIENCES. 

be beneficial 1 and, if so, can legislators or the public be persuaded, or 
otherwise induced, to adopt it? For hardly any notion was enter- 
tained that there were limits to the power of human will over the phe- 
nomena of society, or that any social arrangements which would be 
desirable, could be impracticable from incompatibility with the proper- 
ties of the subject matter : the only obstacle was supposed to lie in the 
private interests or prejudices, which hindered men from being willing 
lo see them tried. Students in politics thus attempted to study the 
piJthology and therapeutics of the social body, before they had laid the 
necessary foundation in its physiology ; to cure disease, without under- 
standing the laws of health. And the result was such as it must always 
be when men even of great ability attempt to deal with the complex 
questions of a science before its simpler and mere elementary proposi- 
tions have been established. 

No wonder that when the phenomena of society have so rarely been 
contemplated in the point of view characteristic of science, the philo- 
sophy of society should have made little progress ; should contain few 
general propositions sufficiently precise and certain, for common in- 
quirers to recognize in them a scientific character. The vulgar notion 
accordingly is, that all pretension to lay down general truths on politics 
and society is quackery ; that no universality and no certainty are 
attainable in such matters. What partly excuses this common notion 
is, that it is really not without foundation in one particular sense. A 
large proportion of those who have laid claim to the character of philo- 
sophic politicians, have attempted, not to ascertain universal sequences, 
but to frame universal precepts. They have had some one form of 
government, or system of laws, to fit all cases; a pretension well 
meriting the ridicule with which it is treated by practitioners, and 
wholly unsupported by the analogy of the art to which, from the nature 
of its subject, that of politics must be the most nearly allied. No one 
now supposes it possible that one remedy can cure all diseases, or even 
the same disease in all constitutions and habits of body. Yet physi- 
ology is admitted to be a science, and medical practice, when it disre- 
gards the indications of the science, to be criminal quackery. 

It is not necessary to even the perfection of a science, that the 
corresponding art should possess universal, or even general niles. 
The phenomena of society might not only be completely dependent 
upon known causes, but the mode of action of all those causes might 
be reducible to laws of considerable simplicity, and yet no two cases 
might admit of being treated in precisely the same manner. So great 
might be the variety of circumstances on which the results in different 
cases depend, that art might not have a single general precept to give, 
except that of watching the circumstances of the case, and adapting 
our measures to the effects which, according to the principles of the 
science, result from those circumstances. But because, in so compli- 
cated a class of subjects, it is absurd to lay down practical maxims of 
universal application, it does not follow that the phenomena do not 
conform to universal laws. 

§ 2. All phenomena of society are phenomena of human nature, 
generated by the action of outward circumstances upon masses of 
human beings : and if, therefore, the phenomena of human thought, 
feeling, and action, are subject to fixed laws, the phenomena of society 



SOCIAL SCIENCE, 549 

cannot but conform to fixed laws, the consequences of the preceding. 
There is, indeed, no hope that these laws, though our knowledge of 
them were as certain and as complete as it is in astronomy, would 
enable us to predict the history of society, like that of the celestial 
appearances, for thousands of years to come. But the difference of 
certainty is not in the laws themselves, it is in the data to which these 
laws are to be applied. In astronomy the causes influencing the result 
are few, and change little, and that little according to known laws : we 
can ascertain what they are now, and thence determine what they will 
be at any epoch of a distant future. The data, therefore, in astronomy, 
are as certain as the laws themselves. The circumstances, on the con- 
trary, which influence the condition and progress of society, are in- 
numerable, and perpetually changing; and though they all change in 
obedience to causes, and therefore to laws, the multitude of the causes 
is so great as to defy our limited powers of calculation. Not to say 
that the impossibility of applying precise numbers to facts of such a 
description, would set an impassable limit to the possibility of calcu- 
lating them beforehand, even if the powers of the human intellect 
were otherwise adequate to the task. 

But, as we before remarked, an amount of knowledge quite insuffi- 
cient for prediction, may be most valuable for guidance. The science 
of society would have attained a very high point of perfection, if it 
enabled us, in any given condition of social affairs, in the condition for 
instance of Europe or any European country at the present time, to 
understand by what causes it had, in any and every particular, been 
made what it was ; whether it was tending to any, and to what, 
changes ; what effects each feature of its existing state was likely to 
produce in the future ; and by what means any of those effects might 
be prevented, modified, or accelerated, or a different class of effects 
superinduced. There is nothing chimerical in the hope that general 
laws, sufficient to enable us to answer these various questions for any 
country or time with the individual circumstances of which we are 
well acquainted, do really admit of being ascertained ; and moreover, 
that the other branches of human knowledge, which this undertaking 
presupposes, are so far advanced that the time is ripe for its accom- 
plishment. Such is the object of the Social Science. 

That the nature of what I consider the true method of the science 
may be made more palpable, by first showing what that method is not ; 
it will be expedient to characterize briefly two radical misconceptions 
of the proper mode of philosophizing on society and government, one 
or other of which is, either explicitly or more often unconsciousl}', 
entertained by almost all who have meditated or argued respecting the 
logic of politics since the notion of ti'eating it by strict rules, and on 
Baconian principles, has been current among the more advanced 
thinkers. These erroneous methods, if the word method can be 
applied to erroneous tendencies arising from the absence of any suf- 
ficiently distinct conception of method, may be aptly termed the 
Experimental, or Chemical, mode of investigation, and the Abstract, 
or Geometrical mode. We shall besrin with the former. 



550 LOGIC OP THE MORAL SCIENCES, 

CHAPTER VII. 

OP THE CHEMICAL, OR EXPERIMENTAL, METHOD IN THE SOCIAL SCIENCE. 

§ 1. The laws of the phenomena of society are, and can be, nothing 
hut the laws of the actions and passions of human beings united to- 
gether in the social state. Men, however, in a state of society, are 
still men ; their actions and passions are obedient to the laws of indi- 
vidual human nature. Men are not, when brought together, converted 
into another kind of substance, with different properties; as hydrogen 
and oxygen are different from water, or as hydrogen, oxygen, carbon, 
and azote, are different from nerves, muscles, and tendons. Human 
beings in society have no properties but those which are derived from, 
and may be resolved into, the laws of the nature of individual man. In 
social phenomena the Composition of Causes is the universal law. 

Now, the method of 'philosophizing which may be termed chemical, 
overlooks this fact, and proceeds as if the nature of man as an indi- 
vidual were not concerned at all, or concerned in a very inferior de- 
gree, in the operations of man in society. All reasoning in politics or 
social affairs, grounded upon principles of human nature, is objected 
to by reasoners of this sort, under such names as " abstract theory." 
For governing their opinions and conduct, they profess to demand, in 
all cases without exception, specific experience. 

This mode of thinking is not only general with practitioners in 
politics, and with that very numerous class who (on a subject which no 
one, however ignorant, thinks himself incompetent to discuss) profess 
to guide themselves by common sense rather than by science ; but is 
often countenanced by persons with greater pretensions to instruction ; 
pe sons who, having sufficient acquaintance with books and with the 
current ideas to have heard that Bacon taught men to follow expe- 
rience, and to ground their conclusions upon facts instead of meta- 
physical dogmas, think that by treating political facts in as directly 
experimental a method as chemical facts, they are showing themselves 
true Baconians, and proving their adversaries to be mere syllogizers 
and schoolmen. As, however, the notion of the applicability of experi- 
mental methods to political philosophy cannot coexist with any just 
conception of these methods themselves, the kind of arguments from 
experience which the chemical theory brings forth as its fruits (and 
which form the staple, in this country especially, of parliamentary and 
hustings' oratory) are such as, at no time since Bacon, would have 
been admitted to be valid in chemistry itself, or in any other branch of 
experimental science. They are such as these : that the prohibition of 
foreign commodities must conduce to national wealth, because England 
has flourished under it, or because countries in general which have 
adopted it have flourished ; that our laws, or our internal administra- 
tion, or our constitution, are excellent for a similar reason ; and the 
eternal arguments from historical examples, from Athens or Rome, 
from the fires in Smithfield, or the French Revolution, 

I will not waste time in contending against modes of argumentation 
which no person, with the smallest practice in estimating evidence, 
could possibly be betrayed into ; which draw conclusions of general 



THE CHEMICAL METHOD. 551 

application from a single unanalyzed instance, or arbitrarily refer an 
effect to some one among its antecedents, without any process of elimi- 
nation or comparison of instances. It is a rule both of justice and of good 
sense to grapple not with the absurdest, but with the most reasonable 
form of a wrong opinion. We shall suppose our inquirer acquainted 
with the true conditions of experimental investigation, and competent in 
point of acquirements for realizing them, if they can be realized in any 
case of the kind. He shall know as much of the facts of history as 
mere erudition can teach — as much as can be proved by testimony, 
without the assistance of any theory; and if those mere facts, properly 
collated, can fulfill the conditions of a real induction, he shall be quali- 
fied for the task. 

But, that no such attempt can have the smallest chance of success, 
has been abundantly shown in the tenth chapter of the Third Book.* 
We there examined whether effects which depend upon a complication 
of causes, can be made the subjects of a true induction by observation 
and experiment ; and concluded, on the most convincing grounds, that 
they cannot. Since, of all effects, none depend upon so great a com- 
plication of causes as social phenomena, we might leave our case to 
rest in safety upon that previous showing. But a logical principle, as 
yet so little familiar to the ordinary run of thinkers, requires to be in- 
sisted upon more than once, in order to make the due impression ; and 
the present being the case which of all others exemplifies it the most 
strongly, there will be advantage in restating the grounds of the general 
maxim, as applied to the specialities of the class of inquiries now under 
consideration. 

§ 2. The first difficulty which meets us in the attempt to apply ex- 
perimental methods for ascertaining the laws of social phenomena, is 
that we are without the means of making artificial experiments. Even 
if we could contrive experiments at leisure, and try them without 
limit, we should do so under immense disadvantages ; both from the im- 
possibility of ascertaining and taking note of all the facts of each case, 
and because (those facts being in a perpetual state of change) before 
sufficient time had elapsed to ascertain the result of the experiment, 
some material circumstances would always have ceased to be the same. 
But it is unnecessary to consider the logical objections which would exist 
to the conclusiveness of our experiments, since we palpably never 
have the power of trying any. We can only watch those which nature 
produces, or those which are produced for other reasons. We cannot 
adapt our logical means to our wants, by varying the circumstances as 
the exigencies of elimination may require. If the spontaneous instances, 
formed by contemporary events and by the successions of phenomena 
recorded in history, afford a sufficient variation of circumstances, an 
induction from specific experience is attainable ; othervnse not. The 
question to be resolved is, therefore, whether the requisites for induc- 
tion respecting the causes of political effects or the properties of 
pohtical agents, are to be met with in history 1 including under the 
term, contemporary history. And in order to give fixity to our con- 
ceptions, it will be advisable to suppose this question asked in reference 
to some special subject of political inquiry or controversy ; such as that 

* Supra, pp. 259-264. 



552 LOGIC OF THE MORAL SCIENCES. 

great topic of debate in the present day, the operation of restrictive and 
prohibitory commercial legislation upon national wealth. Let this, then, 
be the scientific question to be investigated by specific experience. 

§ 3. In order to apply to the case the most perfect of the methods 
of experimental inquiry, the Method of Difference, we require to find 
two instances, which tally in every particular except the one which is 
the subject of inquiry. If two nations can be found which are alike in 
all natural advantages and disadvantages ; whose people resemble each 
other in every quality, physical and moral, innate and acquired ; whose 
habits, usages, opinions, laws, and institutions are the same in all re- 
spects, except that one of them has a more protective tariff, or in other 
respects interferes more with the freedom of industry ; and if one of 
these nations is found to be rich, and the other poor, or one richer 
than the other, this will be an experimentum crucis: a real proof, by 
experience, which of the two systems is most favorable to national 
riches. But the supposition that two such instances can be met with 
is absurd on the face of it. Nor is such a concurrence even abstract- 
edly possible. Two nations which agreed in everything except their 
commercial policy would agree also in that. Differences of legislation 
are not inherent and ultimate diversities ; are not properties of Kinds. 
They are effects of preexisting causes. If the two nations differ in 
this portion of their institutions, it is from some difference in their 
position, and thence in their apparent interests, or in some portion or 
other of their opinions, habits, and tendencies ; which opens a view of 
further differences without any assignable limit, capable of operating 
on their industrial prosperity, as well as on every other feature of their 
condition, in more ways than can be enumerated or imagined. There 
is thus a demonstrated impossibility of obtaining, in the investigations 
of the social science, the conditions required for the most conclusive 
form of inquiry by specific experience. 

In the absence of the direct, we may next try, as in other cases, the 
supplementary resource, called in a former place the Indirect Method 
of Difference : which, instead of two instances differing in nothing but 
the presence or absence of a given circumstance, compares two classes 
of instances respectively agreeing in nothing but the presence of a cir- 
cumstance on the one side and its absence on the other. To choose 
the most advantageous case conceivable (a case far too advantageous 
to be ever obtained), suppose that we compare one nation which has a 
restrictive policy, with two or more nations agi-eeing in nothing but in 
permitting free trade. We need not now suppose that either of these 
nations agrees with the first in all its circumstances ; one may agree 
with it in some of its circumstances, and another in the remainder. 
And it may be argued, that if these nations remain poorer than 
the restrictive nation, it cannot be for want either of the first or of the 
second set of circumstances, but it must be for want of the protecting . 
system. If (we might say) the restrictive nation had prospered from 
the one set of causes, the first of the free-trade nations would have 
prospered equally j if by leason of the other, the second would : but 
neither has: therefore the prosperity was owing to the restrictions. 
This will be allowed to be a very favorable specimen of an argument 
from specific experience in politics, and if this be inconclusive, it would 
not be easy to find another preferable to it. 



THE CHEMICAL METHOD. 553 

Yet, that it is inconclusive, scarcely requires to be pointed out. Why 
must the prosperous nation have prospered from one cause exclusively 1 
National prosperity is alw^ays the collective result of a multitude of 
favorable circumstances : and of these, the restrictive nation may unite 
a gi'eater number than either of the others, although it may have all of 
those circumstances in common with either one or the other of them. 
Its prosperity may be partly owing to circumstances common to it 
with one of those nations, and partly with the other, while they, having 
each of them only half the number of favorable circumstances, have 
remained inferior. So that the closest imitation which can be made, in 
the social science, of a genuine induction from direct experience, gives 
bat a specious semblance of conclusiveness, without any real value 

§ 4. The Method of Difference in either of its forms being thus 
completely out of the question, there remains the Method of Agree- 
ment. But we are already aware of how little value this method is, 
in cases admitting Plurality of Causes : and social phenomena are 
those in which the plurality prevails in the utmost possible extent. 

Suppose that the observer makes the luckiest hit which could be 
given him by any conceivable combination of chances : that he finds 
two nations which agree in no circumstance whatever, except in having 
a restrictive system, and in being prosperous ; or a number of nations, 
all prosperous, which have no antecedent circumstances common to 
them all but that of having a restrictive policy. It is unnecessary to go 
into the consideration of the impossibility of ascertaining from history, 
or even from contemporary observation, that such is really the fact ; 
that the nations agree in no other circumstance capable of influencing 
the case. Let us suppose this impossibility vanquished, and the fact 
ascertained that they agreed only in a restrictive system as an antece- 
dent, and industrial prosperity as a consequent. What degree of pre- 
sumption does this raise, that the restrictive system caused the pros- 
perity ] One so trifling as to be equivalent to none at all. That some 
one antecedent is the cause of a given effect, because all other antece- 
dents have been found capable of being eliminated, is a just inference, 
only if the effect can have but one cause. If it admits of several, no- 
thing is more natural than that each of these shoiild separately admit of 
being eliminated. Now, in the case of political phenomena, the suppo- 
sition of unity of cause is not only wide of the ti'uth, but at an immeas- 
urable distance from it. The causes of every social phenomenon which 
we are particularly interested about, security, wealth, freedom, good 
government, public virtue, public intelligence, or their opposites, are 
infinitely numerous : especially the external or remote causes, which 
alone are, for the most part, accessible to direct observation. No one 
cause suffices of itself to produce any one of these phenomena; while 
there are countless causes which have some influence over them, and 
may cooperate either in their production or in their prevention. From 
the mere fact, therefore, of our having been able to eliminate some 
circumstances, we can by no means infer that this circumstance was not 
instrumental to the effect even in the very instances from which we 
have eliminated it. We may conclude that the effect is sometimes 
produced without it ; but not that, when present, it does not contribute - 
its part. 

Similar objections will be found to apply to the Method of Concom- 
4A 



554 LOGIC OF THE MORAL SCIENCES. 

itaiit Variations. If the causes which act upon the state of any society- 
produced effects differing from one another in kind; if wealth depended 
upon one cause, peace upon another, a third made a people virtuous, a 
fourth intelligent; we might, though unable to sever the causes from 
one another, refer to each of them that property of the effect which 
waxed as it waxed, and which waned as it waned. But every attribute 
of the social body is influenced by innumerable causes ; and such is the 
mutual action of the coexisting elements of society, that whatever 
affects any one of the more important of them, will by that alone, if it 
does not affect the others directly, affect them indirectly. The effects, 
therefore, of different agents not being different in quality, while the 
quantity of each is the mixed result of all the agents, the variations of 
the aggregate cannot bear any unifoi-m proportion to those of any one 
of its component parts. 

§ 5. There remains the Method of Residues ; which appears, on the 
first view, less foreign to this kind of inquiry than the three other meth- 
ods, because it only requires that we should accurately note the circum- 
stances of some one country, or state of society. Making allowance, 
thereupon, for the effect of all causes whose tendencies are known, the 
residue which those causes are inadequate to explain may plausibly be 
imputed to the remainder of the circumstances which are known to 
have existed in the case. Something similar to this is the method 
which Coleridge* describes himself as having followed in his political 
essays in the Morning Post. " On every great occurrence I endeav- 
ored to discover in past history the event that most nearly resembled 
it. I procured, wherever it was possible, the contemporary historians, 
memorialists, and pamphleteers. Then fairly subtracting the points of 
difference from those of likeness, as the balance favored the former or 
the latter, I conjectured that the result would be the same or different. 
As for instance in the series of essays entitled ' A comparison of France 
under Napoleon with Rome under the first Caesars,' and in those which 
followed, 'on the probable final restoration of the Bourbons.' The 
same plan I pursued at the commencement of the Spanish Revolution, 
and with the same success, taking the war of the United Provinces 
with Philip II. as the groundwork of the comparison." In this inquiry 
Coleridge no doubt employed the Method of Residues ; for, in " sub- 
tracting the points of difference from those of likeness," he doubtless 
weighed, and did not content himself with numbering them : he doubt- 
less took those points of agreement only, which might be known from 
their own nature to be capable of influencing the effect, and, allowing 
for that influence, concluded that the remainder of the result would be 
referable to the points of difference. 

Whatever may be the efficacy of this method, it is, as we long ago 
remarked, not a method of pure observation and experiment ; it con- 
cludes, not from a comparison of instances, but firom the comparison 
of an instance with the result of a previous deduction. Applied to so- 
cial phenomena, it presupposes that the causes from which part of the 
effect proceeded are already known ; and as we have shown that these 
cannot have been known by specific experience, they must have been 
learned by deduction from the principles of human nature ; experience 

* Biographia Literaria, i,, 214. 



THE GEOMETRICAL METHOD. 665 

being called in only as a supplementary resource, to determine the causes 
which produced an unexplained residue. But if the principles of hu- 
man nature may be had recourse to for the establishment of some po- 
litical truths, they may for all. If it be admissible to say, England 
must have prospered by reason of her prohibitory system, because 
after allowing for all the other tendencies which have been operating, 
there is a portion of prosperity still to be accounted for ; it must be 
admissible to go to the same source for the effect of the prohibitory 
system, and examine what account the laws of human motives and ac- 
tions will enable us to give of its tendencies. Nor, in fact, will the 
experimental argument amount to anything, except in verification of a 
conclusion drawn from those general laws. For we may subtract the 
effect of one, two, three, or four causes, but we shall never succeed in 
subtracting the effect of all causes except one ; while it would be a 
curious instance of the dangers of too miich caution, if, to avoid 
depending on a priori reasoning concerning the effect of a single 
cause, we should oblige ourselves to depend upon as many separate 
a priori reasonings as there are causes operating concurrently with 
that particular cause in some given instance. 

We have now sufficiently characterized the absurd misconception 
of tlie mode of investigation proper to political phenomena, which I 
have termed the Chemical Method. So lengthened a discussion would 
not have been necessary, if the claim to decide authoritatively on polit- 
ical doctrines were confined to persons who had competently studied 
any one of the higher departments of physical science. But since the 
generality of those who reason on political subjects, satisfactorily to 
themselves and to a more or less numerous body of admirers, know 
nothing whatever of the methods of physical investigation beyond a 
few precepts which they continue to parrot after Bacon, being entirely 
unaware that Bacon's conception of scientific inquiry has done its 
work, and that science has now advanced intQ a higher stage ; there 
are probably many to whom such remarks as the foregoing may still 
be useful. In an age in which chemistry itself, when attempting to 
deal with the more complex chemical sequences, those of the animal 
or even the vegetable organism, has found it necessary to become, and 
has succeeded in becoming, a Deductive Science — it is not to be ap- 
prehended that any person of scientific habits, who has kept pace wdth 
the general progress of the knowledge of nature, can be in danger of 
applying the methods of elementary chemistry to explore the sequences 
of the most complex order of phenomena in existence. 



CHAPTER VIII. 

OF THE GEOMETRICAL, OR ABSTRACT METHOD. 

§ 1. The misconception discussed in the preceding chapter is, as we 
said, chiefly committed by persons not much accustomed to scientific 
investigation : practitioners in politics, who rather employ the common- 
places of philosophy to justify their practice, than seek to guide their 
practice by any philosophic views ; or imperfectly educated men, who, 



556 LOGIC OF THE MOEAL SCIENCES. 

in ignorance of the careful selection and elaborate comparison of 
instances required for the formation of a sound theory, attempt to 
found one upon a few coincidences which they have casually noticed. 
The erroneous method of which we are now to ti'eat is, on the con- 
trary, peculiar to thinking and studious minds. It never could have 
suggested itself but to persons of some familiarity with the nature of 
scientific research ; who — being aware of the impossibility of establish- 
ing, by casual observation or direct experimentation, a true theory of 
sequences so complex as are those of the social phenomena — have 
recourse to the simpler laws which are immediately operative in those 
phenomena, and which are no other than the laws of the nature of the 
human beings therein concerned. These thinkers perceive (what the 
partisans of the chemical or experimental theory do not) that the phi- 
losophy of society is a deductive science. But, from an insufficient 
consideration of the specific nature of the subject matter — and often 
because (their own scientific education having stopped short in too 
early a stage) geometry stands in their minds as the type of all deductive 
science ; it is to geometry, rather than to astronomy and natural phi- 
losophy, that they unconsciously assimilate the deductive science of 
society. 

Among the differences between geometry (a science of coexistent 
facts, altogether independent of the laws of the succession of phe- 
nomena) and those physical Sciences of Causation which have been 
rendered deductive, the following is one of the most conspicuous : 
That geometry affords no room for what so constantly occurs in me- 
chanics and its applications, the case of conflicting forces; of causes 
which counteract or modify one another. In mechanics we continually 
find two or more moving forces producing, not motion, but rest ; or 
motion in a different direction from that which would hav^ been pro- 
duced by either of the generating forces. It is true that the effect of 
the joint forces is the same when they act simultaneously, as if they had 
acted one after another, or by turns; and it is in this that the difference 
between mechanical and chemical laws consists. But still the effects, 
whether produced by successive or by simultaneous action, do, wholly 
or in part, cancel one another : what the one force does, the other, 
partly or altogether, undoes. There is no similar state of things in 
geometry. The result which follows from one geometrical principle 
has nothing that contradicts the result which follows from another. 
What is proved true from one geometrical theorem, what would be 
true if no other geometrical principles existed, cannot be altered and 
made no longer true by reason of some other principle. What is once 
proved true must be true in all cases, whatever supposition may be 
made in regard to any other matter. 

Now a conception, similar to this last, would appear to have been 
formed of the social science, in the minds of the earlier of those who 
have attempted to cultivate it by a deductive method. Mechanics 
would be a science very similar to geometry, if every motion resulted 
from one force alone, and not fi'om a conflict of forces. In the 
geometrical theory of society, it seems to be supposed that this is 
really the case with the social phenomena; and that each of them 
results always from only one force, one single property of human 
nature. 

At the point which we have now reached, it cannot be necessary to 



THE GEOMETRICAL METHOD. 657 

say anything either in proof or in illustration of the assertion that such 
is not the true character of the social phenomena. There is not, 
among these most complex and (for that reason) most modifiable of 
all phenomena, any one over which innumerable forces do not exercise 
influence ; which does not depend upon a conjunction of very many 
causes. We have not, therefore, to prove the notion in question to be 
an error, but to prove that the error has been committed ; that so mis- 
taken a conception of the mode in which the phenomena of society 
are produced, has actually been entertained. 

§ 2. One numerous division of the reasoners who have treated social 
facts according to geometrical methods, not admitting of any modifica- 
tion of one law by another, must for the present be left out of consider- 
ation : because in them this error is complicated with, and is the effect 
of, another fundamental misconception, of which we have already taken 
some notice, and which will be treated of more fully before we con- 
clude. I speak of those who deduce political conclusions not from 
laws of nature, not from sequences of phenomena, real or imaginary, 
but from unbending practical maxims. Such, for example, are all 
who found their theories of politics upon v/hat is called abstract right, 
that is to say, upon universal precepts ; a pretension of which we have 
already noticed the chimerical nature. Such, in like manner, are those 
who make the assumption of a social contract, or any other kind of 
original obligation, and apply it to particular cases by mere interpre- 
tation. But in this the fundamental error is the attempt to treat an art 
like a science, and to have a deductive art ; the irrationality of which 
will be shown in a future chapter. It will be proper to take our ex- 
emplification of the geometrical theory from those thinkers who have 
avoided this additional error, and who entertain, so far, a juster idea 
of the nature of political inquiry. 

We may cite, in the first instance, those who assume, as the princi- 
ple of their political philosophy, that government is founded on fear ; 
that the dread of each other is the one motive by which human beings 
were originally brought into a state of society, and are still held in it. 
Some of the earlier scientific inquirers into politics, in particular 
Hobbes, assumed this proposition, not by implication, but avowedly, 
as the foundation of their doctrine, and attempted to build a complete 
philosophy of politics thereupon. It is true that Hobbes (who is so 
much the most considerable of these, that we need not particularly ad- 
vert to any of the rest) did not find this one maxim sufficient to carry 
him through the whole of his subject, but was obliged to eke it out by 
the double sophism of an original contract. I call this a double 
sophism ; first, as passing off a fiction for a fact, and secondly, as as- 
suming a practical principle, or precept, as the basis of a theory ; 
which is a petitio principii, since (as we noticed in treating of that 
Fallacy) every rule of conduct, even though it be so binding a one as 
the observance of a promise, must rest its own foundations upon the 
theory of the subject, and the theory, therefore, cannot rest upon it. 

§ 3. Passing over less important instances, I shall come at once to 
the most remarkable example afforded by our own times of the 
geometrical method in politics ; emanating from persons who were 
well aware of the distinction between Science and Art ; who knew 



558 LOGIC OF THE MORAL SCIENCES. 

that rules of conduct must follow, not precede, the ascertainment of 
laws of nature, and that the latter, not the former, is the legitimate field 
for the application of the deductive method. I allude to the interest- ' 
philosophy of the Bentham school. 

The profound and original thinkers who are commonly known under 
this description, founded their general theory of government upon one 
comprehensive premiss, namely, that men's actions are always deter- 
mined by their interests. There is an ambiguity in this last expres- 
sion ; for, as the same philosophers, especially Bentham, systematical- 
ly gave the name of an interest to anything which a person likes, the 
proposition may be understood to mean only this, that men's actions 
are always determined by their wishes. In this sense, however, it 
would not bear out any of the consequences which these philosophers 
drew from it : and the word, therefore, in their political reasonings, 
must be understood to mean (which is also the explanation they them- 
selves, on such occasions, gave of it) what is commonly termed pri- 
vate, or worldly, interest. 

Taking the doctrine, then, in this sense, an objection presents itself 
in limine which might be deemed a fatal one, namely, that so sweep- 
ing a proposition is far from being universally true. Men are not 
governed in all their actions by their worldly interests. This, how- 
ever, is by no means so conclusive an objection as it at first appears ; 
because in politics we are for the most part concerned with the con- 
duct not of individual men, but either of a series of men (as a succes- 
sion of kings), or a body or mass of men, as a nation, an aristocracy, 
or a representative assembly. And whatever is true of a large majori- 
ty of mankind, may, without much error, be taken for true of any suc- 
cession of persons, considered as a whole, or of any collection of per- 
sons in which the act of the majority becomes the act of the whole 
body. Although, therefore, the maxim is sometimes expressed in a 
manner unnecessarily paradoxical, the consequences drawn from it will 
hold equally good if the assertion be limited as follows — Any succes- 
sion of men, or the majority of any body of men, will be governed in 
the bulk of their conduct by their personal interests. We are bound 
to allow to this school of philosophers the benefit of this more rational 
statement of their fundamental maxim, which moreover is in strict con- 
formity to the explanations which, when considered to be called for, 
have been given by themselves. 

The theory goes on to infer, correctly enough, that if the actions of 
mankind are determined in the main by their selfish interests, the only 
rulers who will govern according to the interest of the governed, are 
those whose selfish interests are in accordance with it. And to this is 
added a third proposition, namely, that no rulers have their selfish 
interest identical with that of the governed, unless it be rendered so 
by accountability, that is, by dependence upon the will of the governed. 
In other words (and as the result of the whole), that the desire of retain- 
ing or the fear of losing their power, and whatever is thereon consequent, 
is the sole motive which can be relied on for producing, on the part 
of rulers, a course of conduct in accordance with the general interest. 

We have thus a fundamental theorem of political science, consisting 
of three syllogisms, and depending chiefly upon two general premisses, 
in each of which a certain effect is considered as determined only by 
one cause, not by a concurrence of causes. In the one, it is assumed 



THE GEOMETRICAL METHOD. 559 

that the actions of average rulers are determined solely by self-interest ; 
in the other, that the sense of identity of interest with the governed, 
is produced and producible by no other cause than responsibility. 

Neither of these propositions is by any means true ; the last is ex- 
tremely wide of the truth. 

It is not true that the actions even of average rulers are wholly, or 
anything approaching to wholly, determined by their personal interest, 
or even by their own opinion of their personal interest. I do not speak 
of the influence of a sense of duty, or feelings of philanthropy, mo- 
tives never to be exclusively relied on, although (except in countries 
or during periods of great moral debasement) they influence almost all 
rulers in some degree, and some rulers in a very great degree. But I 
insist only upon what is true of all rulers, viz., that the character and 
course of their actions is largely influenced (independently of personal 
calculation) by the habitual sentiments and feelings, the general modes 
of thinking and acting, which prevail throughout the community of 
which they are members ; as well as by the feelings, habits, and modes 
of thought which characterize the particular class in that community 
to which they themselves belong. And no one will understand or be 
able to decipher their system of conduct, who does not take all these 
things into account. They are also much influenced by the maxims and 
traditions which have descended to them from other rulers, their pred- 
ecessors; and which have been knovsni to maintain, during long pe- 
riods, a successful struggle in a direction contrary to the private 
interests of the rulers for the time being. I put aside the influence of 
other less general causes. Although, therefore, the private interest of 
the rulers or of the ruling class is a very powerful force, constantly in 
action, and exercising the most important influence upon their con- 
duct ; there is also, in what they do, a large portion which that private 
interest by no means affords a sufficient explanation of: and even the 
particulars which constitute the goodness or badness of their govern- 
ment, are in some, and no small degree, influenced by those among 
the circumstances acting upon them, which cannot, with any propriety, 
be included in the term self-interest. 

Turning now to the other proposition, that responsibility to the gov- 
erned is the only cause capable of producing in the rulers a sense of 
identity of interest with the community ; this is still less admissible as 
an universal truth, than even the former. We are not speaking of 
perfect identity of interest, which is an impracticable chimera ; which, 
most assuredly, responsibility to the people does not give. We speak 
of identity in essentials; and the essentials are different at different 
places and times. There are a large number of cases in which those 
things which it is most for the interest of the people that their ruler 
should do, are also those which he is prompted to do by his strongest 
personal interest, the consolidation of his power. The suppression, 
for instance, of anarchy and resistance to law — the complete establish- 
ment of the authority of the central government, in a state of society 
like that of Europe in the middle ages — is the strongest interest of the 
people, and also of the rulers, simply because they are the rulers ; and 
responsibility on their part could not strengthen, though in many con- 
ceivable ways it might weaken, the motives prompting them to pursue 
this object. During the gi^eater part of the reign of Queen Elizabeth, 
and of many other monarchs who might be named, the sense of iden- 



560 LOGIC OF THE MORAL SCIENCES. 

tity of interest between the sovereign and the majority of the people 
was probably stronger than it usually is in responsible governments ; 
everything that the people had most at heart, the monarch had at heart 
too. Had Peter the Great, or the rugged savages whom he began to 
civilize, the truest inclination towards the things which were for the 
real interest of those savages 1 

I am not here attempting to establish a theory of government, and 
am not called upon to determine the proportional weight v/hich ought 
to be given to the circumstances which this school of geometrical poli- 
ticians left out of their system, and those which they took into it. I 
am only concerned to show that their method was unscientific ; not to 
measure the amount of error which may have affected their practical 
conclusions. 

It is but justice to them, however, to remark, that their mistake was 
not so much one of substance as of form ; and consisted in presenting 
in a systematic shape, and as the scientific treatment of a great philo- 
sophical question, what should have passed for that which it really 
was, the mere polemics of the day. Although the actions of rulers are 
by no means wholly determined by their selfish interests, it is as a 
security against those selfish interests that constitutional checks are 
required ; and for that purpose such checks, in England, and in many 
other countries, can in no manner be dispensed with. It is true, more- 
over, that in the particular stage of civilization through which Europe 
is now passing, either express or virtual responsibility to the governed 
is the only means practically available to create a feeling of identity of 
interest, in the cases, and on the points, where that feeling does not 
sufficiently exist. To all this, and to the arguments which may be 
founded upon it in favor of measures for the correction of our repre- 
sentative system, I have nothing to object ; but I confess my regret, 
that the small though highly important portion of the philosophy of 
government, which was wanted for the immediate purpose of serving 
the cause of parliamentary reform, should have been held forth by phi- 
losophers of such eminence as a complete theory. 

It is not to be imagined possible, nor is it true in point of fact, that 
these philosophers regarded the few premisses of their theory as in- 
cluding all that is required for explaining social phenomena, or for 
determining the choice of forms of government and measures of legis- 
lation and administration. They were too highly instructed, of too 
comprehensive intellect, and some of them of too sober and practical 
a character, for such an error. They would have applied and did 
apply their principles with innumerable allowances. But it is not 
allowances that are wanted. There is little chance of making due 
amends in the superstructure of a theory for the want of sufficient 
breadth in its foundations. It is unphilosophical to construct a science 
out of a few of the agencies by which the phenomena are determined, 
and leave the rest to the routine of practice or the sagacity of conjec- 
ture. We either ought not to pretend to scientific forms, or we ought 
to study all the determining agencies equally, and endeavor, so far as 
it can be done, to include all of them within the pale of the science ; 
else we shall infallibly bestow a disproportionate attention upon those 
which our theory takes into account, while we mis-estimate the rest, 
and probably underrate their importance. That the deductions should 
be from the whole and not from a part opiy of the laws of nature that 



PHYSICAL METHOD. 561 

are concerned, would be desirable even if those omitted were so insig- 
nificant in comparison with the others, that they might, for most pur- 
poses and on most occasions, be left out of the account. But this is 
far indeed from being true in the social science. The phenomena of 
society do not depend, in essentials, upon any one agency or law of 
human nature, with only inconsiderable modifications from others. 
The whole of the laws of human nature influence those phenomena, 
and there is not one which influences them in a small degree. There 
is not one, the removal or any great alteration of which would not 
materially affect the whole aspect of society, and change more or less 
most of the principal sequences of the social phenomena. 

The theory which has been the subject of these remarks is, in this 
country at least, the principal contemporary example of what I have 
styled the geometrical method of philosophizing in the social science; 
and our examination of it has, for this reason, been more detailed than 
might otherwdse have been deemed necessary in a work like the 
present. Having*now sufficiently illustrated the two erroneous methods, 
we shall pass without further preliminary to the true method ; that 
which proceeds (conformably to the practice of the higher branches 
of physical science) deductively indeed, but by deduction from many, 
not from one or a very few, original premisses ; considering each effect 
as (what it really is) an aggregate result of many causes, operating 
sometimes through the same, sometimes through different mental agen- 
cies, or laws of human nature. 



CHAPTER IX. 

OF THE PHYSICAL, OR CONCRETE DEDUCTIVE, METHOD. 

§ 1. After what has been said to illustrate the nature of the inquiry 
into the social phenomena, the general character of the method pro- 
per to that inquiry is sufficiently evident, and needs only to be recap- 
itulated, not proved. However complex the phenomena, all their 
sequences and coexistences result from the laws of the separate ele- 
ments. The effect which is produced, in social phenomena, by any 
complex set of circumstances, amounts precisely to the sum of the 
effects of the circumstances taken singly : and the complexity does not 
arise from the number of the laws themselves, which is not remarkably 
great; but from the extraordinary number and variety of the data or 
elements — of the agents which, in obedience to that small number of 
laws, cooperate towards the effect. The Social Science, therefore, 
(which I shall henceforth, with M. Comte, designate by the more com- 
pact term Sociology,) is a deductive science ; not, indeed, after the 
model of geometry, but after that of the higher physical sciences. It 
infers the law of each effect from the laws of causation upon which 
that effect depends ; not, however, from the law merely of one cause, 
as in the geometrical method ; but by considering all the causes which 
conjunctly influence the effect, and compounding their laws with one 
another. Its method, in short, is the Concrete Deductive Method : 
that of which astronomy furnishes the most perfect, natural philosophy 
4 B 



562 LOGIC OF THE MORAL SCIENCES. 

a somewhat less perfect example, and the employment of which, with 
the adaptations and precautions required by the subject, is beginning 
to regenerate physiology. 

Nor does it admit of doubt, that similar adaptations and precautions 
are indispensable in sociology. In applying, to that most complex of 
all studies, what is demonstrably the sole method capable of throwing 
the light of science even upon phenomena of a far inferior degree of 
complication, we ought to be aware that the same superior complexity 
which renders the instrument of Deduction more necessary, renders 
it also more precarious ; and we must be prepared to meet, by appro- 
priate contrivances, this increase of difficulty. 

The actions and feelings of human beings in the social state, are, no 
doubt, entirely governed by psychological and ethological laws ; what- 
ever influence any cause exercises upon the social phenomena, it exer- 
cises through those laws. Supposing, therefore, the laws of human 
actions and feelings to be sufficiently known, there is no extraordi- 
nary difficulty in determining from those laws, the natxu-e of the social 
effects which any given cause tends to produce. But when the ques- 
tion is that of compounding several tendencies together, and com- 
puting the aggi-egate result of many coexistent causes ; and especially 
when, by attempting to predict what will actually occur in a given 
case, we incur the obligation of estimating and compounding together 
the influences of all the causes which happen to exist in that case ; we 
attempt a task, to proceed far in which, certainly surpasses the com- 
pass of the human faculties. 

If all the resources of science are not sufficient to enable us to calcu- 
late a priori, with complete precision, the mutual action of three 
bodies gravitating towards one another ; it may be judged with what 
prospects of success we should endeavor, from the laws of human na- 
ture only, to calculate the result of the conflicting tendencies which 
are acting in a thousand different directions and promoting a thousand 
different changes at a given instant in a given society : although we 
might and ought to be able, from the laws of human nature, to distin- 
guish correctly enough the tendencies themselves, so far as they de- 
pend on causes accessible to our observation ; and to determine the 
direction which each of them, if acting alone, would impress upon 
society, as well as, in a general way at least, to pronounce that some 
of these tendencies are more powerful than others. 

But, without dissembling the necessary imperfections of the d priori 
method when applied to such a subject, neither ought we, on the other 
hand, to exaggerate them. The same objections which apply to the 
Method of Deduction in this its most difficult employment, apply to it, 
as we formerly showed,* in its easiest ; and would even there have 
been insuperable if there had not existed, as was then fully explained, 
an appropriate remedy. This remedy consists in the process which, 
under the name of Verification, we have characterized as the third 
essential constituent part of the Deductive Method ; that of collating 
the conclusions of the ratiocination either with the concrete phenom- 
ena themselves, or, when such are obtainable, wdth their empirical 
laws. The ground of confidence in any concrete deductive science is 
not the a priori reasoning, but the consilience between its results and 

* Supra, pp. 268-9. 



PHYSICAL METHOD. 563 

those of observation a posteriori. Either of these processes when di- 
vorced from the other diminishes in value as the subject increases in 
complication, and this in so rapid a ratio as soon to become entirely 
worthless ; but the reliance to be placed in the concurrence of the two 
sorts of evidence, not only does not diminish in anything like the same 
proportion, but is not necessarily much diminished at all. Nothing 
more results than a disturbance in the order of precedency of the two 
processes, sometimes amounting to its actual inversion : insomuch that 
instead of deducing our conclusions by reasoning, and verifying them 
by observation, we in some cases begin by obtaining them conjectu- 
rally from specific experience, and afterwards connect them with the 
principles of human nature by a priori reasonings, which reasonings 
are thus a real Verification. 

The greatest living authority on scientific methods in general, and 
the only philosopher who, with a competent knowledge of those 
methods, has attempted to characterize the Method of Sociology, M. 
Comte, considers this inverse order as inseparably inherent in the 
nature of sociological speculation. He looks upon the social science 
as essentially consisting of generalizations from history, verified, not 
originally suggested, by deduction from the laws of human nature. 
Such an opinion, from such a thinker, deserves the most serious con- 
sideration ; but though I shall presently endeavor to show the emi- 
nent importance of the truth which it contains, I cannot but think that 
this truth is enunciated in too unlimited a manner, and that there is 
considerable scope in sociological inquiry for the direct, as well as for 
the inverse. Deductive Method. 

It will, in fact, be shown in the next chapter, that there is a kind of 
sociological inquiries to which, from their prodigious complication, the 
method of direct deduction is altogether inapplicable, while by a happy 
compensation it is precisely in these cases that we are able to obtain 
the best empirical laws : to these inquiries, therefore, the Inverse 
Method is exclusively adapted. But there are also, as will presently 
appear, other cases in which it is impossible to obtain from direct ob- 
servation anything worthy the name of an empirical law ; and it for- 
tunately happens that these are the very cases in which the Direct 
Method is least affected by the objection which undoubtedly must al- 
ways affect it in a certain degree. 

We shall begin, then, by looking at Sociology as a science of direct 
Deduction, and considering what can be accomplished in it, and under 
what limitations, by that mode of investigation. We shall, then, in a 
separate chapter, examine and endeavor to characterize the inverse 
process. 

§ 2. It is, in the first place, distinctly apparent that Sociology, con- 
sidered as a system of deductions a priori, cannot be a science of pos- 
itive predictions, but only of tendencies. We may be able to con- 
clude, from the laws of human nature applied to the circumstances of 
a given state of society, that a particular cause will operate in a cer- 
tain manner unless counteracted ; but we can never be assured to 
what extent or amount it will so operate, or afiirm with certainty that 
it will not be counteracted ; because we can seldom know, even ap- 
proximatively, all the agencies which may coexist with it, and still less 
calculate the collective result of so many combined elements. The 



564 LOGIC OF THE MORAL SCIENCES. 

remark, however, must here be once more repeated, that knowledge 
insuificient for prediction may be most valuable for guidance.' It is 
not necessary for the wise conduct of the affairs of society, no more 
than of any man's private concerns, that we should be able to foresee 
infallibly the results of what we do. We must seek our objects by 
means which may perhaps be defeated, and take precautions against 
dangers which possibly may never be reaHzed. The aim of practical 
politics is to surround the society which is under our superintendence 
with the greatest possible number of circumstances of which the ten 
dencies are beneficial, and to remove or counteract, as far as practi- 
cable, those of which the tendencies are injurious. A knowledge of 
the tendencies only, though without the power of accurately predicting 
their conjunct result, gives us to a certain extent this power. 

It would, however, be an error to suppose that even with respect to 
tendencies, we could arrive in this manner at any gi-eat number of prop- 
ositions which will be true in all societies without exception. Such a 
supposition would be inconsistent with the eminently modifiable nature 
of the social phenomena, and the multitude and variety of the circum- 
stances by which they are modified ; circumstances never the same, or 
even nearly the same, in two different societies, or in two different 
periods of the same society. This would not be so serious an obstacle 
if, though the causes acting upon society in general are numerous, 
those which influence any one feature of society were limited in num- 
ber; for we might then insulate any particular social phenomenon, and 
investigate its laws without disturbance from the rest. But the truth 
is the very opposite of this. Whatever affects, in an appreciable degree, 
any one element of the social state, affects through it all the other ele- 
ments. The mode of production of all social phenomena is one great 
case of Intermixture of Laws. We can never either understand in 
theory or command in practice the condition of a society in any one 
respect, without taking into consideration its condition in all other 
respects. There is no social phenomenon which is not more or less 
influenced by every other part of the condition of the same society, 
and therefore by every cause which is influencing any other of the 
contemporaneous social phenomena. There is, in short, a consensus 
(to borrow an expression from physiology) similar to that existing 
among the various organs and functions of the physical frame of man 
and the more perfect animals ; and constituting one of the many anal- 
ogies which have rendered universal such expressions as the **body 
politic " and " body natural." It follows from this consensus, that unlesjs 
two societies could be alike in all the circumstances which surround 
and influence them (which would imply their being alike in their pre- 
vious history), no portion whatever of their phenomena will, unless by 
accident, precisely coiTespond ; no one cause will produce exactly the 
same effect in both. Every cause, as its effect spreads through society, 
comes somewhere in contact with different sets of agencies, and thus has 
its effects on some of the social phenomena differently modified ; and 
these differences, by their reaction, produce a difference even in those of 
the effects which would otherwise have been the same. We can never, 
therefore, affirm with certainty that a cause which has a particular ten- 
dency in one people or in one age will have exactly the same tendency 
in another, without referring back to our premisses, and performing 
over again for the second age or nation, that analysis of the whole of 



PHYSICAL METBOD, 565 

its influencing circumstances which we had already performed for the 
first. The deductive sc'.ence of society does not lay down a theorem, 
asserting in an universal manner the effect of any cause ; but rather 
teaches us how to frame the proper theorem for the circumstances of 
any given case. It does not give us the laws of society in general, but 
the means of determining the phenomena of any given society from the 
particular elements or data of that society. 

All the general propositions of the deductive science are therefore, 
in the strictest sense of the word, hypothetical. They are gi'ounded 
on some supposititious set of circumstances, and declare how some 
given cause will operate in those circumstances, supposing that no 
others are combined with them. If the set of circumstances supposed 
has been taken from those of any existing society, the conclusions 
will be true of that society, provided, and in as far as, the effect of those 
circumstances shall not be modified by others which have not been 
taken into the account. If we desire a nearer approach to concrete 
truth, we can only aim at it by taking, or endeavoring to take, a greater 
number of individualizing circumstances into the computation. 

Considering, however, in how accelerating a ratio the uncertainty of 
our conclusions increases, as we attempt to take the effect of a greater 
number of concurrent causes into our calculations ; the hypothetical 
combinations of circumstances upon which we construct the general 
theorems of the science, cannot be made very complex, without so 
rapidly accumulating a liability to error as must soon deprive our con- 
clusions of all value. This mode of inquiry, considered as a means of 
obtaining general propositions, must therefore, on pain of entire fri- 
volity, be limited to those classes of social facts which, though influenced 
like the rest by all sociological agents, are under the immediate influ- 
ence, principally at least, of a few only. 

§ 3. Notwithstanding the universal consensus of the social phenomena, 
whereby nothing which takes place in any part of the operations of 
society is without its share of influence on every other part ; and not- 
withstanding the paramount ascendency which the general state of 
civilization and social progress in any given society must hence exercise 
over all the partial and subordinate phenomena ; it is not the less true 
that different species of social facts are in the main dependent, imme- 
diately and in the first resort, upon different kinds of causes ; and there- 
fore not only may with advantage, but must, be studied apart : just as 
in the natural body we study separately the physiology and pathology 
of each of the principal organs and tissues, although every one is acted 
upon by the state of all the others ; and although the peculiar consti- 
tution and general state of health of the organism cooperates with and 
often preponderates over the local causes, in determining the state of 
any particular organ. 

On these considerations is grounded the existence of distinct and 
separate, though not independent, branches or departments of socio- 
logical speculation. 

There is, for example, one large cIelss of social phenomena, in which 
the immediately determining causes are principally those which act 
through the desire of wealth; and in which the psychological law main- 
ly concerned is the familiar one, that a gi^eater gain is preferred to a 
smaller. I mean, of course, that portion of the phenomena of society 



566 LOGIC OF THE MOBAL SCIENCES. 

which emanate from the industrial, or productive, operations of man- 
kind ; and from those of their acts through which the distribution of 
the products of those industrial operations takes place, in so far as not 
effected by force, or modified by voluntary gift. By reasoning from 
that one law of human nature, and from the principal outward circum- 
stances (whether universal or confined to particular states of society) 
which operate upon the human mind through that law, we may be 
enabled to explain and predict this portion of the phenomena of soci- 
ety, so far as they depend upon that class of circumstances only ; over- 
looking the influence of any other of the circumstances of society; and 
therefore neither tracing back the circumstances which we do take into 
account, to their possible origin in some other facts in the social state, 
nor making allowance for the manner in which any of those other 
circumstances may interfere with, and counteract or modify, the effect 
of the former. A science is thus constructed, which has received the 
name of Political Economy. 

The motive which suggests the separation of this portion of the 
social phenomena from the rest, and the creation of a distinct science 
relating to them, is — that they do mainly depend, at least in the first 
resort, upon one class of circumstances only ; and that even when 
other circumstances interfere, the ascertainment of the effect due to 
the one class of circumstances alone, is a sufficiently intricate and 
difficult business to make it expedient to perform it once for all, and 
then allow for the effect of the modifying circumstances ; especially as 
certain fixed combinations of the former are apt to recur often, in con- 
junction with ever-varying circumstances of the latter class. 

Political Economy, as I have said on another occasion, concerns 
itself only with " such of the phenomena of the social state as take 
place in consequence of the pursuit of wealth. It makes entire abstrac- 
tion of every other human passion or motive ; except those which may 
be regarded as pei"petually antagonizing principles to the desire of 
wealth, namely, aversion to labor, and desire of the present enjoyment 
of costly indulgences. These it takes, to a certain extent, into its cal- 
culations, because these do not merely, like our other desires, occa- 
sionally conflict with the pursuit of wealth, but accompany it always 
as a drag or impediment, and are therefore inseparably mixed up in 
the consideration of it. Political Economy considers mankind as oc- 
cupied solely in acquiring and consuming wealth ; and aims at showing 
what is the course of action into which mankind, living in a state of 
society, would be impelled, if that motive, except in the degree in 
which it is checked by the two perpetual counter-motives above ad- 
verted to, were absolute ruler of all their actions. Under the influence 
of this desire, it shows mankind accumulating wealth, and employing 
that wealth in the production of other wealth ; sanctioning by mutual 
agreement the institution of property ; establishing laws to prevent 
individuals from encroaching upon the property of others by force or 
fraud ; adopting various contrivances for increasing the productiveness 
of their labor ; settling the division of the produce by agreement, under 
the influence of competition (competition itself being governed by cer- 
tain laws, w^hich laws are therefore the ultimate regulators of the 
division of the produce) ; and employing certain expedients (as money, 
credit, &c.) to facilitate the distribution. All these operations, though 
many of them are really the result of a plurality of motives, are con- 



PHYSICAL METHOD. 567 

sidered by political economy as flowing solely from the desire of wealth. 
The science then proceeds to investigate the laws which govern these 
several operations, under the supposition that man is a Being who is 
determined, by the necessity of his nature, to prefer a greater portion 
of wealth to a smaller, in all cases, without any other exception than 
that constituted by the two counter-motives already specified. Not 
that any political economist was ever so absurd as to suppose that 
mankind are really thus constituted, but because this is the mode in 
which science must necessarily proceed. When an effect depends 
upon a concuiTence of causes, these causes must be studied one at a 
time, and their laws separately investigated, if we wish, through the 
causes, to obtain the power of either predicting or controlling the 
effect ; since the law of the effect is compounded of the laws of all 
the causes which determine it. The law of the centripetal and that of 
the tangential force must have been known, before the motions of the 
earth and planets could be explained, or many ofthem predicted. 
The same is the case with the conduct of man in society. In order to 
judge how he will act under the variety of desires and aversions which 
are concurrently operating upon him, we must know how he would act 
under the exclusive influence of each one in particular. There is, 
perhaps, no action of a man's life in which he i^ neither under the 
immediate nor under the remote influence of any impulse but the mere 
desire of wealth. There are many parts of human conduct of which 
wealth is not even the piincipal object, and to these political economy 
does not pretend that its conclusions are applicable. But there are 
also certain departments of human affairs, in which the acquisition of 
wealth is the main and acknowledged end. It is only of these that 
political economy takes notice. The manner in which it necessarily 
proceeds is that of treating the main and acknowledged end as if it 
were the sole end ; which, of all hypotheses equally simple, is the 
nearest to the truth. The political economist inquires, what are the 
actions which would be produced by this desire, if within the depart- 
ments in question it were unimpeded by any other. In this way a 
nearer approximation is obtained than would otherwise be practicable 
to the real order of human affairs in those departments. This approxi- 
mation has then to be corrected by making proper allowance for the 
effects of any impulses of a different description, which can be shown 
to interfere with the result in any particular case. Only in a few of 
the most striking cases (such as the important one of the principle of 
population) ai'e these corrections interpolated into the expositions of 
political economy itself; the strictness of purely scientific arrangement 
being thereby somewhat departed from, for the sake of practical utility. 
So far as it is known, or may be presumed, that the conduct of man- 
kind in the pursuit of wealth is under the collateral influence of any 
other of the properties of our nature, than the desire of obtaining the 
gi'eatest quantity of wealth with the least labor and self-denial, the 
conclusions of political economy will so far fail of being applicable to 
the explanation or prediction of real events, until they are modified by 
a correct allowance for the degree of influence exercised by the other 
cause." 

When M. Comte (for of the objections raised by inferior thinkers it 
is unnecessary here to take account) pronounces the attempt to treat 
political economy, even provisionally, as a science apart, to be a mis- 



568 LOGIC OF THE MORAL SCIENCES. 

apprehension of the scientific method proper to Sociology ; I cannot 
but think that he has overlooked the extensive and important practical 
guidance which may be derived, in any given state of society, from 
general propositions such as those above indicated ; even though the 
modifying influence of the miscellaneous causes which the theory does 
not take into account, as well as the effect of the general social changes 
in progress, be provisionally overlooked. And although it has been 
a very common error of political economists to draw conclusions 
from the elements of one state of society, and apply them to other 
states in which many of the elements are not the same; it is even 
then not difficult, by tracing back the demonstrations, and intro- 
ducing the new premisses in their proper places, to make the same 
general course of argument which serve for the one case, serve for 
the others too. 

For example, it has been greatly the custom of English political 
economists to diftcuss the natural laws of the distribution of the pro- 
duce of industry, on a supposition which is scarcely realized anywhere 
out of England and Scotland, namely, that the produce is "shared 
among three classes, altogether distinct from one another, laborers, 
capitalists, and landlords ; and that all these are free agents, permitted 
in law and in fact to set upon their labor, their capital, and their land, 
whatever price they are able to get for it. The conclusions of the 
science, being all adapted to a society thus constituted, require to be 
revised whenever they are applied to any other. They are inapplica- 
ble where the only capitalists are the landlords, and the laborers are 
their property, as in slave countries. They are inapplicable where 
the universal landlord is the state, as in India. They are inapplicable 
where the agricultural laborer is generally the owner both of the land 
itself and of the capital, as in France, or of the capital only, as in 
Ireland." But although it may often be very justly objected to the 
existing race of political economists " that they attempt to construct a 
permanent fabric out of transitory materials ; that they take for granted 
the immutability of arrangements of society, many of which are in 
their nature fluctuating or progressive, and enunciate with as little 
qualification as if they were universal and absolute truths^ propositions 
which are perhaps applicable to no state of society except the particular 
one in which the writer happened to live ;" this does not take away 
the value of the propositions, considered with reference to the state of 
society from which they were drawn. And even as applicable to other 
states of society, " it must not be supposed that the science is so incom- 
plete and unsatisfactory as this might seem to prove. Though many of 
its conclusions are only locally true, its method of investigation is appli- 
cable universally; and as he who has solved a certain number of alge- 
braic equations, can without difficulty solve all others of the same kind, 
so he who knows the political economy of England, or even of York- 
shire, knows that of all nations, actual or possible, provided he have 
good sense enough not to expect the same conclusion to issue from 
varying premisses." Whoever is thoroughly master of the laws which, 
under free competition, determine the rent, profits, and wages, received 
by landlords, capitalists, and laborers in a state of society in which 
the three classes are completely separate, will have no difficulty in 
determining the very different laws which regulate the distribution 
of the produce among the classes interested in it, in any of the 



PHYSICAL METHOD. 569 

States of cultivation and landed property set forth in tli6 foregoing 
extract.* 

§ 4. I would not here undertake to decide what other hypothetical 
or abstract sciences, similar to Political Economy, may admit of being 
carved out of the general body of the social science ; what other por- 
tions of the social phenomena are in a sufficiently close and complete 
dependence, in the first resort, upon a peculiar class of causes, to make 
it convenient to create a preliminary science of those causes ; post- 
poning the consideration of the causes whic,^ act through them, or in 
concurrence with them, to a later period of the inquiry. There is 
however among these separate departments one which cannot be 
passed over in silence, being of a more comprehensive and command- 
ing character than any of the other branches into which the social 
science may admit of being divided. Like them, it is directly con- 
versant with the causes of only one class of social facts, but a class 
which exercises, immediately or remotely, a paramount influence over 
the rest. I allude to what may be termed Political Ethology, or the 
science of the causes which determine the type of character belonging 
to a people or to an age. Of all the subordinate branches of the social 
science, this is the most completely in its infancy. The causes of 
national character are scarcely at all understood, and the effect of 
institutions or social arrangements upon national character is generally 
that portion of their effects which is least attended to, and least com- 
prehended. Nor is this wonderful, when we consider the infant state 
of the Science of Ethology itself, from whence the laws must be drawn 
of which the truths of political ethology are but results and exemplifi- 
cations. 

Yet, to whoever well considers the matter, it must appear that the 
laws of national character are by far the most important class of socio- 
logical laws. In the first place, the character which is formed by any 
state of social circumstances is in itself the most interesting phe- 
nomenon which that state of society can possibly present. Secondly, 
it is also a fact which enters largely into the production of all the other 
phenomena. And above all, the character, that is, the opinions, feel- 
ings, and habits, of the people, though greatly the results of the state 
of society which precedes them, are also greatly the causes of the 
state of society which follows them ; and are the power by which all 
those of the circumstances of society which are artificial, laws and 
customs for instance, are altogether moulded : customs evidently, laws 
no less really, either by the direct influence of public sentiment upon 
the ruling powers, or by the effect which the state of national opinion 
and feeling has in determining the form of government and shaping the 
character of the governors. 

As might be expected, the most imperfect part of those branches of 
sociology which have been cultivated as separate sciences, is the 
theory of the manner in which their conclusions are affected by etho- 
logical considerations. The omission is no defect in them as abstract 
or hypothetical sciences, but it vitiates them in their practical applica- 
tion as branches of the comprehensive social science. In politicEil 

* The quotations in this paragraph are from a paper written by the author, and pubhshod 
in a periodical in 1834. 

4C 



570 LOGIC OF THE MORAL SCIENCES. 

economy, for instance, empirical laws of human nature are tacitly 
assumed by English thinkers, which are calculated only for Great 
Britain and the United States. Among other things, an intensity of 
competition is constantly supposed, which, as a general mercantile fact.. 
exists in no country in the world except those two. An English political 
economist, like his countrymen in general, has seldom learned that it 
is possible that men, in conducting the business of selling their goods 
over a counter, should care more about their ease or their vanity than 
about their pecuniary gain. Yet those who know the habits of the 
Continent of Europe are^aware how apparently small a motive often 
outweighs the desire of money-getting, even in the operations which 
have money-getting for their direct object. The more highly the 
science of ethology is cultivated, and the better the diversities of 
national character are understood, the smaller, probably, will the 
number of propositions become, which it will be considered safe to 
build upon as universal principles of human nature. 

These considerations show that the process of dividing off the social 
science into compartments, in order that each may be studied sepa- 
rately, and its conclusions afterwards corrected for practice by the 
modifications supplied by the others, must be subject to at least one 
important limitation. Those portions alone of the social phenomena 
can with advantage be made the subjects, even provisionally, of dis- 
tinct branches of science, into which the diversities of character be- 
tween different nations or different times enter as influencing causes 
only in a secondary degree. Those phenomena, on the contrary, with 
which the influences of the ethological state of the people are mixed 
up at every step (so that the connexion of effects and causes cannot be 
even rudely marked out without taking those influences into considera- 
tion) could not with any advantage, nor without great disadvantage, 
be treated independently of political ethology, nor, therefore, of all the 
circumstances by which the qualities of a people are influenced. For 
this reason (as well as for others which will hereafter appear) there 
can be no separate Science of Government ; that being the fact which, 
of all others, is most mixed up, both as cause and effect, vdth the 
qualities of the particular people or of the particular age. All 
questions respecting the tendencies of forms of government must 
stand part of the general science of society, not of any separate branch 
of it. 

This general Science of Society, as distinguished fi'om the separate 
departments of the science (each of which asserts its conclusions only 
conditionally, subject to the paramount control of the laws of the 
general science), it now remains for us to characterize. And, as will 
be showm presently, nothing of a really scientific character is here 
possible, except by the inverse deductive method. But before we 
quit the subject of those sociological speculations which proceed by 
way of direct deduction, we must examine in what relation they stand 
to that indispensable element in all deductive sciences. Verification by 
Specific Experience — the comparison between the conclusions of 
reasoning and the results of observation. 

§ 5. We have seen that, in most deductive sciences, and among the 
rest in Ethology itself, which is the immediate foundation of the Social 
Science, a preliminary work of preparation is performed upon the 



PHYSICAL METHOD. 571 

observed facts, to fit them for being rapidly and accurately collated, 
sometimes even for being collated at all, with the conclusions of theory. 
This preparatory treatment consists in finding general propositions 
which express concisely w^hat is common to large classes of observed 
facts : and these are called the empirical lavv^s of the phenomena. We 
have, therefore, to inquire, w^hether any similar preparatory process 
can be performed upon the facts of the social science ; whether there 
xire any empirical laws in history or statistics. 

In statistics, it is evident that empirical laws may sometimes be 
traced ; and the tracing them forms an important part of that system 
of indirect observation on which we must often rely for the data of the 
Deductive Science. The process of the science consists in inferring 
effects from their causes ; but we have often no means of observing 
the causes, except through the medium of their effects. In such cases 
the deductive science is unable to predict the effects for want of the 
necessary data ; it can tell us what causes are capable of producing 
any given effect, but not with what frequency and in what quantities 
those causes exist. An instance in point is afforded by a newspaper 
now lying before me. A statement was furnished by one of the official 
assignees in bankruptcy, showing, among the various bankruptcies 
which it had been his duty to investigate, in how many cases the losses 
had been caused by misconduct of different kinds, and in how many 
by unavoidable misfortunes. The result was, that the number of fail- 
ures caused by misconduct greatly preponderated over those arising 
from all other causes whatever. Nothing but specific experience 
could have given sufficient ground for a conclusion to this purport. 
To collect, therefore, such empirical laws (which are never more than 
approximate generalizations) from direct observation, is an important 
part of the process of sociological inquiry. 

The experimental process is not here to be regarded as a distinct 
road to the truth, but as a means (happening accidentally to be the 
only, or the best available) for obtaining the data which the deductive 
science cannot do without. When the immediate causes of social facts 
are not open to direct observation, the empirical law of the effects 
gives us the empirical law (which in that case is all that we can obtain) 
of the causes likewise. But those immediate causes depend upon 
remote causes ; and the empirical law, obtained by this indirect mode 
of observation, can only be relied upon as applicable to unobserved 
cases, so long as there is reason to think that no change has taken 
place in any of the remote causes on which the immediate causes de- 
pend. In making use, therefore, of even the best statistical generali- 
zations for the purpose of inferring (though it be only conjecturally) 
that the same empirical laws will hold in any new case, it is necessary 
that we be perfectly well acquainted with the remoter causes, in order 
that we may scrupulously avoid applying the empirical law to cases 
which differ in any of the circumstances on which the truth of the law 
ultimately depends. And thus, even where conclusions derived from 
specific observation are available for practical inferences in new cases, 
it is necessary that the deductive science should stand sentinel over 
the whole process ; that it should be constantly referred to, and its 
sanction obtained to every inference. 

The same thing holds true of all generalizations which can be 
grounded on history. Not only there are such generalizations, but it 



572 LOGIC OF THE MORAL SCIENCES. 

will presently be shown that the general science of society, which 
inquires into the laws of succession and coexistence of the great facts 
constituting the state of society and civilization at any time, can pro- 
ceed in no other manner than by making such generalizations — after- 
wards to be confirmed by connecting them with the psychological and 
ethological laws on which they must really depend. 

§ 6. But (reserving this question for its proper place), in those more 
special sociological inquiries which form the subject of the separate 
branches of the social science, this two-fold logical process and recip- 
rocal verification is not possible ; specific experience affords nothing 
amounting to empirical laws. This is particularly the case where the 
object is to determine the effect of any one sociological cause among 
a gi'eat number acting simultaneously; the effect, for example, of 
corn laws, or of a prohibitive commercial system generally. Although 
it may be perfectly certain, from theory, what kind of effects corn laws 
must produce, and in what general direction their influence must tell 
upon industrial prosperity ; their effect is yet of necessity so much 
disguised by the similar ar contrary effects of other influencing 
agents, that specific experience can at most only show that in the 
average of some great number of instances, the cases where there 
were corn laws exhibited the effect in a greater degree than those 
where there were not. Now the number of instances necessary to 
take in the whole round of combinations of the various influential cir- 
cumstances, and thus afford a fair average, never can be obtained. 
Not only we can never learn with sufficient authenticity the facts of so 
many instances, but the world itself does not afford them in sufficient 
numbers, within the limits of the given state of society and civilization 
which such inquiries always presuppose. Having thus no previous 
empirical generalizations with which to collate the conclusions of the- 
ory, the only mode of direct verification which remains is to compare 
those conclusions with the result of an individual experiment or in- 
stance. But here the difficulty is equally great. For in order to ver- 
ify a theory by an experiment, the circumstances of the experiment 
must be exactly the same with those contemplated in the theory. But 
in social phenomena the circumstances of no two experiments are ex- 
actly alike. A trial of com laws in another country, or in a former 
generation, would go a very little way towards verifying a conclusion 
drawn respecting their effect in this generation and in this country. It 
thus happens in most cases that the only individual instance really fitted 
to verify the predictions of theory is the very instance for which the 
predictions were made ; and the verification comes too late to be of 
any avail for practical guidance. 

Although, however, direct verification is impossible, there is an in- 
direct verification, which is scarcely of less value, and which is always 
practicable. The conclusion drawn as to the individual case, can only 
be directly verified in that case ; but it is verified indirectly, by the 
verification of other conclusions, drawn in other individual cases from 
the same laws. The experience which comes too late to verify the 
particular proposition to which it refers, is not too late to help towards 
verifying the general sufficiency of the theory. The test of the degree 
in which the science affords safe ground for predicting (and conse- 
quently for practically dealing with) what has not yet happened, is 



PHYSICAL METHOD. 573 

the degree in which it would have enabled us to predict what has ac- 
tually occurred. Before our theory of the influence of a particular 
cause, in a given state of circumstances, can be trusted, we must be 
able to explain and account for the existing state of all that portion of 
the social phenomena which that cause has a tendency to influence. 
If, for instance, we would apply our speculations in political economy 
to the prediction or guidance of the phenomena of any country, we 
must be able to explain all the mercantile or industrial facts of a gen- 
eral character, appertaining to the present state of that country : to point 
out causes suflacient to account for all of them, and prove, or show good 
ground for supposing, that these causes did really exist. If we cannot 
do this, it is a proof either that the facts which ought to be taken into 
account are not yet completely known to us, or tliat although we know 
the facts, we are not masters of a sufficiently perfect theory to enable 
us to assign their consequences. In either case we are not, in the 
present state of our knowledge, competent to draw conclusions, either 
speculative or practical, for that country. In like manner, if we would 
attempt to judge of the effect which any political institution would 
have, supposing that it could be introduced into any given country ; 
we must be able to show that the existing state of the practical govern- 
ment of that country, and of whatever else depends thereon, together 
with the particular character and tendencies of the people, and their 
state in respect to the various elements of social well-being, are such 
as the institutions they have lived under, in conjunction with the other 
circumstances of their nature or of their position, were calculated to 
produce. 

It is therefore well said by M. Comte, that in order to prove that 
our science, and our knowledge of the particular case, render us com- 
petent to predict the fliture, we must show that they would have ena- 
bled us to predict the present and the past. If there be anything 
which we could not have predicted, this constitutes a residual phenom- 
enon, requiring further study for the purpose of explanation ; and we 
must either search among the circumstances of the particular case 
until we find one which, on the principles of our existing theory, ac- 
counts for the unexplained phenomenon, or we must turn back, and 
seek the explanation by an extension and improvement of the theory 
itself. 



'>74 LOGIC OF THE MORAL SCIENCES. 

CHAPTER X. 

OF THE INVERSE DEDUCTIVE, OR HISTORICAL METHOD. 

§ 1. There are two kinds of sociological inquiry. In the first kind, 
the question proposed is, what effect will follow from a given cause, a 
certain general condition of social circumstances being presupposed. 
As, for example, what would be the effect of imposing or of repealing 
corn laws, of abolishing monarchy, or introducing universal suffrage, 
in the present condition of society and civilization in any European 
country, or under any other given supposition with regard to the cir- 
cumstances of society in general : without reference to the changes 
which might take place, or which may already be in progress, in those 
circumstances. But there is also a second inquiry, namely, what are 
the laws which determine those general circumstances themselves. In 
this last the question is, not what will be the effect of a given cause in 
a certain state of society, but what are the causes which produce, and 
the phenomena which characterize, States of Society generally. In 
the solution of this question consists the general Science of Society ; by 
which all the conclusions of the other and more special kind of inquiry 
must be limited and controlled. 

§ 2. In order to conceive correctly the scope of this general science, 
and distinguish it from the subordinate departments of sociological 
speculation, it is necessary to fix with precision the ideas attached to 
the phrase, " A State of Society." What is called a state of society, 
is the simultaneous state of all the greater social facts, or phenomena. 
Such are, the degree of knowledge, and of intellectual and moral cul- 
ture, existing in the community, and in every class of it ; the state of 
industry, of wealth and its distribution ; the habitual occupations of the 
community ; their division into classes, and the relations of those 
classes to one another ; the common beliefs which they entertain on 
all the subjects most important to mankind, and the degree of assur- 
ance with which those beliefs are held ; their tastes, and the character 
and degree of their aesthetic development ; their form of government, 
and the more important of their laws and customs. The condition of 
all these things, and of many more which will spontaneously suggest 
themselves, constitute the state of society or the state of civilization at 
any given time. 

When states of society, and the causes which produce them, are 
spoken of as a subject of science, it is implied that there exists a natu- 
ral correlation among these different elements ; that not every variety 
of combination of these general social facts is possible, but only cer- 
tain combinations ; that, in short, there exist Uniformities of Coexist- 
ence between the states of the various social phenomena. And such 
is the truth : as is indeed a necessary consequence of the influence ex- 
ercised by every one of those phenomena over every other. It is a 
fact implied in the consensus of the various parts of the social body. 

States of society are like different constitutions or different ages in 
the physical frame ; they are conditions not of one or a few organs or 
functions, but of the whole organism. Accordingly, the infonnation 



HISTORICAL METHOD. 576 

wliich we possess respecting past ages, and respecting the various states 
of society now existing in different regions of the earth, does, when 
duly analyzed, exhib it suchuniformities. It is found that when one 
of the features of society is in a particular state, a state of all the other 
features, more or less precisely determinate, always coexists with it. 

But the uniformities of coexistence obtaining among phenomena 
which are effects of causes, must (as we have so often observed) be mere 
corollaries from the laws of causation by which these phenomena are 
actually determined. The mutual correlation between the different 
elements of each state of society, is therefore a derivative law, result- 
ing fi-om the laws which regulate the succession between one state of 
society and another : for the proximate cause of every state of society 
is the state of society immediately preceding it. The fundamental 
problem, therefore, of sociology is to find the laws according to which 
any state of society produces the state which succeeds it and takes its 
place. This opens the great and vexed question of the progressive- 
ness of man and society ; an idea involved in every just conception of 
social phenomena as the subject of a science. 

§ 3. It is one of the characters, not absolutely peculiar to the 
sciences of human nature and society, but belonging to them in a pe- 
culiar degree, to be conversant with a subject matter whose properties 
are changeable. I do not mean changeable from day to day, but from 
age to age : so that not only the qualities of individuals vary, but those 
of the majority are not the same in one age as in another. 

The principal cause of this peculiarity is the extensive and constant 
reaction of the effects upon their causes. The circumstances in which 
mankind are placed, operating according to their own laws and to the 
laws of human nature, form the characters of the men ; but the men, 
in their turn, mould and shape the circumstances, for themselves and 
for those who come after them. From this reciprocal action there must 
necessarily result either a cycle or a progress. In astronomy also 
every fact is at once effect and cause ; the successive positions of the 
various heavenly bodies produce changes both in the direction and in 
the intensity of the forces by which those positions are determined. 
But, in the case of the solar system, these mutual actions bring round 
again, after a certain number of changes, the former state of circum- 
stances, which of course leads to the perpetual recurrence of the same 
series in an unvarying order. Those bodies, in short, revolve in 
orbits : but there are (or, conformably to the laws of astronomy, there 
might be) others which, instead of an orbit, describe a trajectory, or a 
course not returning into itself. One or other of these must be the 
type to which human affairs must also conform. 

One of the thinkers who earliest conceived the succession of histori- 
cal events as subject to fixed laws, and endeavored to discover these 
laws by an analytical surv^ey of history, Vico, the celebrated author of 
the Scienza Nuova, adopted the former of these opinions. He con- 
ceived the phenomena of human society as revolving in an orbit ; as 
going through periodically the same series of changes. Though there 
were not wanting circumstances tending to give some plausibility to 
this view, it would not bear a close scrutiny : and those who have suc- 
ceeded Vico in this kind of speculations have universally adopted the 
idea of a trajectory or progress, in lieu of an orbit or cycle. 



576 LOGIC OF THE MORAL SCIENCES. 

The words Progress and Progressi\ enesa, are not here to be under- 
stood as synonymous with improvement and tendency to improvement. 
It is conceivable that the laws of human nature might determine, and 
even necessitate, a certain series of changes in man and society, which 
might not in every case, or which might not on the whole, be improve- 
ments. It is my belief indeed that the general tendency is, and vrill 
continue to be, saving occasional exceptions, one of improvement ; a 
tendency towards a better and happier state. But this is not a ques- 
tion of the method of the social science, but an ultimate result of the 
science itself. For our purpose it is sufficient, that there is a progress- 
ive change both in the character of the human race, and in their out- 
ward circumstances so far as moulded by themselves : that in each suc- 
cessive age the principal phenomena of society are different from what 
they were in the age preceding, and still more different from any pre- 
vious age. The periods at which these sticcessive changes are most 
apparent (according to the judicious remark of M. Comte) are inter- 
vals of one generation, during which a new set of human beings have 
been educated, have grown up from childhood, and taken possession 
of society. 

The progressiveness of the human race is the foundation on which a 
method of philosophizing in the social science has been of late years 
erected, far superior to either of the two modes which had previously 
been prevalent, the chemical or experimental, and the geometrical 
modes. This method, which is now generally adopted by the most 
advanced thinkers on the Continent, and especially in France, consists 
in attempting, by a study and analysis of the general facts of history, 
to discover (what these philosophers term) the law of progress : which 
law, ouce ascertained, must according to them enable us to predict 
future events, just as after a few terms of an infinite series in algebra 
we are able to detect the principle of regularity in their recurrence, 
and to predict the rest of the series to any number of terms we please. 
The principal aim of historical speculation in France, of late years, 
has been to ascertain the law. But while I gladly acknowledge the 
great services which have been rendered to historical knowledge by 
this school, I cannot but deem them (with the single exception of M. 
Comte) to be chargeable with a fundamental misconception of the 
true method of social philosophy. The misconception consists in sup- 
posing that the order of succession which we may be able to trace 
among the different states of society and civilization which history 
presents to us, even if that order were more rigidly uniform than it 
has yet been proved to be, could ever amount to a law of nature. It 
can only be an empirical law. The succession of states of the human 
mind and of human society cannot have an independent law of its own; 
it must depend upon the psychological and ethological laws which 
govern the action of circumstances on men and of men on circum- 
stances. It is conceivable that those laws may be such, and the 
general circumstances of the human race such, as to determine the 
successive transformations of man and society to one given and un- 
varying order. But even if the case be so, it cannot be the ultimate 
aim of science to discover an empirical law. Until that law can be 
connected with the psychological and ethological laws upon which it 
depends, and, by the consilience of deduction a priori with historical 
evidence, can bo converted from an empirical law into a scientific one, 



HISTORICAL METHOD. 577 

it cannot be relied upon for the prediction of future events, beyond, at 
most, strictly adjacent cases. Now, M. Comte alone has seen the 
necessity of thus connecting all our generahzations from history with 
the laws of human nature ; and he alone, therefore, has arrived at 
any results truly scientific ; though in the speculations of others there 
will be found many happy aperqus, and valuable hints for future 
philosophers. 

§ 4. But, while it is an imperative rule never to introduce any 
generalizations from history into the social science unless sufficient 
gi'ounds can be pointed out for it in human nature, I do not think any 
one will contend that it would have been possible, sotting out from the 
principles of human nature and from the general circumstances of 
man's position in the universe, to determine a priori the order in which 
human development must take place, and to predict, consequently, 
the general facts of history ujp to the present time. The initial stages 
of human progress — when man, as yet unmodified by society, and 
characterized only by the instincts resulting directly from his organi- 
zation, was acted upon by outward objects of a comparatively simple 
aad universal character — might indeed, as M. Comte remarks, be 
deduced from the laws of human nature ; which moreover is the only 
possible mode of ascertaining them, since of that form of human ex- 
istence no direct memorials are preserved. But (as he justly observes) 
after the first few terms of the series, the influence exercised over each 
generation by the generations which preceded it, becomes more and 
more preponderant over all other influences ; until at length what we 
now are and do, is in a very small degree the result of the universal 
circumstances of the human race, or even of our owti circumstances 
acting through the original qualities of our species, but mainly of the 
qualities produced in us by the whole previous history of humanity. 
So long a series of actions and reactions between Circumstances and 
Man, each successive term being composed of an ever greater number 
and variety of parts, could not possibly be calculated from the elemen- 
tary laws which produce it, by merely human faculties. The mere 
length of the series would be a sufficient obstacle, since a slight error 
in any one of the terms would augment in rapid progression at every 
subsequent step. 

If, therefore, the series of the effects themselves did not, when ex- 
amined as a whole, manifest any regularity, we should in vain attempt 
to construct a general science of society. We must in that case have 
contented ourselves with that subordinate order of sociological specu- 
lation formerly noticed, namely, with endeavoring to ascertain what 
would be the effect of the introduction of any new cause, in a state of 
society supposed to be fixed ; a knowledge sufficient for most of the 
ordinary exigencies of daily political practice, but liable to fail in all 
cases in which the progressive movement of society :s one of the in- 
fluencing elements ; and therefore more precarious in proportion as 
the case is more important. But since both the natural varieties of 
mankind, and the original diversities of local circumstances, are much 
less considerable than the points of agreement, there will naturally be 
a certain degi*ee of uniformity in the progressive development of man 
and of his works. And this uniformity (as M. Comte remarks with 
much justice) tends to become greater, not less, as society advances 
4D 



578 LOGIC OF THE MORAL SCIENCES. 

since tlie evolution of each people, which is at first determined exclu- 
sively by the nature and circumstances of that people, is gradually 
brought under the influence (v^^hich becomes stronger as civilization 
advances) of the other nations of the earth, and of the circumstances 
by w^hich they have been influenced. History accordingly does, v^^hen 
judiciously examined, afford Empirical Law^s of Society. And the 
problem of general sociology is to ascertain these, and connect them 
with the laws of human nature by deductions showing that such were 
the derivative laws naturally to be expected as the consequences of 
those ultimate ones. 

It is indeed, in most cases, hardly possible, even after history has 
suggested the derivative law, to demonstrate a priori that such was 
the only order of succession or of coexistence in which the effects 
could, consistently with the laws of human nature, have been pro- 
duced. We can at most make out that there were strong a priori 
reasons for expecting it, and that no other order of succession or co- 
existence would have been by any means so likely to result from the 
nature of man and his position upon earth. This, however — which 
in the Inverse Deductive Method that we are now characterizing > is a 
real process of verification — is as indispensable (to be more so is irn- 
possible) as verification by specific experience has been shown to bfc 
where the conclusion is originally obtained by the direct way of deduc- 
tion. The empirical laws must be the result of but a few instances, 
since few nations have ever attained at all, and still fewer by their ovm 
independent development, a high stage of social progi'ess. If, there- 
fore, even one or two of these few instances be insuflSciently knovvna, or 
imperfectly analyzed into its elements, and therefore not adequately 
compared with other instances, nothing is more probable than that a 
wrong empirical law will result instead of the right one. Accordingly, 
the most erroneous generalizations are continually made from the 
course of history : not only in this country, where history cannot yet 
be said to be at all cultivated as a science, but in other countries, 
where it is so cultivated., and by persons well versed in it. The only 
check or corrective is, constant verification by psychological and etho- 
logical laws. We may add to this, that no one but a person compe- 
tently skilled in those laws is capable of preparing the materials for 
historical generalization by analyzing the facts of history, or even by 
observing the social phenomena of his own time. No other will be 
aware of the comparative importance of different facts, nor conse- 
quently know what facts he is to look out for, or what to observe ; still 
less wdll he be capable of estimating the evidence of those facts which, 
as is the case with most, cannot be observed directly, but must be in- 
ferred from marks. 

§ 5. The Empirical Laws of Society are of two kinds ; some are 
uniformities of coexistence, some of succession. According as the 
science is occupied in ascertaining and verifying the former sort of 
uniformities, or the latter, M. Comte gives it the title of Social Statics, 
or of Social Dynamics ; conformably to the distinction in mechanics 
between the conditions of equilibrium and those of movement ; or in 
biology, between the laws of organization and those of life. The first 
branch of the science ascertains the conditions of stability in the social 
union ; the second, the laws of progress. Social Dynamics is the the- 



HISTORICAL METHOD. 579 

ory of Society considered in a state of progressive movement ; while 
Social Statics is the theory of the consensus already spoken of as exist- 
ing among the different parts of the social organism ; in other words, 
the theory of the mutual actions and reactions of contemporaneous so- 
cial phenomena ; '* making provisionally, as far as possible, abstrac- 
tion, for scientific purposes-, of the fundamental movement which is at 
all times gradually modifying the whole of them. 

*' In this first point of view," continues M. Comte,* "the previsions 
of sociology will enable us to infer one from another (subject to ulte- 
rior verification by direct observation) the various characteristic marks 
of each distinct mode of social existence ; in a manner essentially anal- 
ogous to what is now habitually practised in the anatomy of the physi- 
cal body. This preliminary aspect, therefore, of political science, of 
necessity supposes that (contrary to the existing habits of philosophers) 
each of the numerous elements ofithe social state, ceasing to be looked 
at independently and absolutely, shall be always and exclusively con- 
sidered relatively to all the other elements, with the whole of which it 
is united by mutual interdependence. It would be superfluous to 
insist here upon the great and constant utility of this branch of socio- 
logical speculation ; it is, in the first place, the indispensable basis of 
the theory of social progress, every rational conception of which pre- 
supposes the continued preservation of the corresponding social or- 
ganism. It may, moreover, be employed, immediately and of itself, 
to supply the place, provisionally at least, of direct obsei-vation, which 
in many cases is not always practicable for some oi the elements of 
society, the real condition of which may however be sufficiently judged 
of by means of the relations which connect them with others previously 
known. The history of the sciences may give us some notion of the 
habitual importance of this auxiliary resource, by reminding us, for 
example, how the vulgar errors of mere erudition concerning the pre- 
tended acquirements of the ancient Egyptians in the higher astronomy, 
were irrevocably dissipated (even before sentence had been passed 
upon them by a sounder erudition) from the single consideration of the 
inevitable connexion between the general state of astronomy and that 
of abstract geometry, then evidently in its infancy. It would be easy 
to cite a multitude of analogous cases, the character of which could 
admit of no dispute. In ^rder to avoid exaggeration, however, it 
should be remarked, that these necessary relations among the different 
aspects of society canuot, from their very nature, be so simple and 
precise that the results observed could only have arisen from some 
one mode of mutual coordination. Such a notion, already too narrow 
in the science of life, would be completely at variance with the still 
more complex nature of sociological speculations. But the exact 
estimation of these limits of variation, both in the healthy and in the 
morbid state, constitutes, at least as much as in the anatomy of the 
natural body, an indispensable complement to every theory of Socio- 
logical Statics; without which the indirect exploration above spoken 
of would often lead into eiTor. 

"■ This is not the place for methodically demonstrating the existence 
of a necessary relation between all the possible aspects of the same 
social organism; a point on which, moreover, in principle at least, 

* Cours de Philosophie Positive, iv., 325-9. 



580 LOGIC OF THE MORAL SCIENCES. 

tliere is now little difference of opinion among sound thinkers. From 
whichever of the social elements we choose to set out, we may easily 
recognize that it has always a connexion, more or less immediate, with 
all the other elements, even with those which at first sight appear the 
most independent of it. The dynamical consideration of the progress- 
ive development of civilized humanity, affords, no doubt, a still more 
efficacious means of effecting this interesting verification of the consen- 
sus of the social phenomena, by displaying the manner in which every 
change in any one part, operates immediately, or very speedily, upon 
all the rest. But this indication may be preceded, or at all events 
followed, by a confirmation of a purely statical kind; for, in politics 
as in mechanics, the communication of motion from one object to 
another proves a connexion between them. Without descending to 
the minute interdependence of the different branches of any one 
science or art, is it not evident that* among the different sciences, as 
well as among most of the arts, there exists such a connexion, that if 
the state of any one well-marked division of them is sufficiently knowti 
to us, we can with real scientific assurance infer, from their necessary 
con-elation, the contemporaneous state of every one of the others ] By 
a further extension of this consideration, we may conceive the neces- 
sary relation which exists between the condition of the' sciences in 
general and that of the arts in general, except that the mutual depen- 
dence is less intense in proportion as it is more indirect. The same is 
the case when, instead of considering the aggregate of the social phe- 
nomena in some one people, we examine it simultaneously in different 
contemporaneous nations ; between which the perpetual reciprocity of 
influence, especially in modern times, cannot be contested, although 
the consensus must in this case be ordinarily of a less decided charac- 
ter, and must decrease gradually with the affinity of the cases and the 
multiplicity of the points of contact, so as at last, in some cases, to 
disappear almost entirely; as for example between Western Europe 
and Eastern Asia, of which the various general states of society appear 
to have been hitherto almost independent of one another." 

M. Comte proceeds to illustrate, with his usual sagacity and discrimi- 
nation, one of the most important, and until lately, most neglected, of 
the great principles which, in this division of the social science, may 
be considered as established; namely, the necessary correlation be- 
tween the form of government existing in an^ society, and the contem- 
poraneous state of civilization : a natural law, which stamps the endless 
discussions and innumerable theories respecting forms of government in 
the abstract, as fruitless and worthless, save only (in some few of the 
more remarkable cases) as a preparatory treatment of some small 
portion of what may be afterwards used as material for a better 
philosophy. 

As already remarked, one of the main results of the science of social 
statics would be to ascertain the requisites of stable political union. 
There are some circumstances which, being found in all societies with- 
out exception, and in the greatest degree where the social union is 
most complete, may be considered (when psychological and ethological 
laws confirm the indication) as conditions of the existence of society. 
For example, no society has ever been held together without laws, or 
usages equivalent to them ; without tribunals, and an organized force 
of some sort to execute their decisions. There have always been a 



HrSTORICAL METHOD. • 581 

chief, or chiefs, whom, with more or less strictness and in cases more 
or less accurately defined, the rest of the community obeyed, or ac- 
cording to general opinion were bound to obey. By following out this 
course of inquiry, we should find a number of requisites, which have 
been present in every society that has held together ; and on the ces- 
sation of which it has ceased to be a society, or has reconstructed itself 
as such upon some new basis, in which the conditions were conformed 
to. Although these results, obtained by comparing different forms and 
states of society, amount in themselves only to empirical laws ; some of 
them, when once suggested, are found to follow with so much proba- 
bility from general laws of human nature, that the consilience of the 
two processes raises the evidence to complete proof, and the generali- 
zations to the rank of scientific truths. 

This seems to be affirmable (for instance) of the conclusions arrived 
at in the following passage ; forming part of a criticism on the negative 
philosophy of the eighteenth century, and which I quote, although (as 
in some former instances) fit-om myself, because I have no better way 
of illustrating the conception I have .formed of the kind of theorems of 
which sociological statics would consist. 

" The very first element of the social union, obedience to a govern- 
ment of some sort, has not been found so easy a thing to establish in 
the world. Among a timid and spiritless race, like the inhabitants of 
the vast plains of tropical countries, passive obedience may be of 
natural growth ; though even there we doubt whether it has ever been 
found among any people with whom fatalism, or in other words, sub- 
mission to the pressure of circumstances as the decree of God, did not 
prevail as a religious doctrine. But the difficulty of inducing a brave 
and warlike race to submit their individual arhitrium, to any common 
umpire, has always been felt to be so great, that nothing short of 
supernatural power has been deemed adequate to overcome it ; and 
such tribes have always assigned to the first institution of civil society 
a divine origin. So differently did those judge who knew savage man 
by actual experience, from those who had no acquaintance with him 
except in the civilized state. In modern Europe itself, after the fall of 
the Roman empire, to subdue the feudal anarchy and bring the whole 
people of any European nation into subjection to government (although 
Christianity in its most concentrated form was cooperating with all its 
influences in the work) required thrice as many centuries as have 
elapsed since that time. 

** Now if these philosophers had known human nature under any 
other type than that of their own age, and of the particular classes of 
society among whom they moved, it would have occurred to them, 
that wherever this habitual submission to law and government has been 
firmly and durably established, and yet the vigor and manliness of char- 
acter which resisted its establishment have been in any degree pre- 
served, certain requisites have existed, certain conditions have been 
fulfilled, of which the following may be regarded as the principal. 

"First: there has existed, for all who w^ere accounted citizens — for 
all who were not slaves, kept down by brute force — a system of edu- 
cation, beginning with infancy and continued through life, of which, 
whatever else it might include, one main and incessant ingi'edient was 
restraining discipline. To train the human being in the habit, and 
thence the power, of subordinating his personal impulses and aims to 



582 LOGIC OF THE MORAL SCIENCES. 

what were considered the ends of society; of adhering, against all 
temptation, to the course of conduct which those ends prescribed; of 
controlling in himself all those feelings which were liable to militate 
against those ends, and encouraging all such as tended towards them ; 
this was the purpose, to which every outward motive that the authority 
directing the system could command, and every inward power or prin- 
ciple which its knowledge of human nature enabled it to evoke, were 
endeavored to be rendered instrumental. This system of discipline 
wrought, in the Grecian states, by the conjunct influences of religion, 
poetry, and law ; among the Romans, by those of religion and law ; in 
modern and Christian countries, mainly by religion, with little of the 
direct agency, but generally more or less of the indirect support and 
countenance, of law. And whenever and in proportion as the strict- 
ness of this discipline was relaxed, the natural tendency of mankind to 
anarchy reasserted itself; the state became disorganized from within ; 
mutual conflict for selfish ends, neutralized the energies which were 
required to keep up the contest against natural causes of evil ; and the 
nation, after a longer or briefer interval of progressive decline, became 
either the slave of a despotism, or the prey of a foreign invader. 

" The second condition of permanent political society has been 
found to be, the existence, in some form or other, of the feeling of 
allegiance or loyalty. This feeling may vary in its objects, and is not 
confined to any particular form of government ; but whether in a 
democracy or in a monarchy, its essence is always the same ; viz., 
that there be in the constitution of the state something which is settled, 
something permanent, and not to be called in question; something 
which, by general agreement, has a right to be where it is, and to be 
secure against disturbance, whatever else may change. This feeling 
may attach itself, as among the Jews (and indeed in most of the com- 
monwealths of antiquity), to a common God or gods ; the protectors 
and guardians of their state. Or it may attach itself to certain persons, 
who are deemed to be, whether by divine appointment, by long pre- 
scription, or by the general recognition of their superior capacity and 
"worthiness, the rightful guides and guardians of the rest. Or it may 
attach itself to laws ; to ancient liberties, or ordinances ; to the whole 
or some part of the political, or even the domestic, institutions of the 
state. But in all political societies which have had a durable existence, 
there has been some fixed point; something which men agi'eed in 
holding sacred ; which it might or might not be lawful to contest in 
theory, but which no one could either fear or hope to see shaken in 
practice; which, in short (except perhaps during some temporary 
crisis), was in the common estimation placed above discussion. And 
the necessity of this may easily be made evident. A state never is, 
nor until mankind are vastly improved, can hope to be, for any long 
time exempt from internal dissension ; for there neither is nor has ever 
been any state of society in which collisions did not occur between the 
immediate interests and passions of powerful sections of the people. 
What, then, enables society to weather these storms, and pass through 
turbulent times without any permanent weakening of the ties which 
liold it together ? Precisely this — that however important the interests 
about which men fall out, the conflict does not affect the fundamental 
principles of the system of social union which happens to exist; nor 
threaten large portions of the community with the subversion of that 



HISTORICAL METHOD. 583 

on which they have built their calculations, and with which their hopes 
and aims have become identified. But when the questioning of these 
fundamental principles is (not an occasional disease, but) the habitual 
condition of the body politic ; and when all the violent animosities are 
called forth, which spring naturally from such a situation, the state is 
virtually in a position of civil war ; and can never long remain free 
from it in act and fact. 

" The third essential condition, which has existed in all durable politi- 
cal societies, is a strong and active principle of nationality. We need 
scarcely say that we do not mean a senseless antipathy to foreigners ; 
or a cherishing of absurd peculiarities because they are national ; or a 
refusal to adopt what has been found good by other countries. In all 
these senses, the nations which have had the strongest national spirit 
have had the least nationality. We mean a principle of sympathy, not 
of hostility ; of union, not of separation. We mean a feeling of com- 
mon interest among those who live under the same government, and 
are contained within the same natural or historical boundaries. We 
mean, that one part of the community shall not consider themselves as 
foreigners with regard to another part; that they shall cherish the tie 
which holds them together ; shall feel that they are one people, that 
their lot is cast together, that evil to any of their fellow-countrymen is 
evil to themselves, and that they cannot selfishly free themselves from 
their share of any common inconvenience by severing the connexion. 
How strong this feeling was in the ancient commonwealths every one 
knows. How happily Rome, in spite of all her tyranny, succeeded 
in establishing the feeling of a common country among the provinces 
of her vast and divided empire, will appear when any one who has 
given due attention to the subject shall take the trouble to point it out. 
In modem times the countries which have had that feeling in the 
strongest degree have been the most powerful countries ; England, 
France, and, in proportion to their territory and resources, Holland 
and Switzerland ; while England, in her connexion wdth Ireland, is one 
of the most signal examples of the consequences of its absence. Every 
Italian knows why Italy is under a foreign yoke ; every German knows 
what maintains despotism in the Austrian empire ; the evils of Spain 
flow as much from the absence of nationality among the Spaniards 
themselves, as from the presence of it in their relations with foreigners ; 
while the completest illustration of all is afforded by the republics of 
South America, where the parts of one and the same state adhere so 
slightly together, that no sooner does any province think itself ag- 
grieved by the general government than it proclaims itself a separate 
nation." 

§ 6. While the derivative laws of social statics are ascertained by 
analyzing different states of society, and comparing them with one 
another, without regard to the order of their succession ; the considera- 
tion of the successive order is, on the contrary, predominant in the 
study of social dynamics, of which the aim is to obsers'^e and explain 
the sequences of social conditions. This branch of the social science 
would be as complete as it can be made, if every one of the leading 
general circumstances of each generation were traced to its causes in 
the generation immediately preceding. But the consensus is so com- 
plete (especially in modern history), that in the filiation of one gener- 



584 LOGIC OF THE MORAL SCIENCES. 

ation and another, it is the whole which produces the whole, rather 
than any part a part. Little progress therefore can be made in estab- 
lishing the filiation, directly from laws of human nature, without having 
first ascertained the immediate or derivative laws according to which 
social states generate one another as society advances ; the axiomata 
media of General Sociology. 

The empirical laws which are most readily obtained by generaliza- 
tion from history do not amount to this ; they are not the *' middle 
principles" themselves, but only evidence towards the establishment 
of such principles. They consist of certain general tendencies which 
may be perceived in society; a progressive increase of some social 
elements and diminution of others, or a gradual change in the general 
character of certain elements. It is easily seen, for instance, that, as 
society advances, mental tend more and more to prevail over bodily 
qualities, and masses over individuals : that the occupation of all that 
portion of mankind who are not under external restraint is at first 
chiefly military, but society becomes progressively more and more en- 
grossed with productive pursuits, and the military spirit gradually gives 
way to the industrial : to which many other similar truths might easily 
be added. And with generalizations of this description, ordinary in- 
quirers, even of the historical school now predominant on the Conti- 
nent, are satisfied. But these and all such results are still at too gi-eat 
a distance from the elementary laws of human nature on which they 
depend, — too many links intervene, and the concurrence of causes at 
each link is far too complicated, — to enable these propositions to be 
presented as direct corollaries from those elementary principles. They 
have, therefore, in the minds of most inquirers, remained in the state 
of empirical laws, applicable only within the bounds of actual obser- 
vation ; without any means of determining their real limits, and of 
judging whether the changes which have hitherto been in progress 
are destined to continue indefinitely, or to terminate, or even to be 
reversed. 

§ 7. In order to obtain better empirical laws, we must not rest sat- 
isfied with noting the progressive changes which manifest themselves 
in the separate elements of society, and in which nothing is indicated 
but the relation of the fragments of the effect to corresponding frag- 
ments of the cause. It is necessary to combine the statical view of 
social phenomena with the dynamical, considering not only the pro- 
gressive changes of the different elements, but the contemporaneous 
condition of each ; and thus obtain empirically the law of correspond- 
ence not only between the simultaneous states, but between the simul- 
taneous changes, of those elements. This law of correspondence it is, 
which, after being duly verified a priori^ will become the real scien- 
tific derivative law of the development of humanity and human affairs. 

In the difficult process of obsei-vation and comparison which is here* 
required, it would evidently be a very great assistance if it should 
happen to be the fact, that some one element in the complex existence 
of social man is preeminent over all others as the prime agent of the 
social movement. For we could then take the progress of that one 
element as the central chain, to each successive link of which, the cor- 
responding links of all the other progxessions being appended, the suc- 
cession of the facts would by this alone be presented in a kind of spon- 



HISTORICAL METHOD. 585 

taneous order, far more nearly approaching to the real order of their 
filiation than could be obtained by any other merely empirical process. 

Now, the evidence of history and the evidence of human nature 
combine, by a most striking instance of consilience, to show that there 
is really one social element which is thus predominant, and almost 
paramount, among the agents of the social progression. This is, the 
state of the speculative faculties of mankind ; including the nature of 
the speculative beliefs which by any means they have arrived at, con- 
cerning themselves and the world by which they are surrounded. 

It would be a great error, and one very little likely to be committed, 
to assert that speculation, intellectual activity, the pursuit of truth, is 
among the more powerful propensities of human nature, or fills a large 
place in the lives of any, save decidedly exceptional individuals. But 
notwithstanding the relative weakness of this principle among other 
sociological agents, its influence is the main determining cause of the 
social progress ; all the other dispositions of our nature which con- 
tribute to that progress, being dependent upon it for the means of 
accomplishing their share of the work. Thus (to take the most obvious 
case first), the impelling force to most of the improvements effected in 
the arts of life, is the desire of increased material comfort ; but as we 
can only act upon external objects in proportion to our knowledge of 
them, the state of knowledge at any time is the impassable limit of 
the industrial improvements possible at that time ; and the progress of 
industry must follow, and depend upon, the progress of knowledge. 
The same thing may be shown to be true, though it is not quite so 
obvious, of the progress of the fine arts. Further, as the strongest 
propensities of human nature (being the purely selfish ones, and those 
of a sympathetic character which partake most of the nature of selfish- 
ness) evidently tend in themselves to disunite mankind, not to unite 
them— to make them rivals, not confederates; social existence is only 
possible by a disciplining of those more powerful propensities, which 
consists in subordinating them to a common system of opinions. The 
degree of this subordination is the measure of the completeness of the 
social union, and the nature of the common opinions determines its 
kind. But in order that mankind should conform their actions to any 
set of opinions, these opinions must exist, must be believed by them. 
And thus, the state of the speculative faculties, the character of the 
propositions assented to by the intellect, essentially determines the 
moral and political state of the community, as we have already seen 
that it determines the physical. 

These conclusions, deduced from the laws of human nature, are in 
entire accordance with the general facts of history. Every considera- 
ble change historically known to us in the condition of any portion of 
mankind, has been preceded by a change, of proportional extent, in 
the state of their knowledge, or in their prevalent beliefs. As between 
any given state of speculation, and the correlative state of everything 
else, it was almost always the former which first showed itself; though 
the effects, no doubt, reacted potently upon the cause. Every con- 
siderable advance in material civilization has been preceded by an 
advance in knowledge ; and when any great social change has come 
to pass, a great change in the opinions and modes of thinking of society 
had taken place shortly before. Polytheism, Judaism, Christianity, 
Protestantism, the negative philosophy of modem Europe, and its 
4E 



586 LOGIC OF THE MORAL SCIENCES. 

positive science — each of these has been a primary agent in making 
society what it was at each successive period, while society was but 
secondarily instrumental in making them, each of them (so far as causes 
can be assigned for its existence) being mainly an emanation not from 
the practical life of the period, but from the state of belief and thought 
during some time previous. The weakness of the speculative pro- 
pensity has not, therefore, prevented the progress of speculation from 
governing that of society at large ; it has only, and too often, prevented 
progress altogether, where the intellectual progression has come to an 
early stand for want of sufficiently favorable circumstances. 

From this accumulated evidence, we are justified in concluding, that 
the order of human progression in all respects will be a corollary dedu- 
cible from the order of progression in the intellectual convictions of 
mankind, that is, from the law of the successive transformations of 
religion and science. The question remains, whether this law can be 
determined ; at first from history as an empirical law, then converted 
into a scientific theorem by deducing it d priori from the principles of 
human nature. As the progress of knowledge and the changes in the 
opinions of mankind are very slow, and manifest themselves in a well- 
defined manner only at long intervals ; it cannot be expected that the 
general order of sequence should be discoverable from the examination 
of less than a very considerable part of the duration of the social 
progress. It is necessary to take into consideration the whole of past 
time, from the first recorded condition of the human race ; and it is 
probable that all the terms of the series already past were indispensable 
to the operation ; that the memorable phenomena of the last generation, 
and even those of the present, were necessary to manifest the law, and 
that consequently the Science of History has only become possible in 
cur own time. 

§ 8. The investigation which I have thus endeavored to characterize, 
has been systematically attempted, up to the present time, by M. Comte 
alone. It is not here that a critical examination can be undertaken or 
the results of his labors ; which besides are as yet, comparatively speak- 
ing, only in their commencement. But his works are the only source 
to which the reader can resort for practical exemplification of the study 
of social phenomena on the true principles of the Historical Method. 
Of that method I do not hesitate to pronounce them a model : what is 
the value of his conclusions is another question, and one on which this 
is not the place to decide. 

I cannot, however, omit to mention one important generalization, 
which he regards as the fundamental law of the progress of human 
knowledge. Speculation he conceives to have, on every subject of 
human inquiry, three successive stages ; in the first of which it tends 
to explain the phenomena by supernatural agencies, in the second by 
metaphvsical abstractions, and in the third or final state confines itself 
to ascertaining their laws of succession and similitude. This general- 
ization appears to me to have that high degree of scientific evidence, 
which is derived from the concurrence of the indications of history 
with the probabilities derived from the constitution of the human mind. 
Nor could it be easily conceived, from the mere enunciation of such a 
proposition, what a flood of light it lets in upon the whole course of 
history ; when its consequences are traced, by connecting with each of 



HISTORICAL METHOD. 587 

the three states of human intellect which it distinguishes, and with each 
successive modification of those three states, the correlative condition 
of all other social phenomena. 

But whatever decision competent judges may pronounce on the 
results arrived at by any individual inquirer, the method has been found 
by which an indefinite number of the derivative laws both of social 
order and of social progress may in time be ascertained. By the aid 
of these we may hereafter succeed not only in looking far forward into 
the future history of the human race, but in determining what artificial 
means may be used, and to what extent, to accelerate the natural pro- 
gress in so far as it is beneficial ; to compensate for whatever may be 
its inherent inconveniences or disadvantages ; and to guard against the 
dangers or accidents to which our species is exposed from the neces- 
sary incidents of its progression. Such practical instructions, founded 
on the highest branch of speculative sociology, will form the noblest 
and most beneficial portion of the Political Art. 

That of this science and art even the foundations are but beginning 
to be laid, is sufficiently evident. But the most powerful and accom- 
plished minds of the present age are fairly turning themselves towards 
that object, and it is the point towards which the speculative tenden- 
cies of mankind have now for some time been converging. For the 
first time, it has become the aim of the greatest scientific thinkers to 
connect by theories the facts of universal history : for the first time it 
is acknowledged, that no social doctrine is of any value unless it can 
explain the whole and every part of history, so far as the data exist ; 
and that a Philosophy of History is at once the verification, and the 
initial form, of the Philosophy of the Progress of Society. 

If the endeavors now making in all the more cultivated nations, and 
beginning to be made even in England (generally the last to adopt 
whatever does not originate wdth herself), for the construction of a 
Philosophy of History, shall be directed and controlled by those views 
of the nature of sociological evidence which I have attempted to state, 
but which hitherto are to my knowledge exemplified nowhere but in 
the writings of M. Comte ; they cannot fail to give birth to a sociologi- 
cal system widely removed from the vague and conjectural character 
of all former attempts, and worthy to take its place, at last, among 
established sciences. When this time shall come, no important branch 
of human affairs will be any longer abandoned to empiricism and un- 
scientific surmise : the circle of human knowledge will be complete, 
and it can only thereafter receive further enlargement by perpetual 
expansion from within. 



588 LOGIC OF THE MORAL SCIENCES. 

CHAPTER XI. 

OF THE LOGIC OF PRACTICE, OR ART ; INCLUDING MORALITY AND POLICY. 

§ 1. In the preceding chapters we have endeavored to characterize 
the present state of those among the branches of knoM^ledge called 
Moral, which are sciences in the only proper sense of the term, that 
is, inquiries into the course of nature. It is customary, however, to 
include under the term moral knowledge, and even (though improper- 
ly) under that of moral science, an inquiry the results of which do not 
express themselves in the indicative, but in the imperative mood, or in 
periphrases equivalent to it ; what is called the knowledge of duties ; 
practical ethics, or morality. 

Now, the imperative mood is the characteristic of Art, as distin- 
guished from Science. Whatever speaks in rules or precepts, not in 
assertions respecting matters of fact, is art ; and ethics, or morality, is 
properly a portion of the art corresponding to the sciences of human 
nature and society : the remainder consisting of prudence or policy, and 
the art of education. 

The Method, therefore, of Ethics, can be no other than that of Art, 
or Practice, in general : and the portion yet uncompleted, of the task 
which we proposed to ourselves in the concluding Book, is to charac- 
terize the general Method of Art, as distinguished from Science. 

§ 2. In all branches of practical business, there are cases in which 
an individual is bound to conform his practice to a pre-established rule, 
while there are others in which it is part of his task to find or construct 
the rule by which he is to govern his conduct. The first, for example, 
is the case of a judge, under a definite written code. The judge is not 
called upon to determine what course would be intrinsically the most 
advisable in the particular case in hand, but only within what rule of 
law it falls ; what the legislator has commanded to be done in the kind 
of case, and must therefore be presumed to have intended in the in- 
dividual case. The method must here be wholly and exclusively one 
of ratiocination or syllogism ; and the process is obviously, what in our 
analysis of the syllogism we showed that ail ratiocination is, namely, 
the interpretation of a formula. 

In order that an illustration of the opposite case may be taken from 
the same class of subjects as the former, we will suppose, in contrast 
with the situation of the judge, the position of a legislator. As the 
judge has laws for his guidance, so the legislator has rules, and maxims 
of policy ; but it would be a manifest error to suppose that the legis- 
lator is bound by these maxims, in the same manner as the judge is 
bound by the laws, and that all he has to do is to argue down from 
them to the particular case, as the judge does from the laws. The legis- 
lator is bound to take into consideration the reason or grounds of the 
maxim ; the judge has nothing to do with those of the law, except so 
far as a consideration of them may throw light upon the intention of 
the law-maker, where his words have left it doubtful. To the judge, 
the rule, once positively ascertained, is final ; but the legislator, or 
other practitioner, who goes by rules rather than by their reasons, like 



LOGIC OF PRACTICE, OR ART. 589 

the old-fasliioned German tacticians who were vanquished by Napoleon, 
or the physician who preferred that his patients should die by rule 
rather than recover contrary to it, is rightly judged to be a mere ped- 
ant, and the slave of his formulas. 

Now, the reasons of a maxim of policy, or of any other rule of art, 
can be no other than the theorems of the corresponding science. 

The relation in which rules of art stand to doctrines of science may 
be thus characterized. The art proposes to itself an end to be at- 
tained, defines the end, and hands it over to the science. The science 
receives it, considers it as a phenomenon or effect to be studied, and 
having investigated its causes and conditions, sends it back to Art with 
a theorem of the combinations of circumstances by which it could be 
produced. Art then examines these combinations of circumstances, 
and according as any of them are or are not in human power, pro- 
nounces the end attainable or not. The only one of the premisses, 
therefore, which Art supplies, is the original major premiss, which as- 
serts that the attainment of the given end is desirable. Science then 
lends to Art the proposition (obtained by a series of inductions or 
of deductions) that the performance of certain actions will attain the 
end. From these premisses Art concludes that the performance of 
these actions is desirable, and finding it also practicable, converts the 
theorem into a rule or precept. 

§ 3. It deserves particular notice, that the theorem or speculative 
truth is not ripe for being turned into a precept, until all that part of 
the operation which belongs to science has been completely performed. 
Suppose that we have completed the scientific process only up to a 
certain point ; have discovered that a particular cause will produce 
the desired effect, but not ascertained all the negative conditions which 
are necessary, that is, all the circumstances which, if present, would 
prevent its production. If, in this imperfect state of the scientific the- 
ory, we attempt to frame a rule of art, we perform that operation 
prematurely. Whenever any counteracting cause, overlooked by the 
theorem, takes place, the rule will be at fault : we shall employ the 
means and the end will not follow. No arguing from or about the 
rule itself will then help us through the difficulty : there is nothing for 
it but to turn back and finish the scientific process which should have 
preceded the formation of the rule. We must reopen the investigation, 
to inquire into the remainder of the conditions upon which the effect 
depends ; and only after we have ascertained the whole of these, are 
we prepared to transform the completed law of the effect into a pre- 
cept, in which those circumstances or combinations of circumstances 
which the science exhibits as conditions, are prescribed as means. 

It is true that, for the sake of convenience, rules must be formed 
from something less than this ideally perfect theory ; in the fb'st place, 
because the theory can seldom be made ideally perfect ; and next, 
because, if all the counteracting contingencies, whether of fi'equent or 
of rare occurrence, were included, the rules would be too cumbrous to 
be apprehended and remembered by ordinary capacities, on the com- 
mon occasions of life. The rules of art do not attempt to comprise more 
conditions than require to be attended to in ordinary cases, and are 
therefore always imperfect. In the manual arts, where the requisite 
conditions are not numerous, and where those which the rules do not 



690 LOGIC OF THE MORAL SCIEXCES. 

Specify, are generally either plain to common observation or speed- 
ily learnt from practice, rules may be safely acted upon by persons 
who know nothing more than the rule. But in the complicated affairs 
of life, and still more in those of states and societies, rules cannot be 
relied on, without constantly referring back to the scientific laws on 
which they are founded. To know what are the practical contingen- 
cies which require a modification of the rule, or which are altogether 
exceptions to it, is to know what combinations of circumstances would 
interfere with, or entirely counteract, the consequences of those laws : 
and this can only be learnt by a reference to the theoretical grounds 
of the rule. 

By a wise practitioner, therefore, rules of conduct will only be con- 
sidered as provisional. Being made for the most numerous cases, or 
for those of most ordinary occurrence, they point out the manner in 
which it will be least perilous to act^ where time or means do not exist 
for analyzing the actual circumstances of the case, or where for any 
reason we cannot trust our judgment in estimating them. But they do 
not at all supersede the propriety of going through (when circum- 
stances permit) the scientific process requisite for framing a rule from 
the data of the particular case before us. At the same time, the com- 
mon rule may very properly serve as an admonition, that a certain 
mode of action has been found by ourselves and others to succeed in 
the cases of most common occurrence ; so that if it be unsuitable in the 
case in hand, the reason of its being so will be likely to arise from 
some unusual circumstance. 

§ 4. The error is therefore apparent, of those who would deduce the 
line of conduct proper to particular cases, from supposed universal 
practical maxims ; overlooking the necessity of constantly referring 
back to the principles of the speculative science, in order to be sure of 
attaining even the specific end which the rules have in view. How 
much gieater still, then, must the error be, of setting up such unbend- 
ing principles, not merely as universal rules for attaining a given end, 
but as rules of conduct generally ; without regard to the possibility, 
not only that some modifying cause may prevent the attainment of 
the given end by the means which the rule prescribes, but that success 
itself may conflict with some other end, which may possibly chance to 
be more desirable. 

This is the habitual error of many of the political speculators whom 
I have characterized as the geometrical school ; especially in France, 
where ratiocination from rules of practice forms the staple commodity 
of journalism and political oratory; a misapprehension of the functions 
of Deduction which has brought much discredit, in the estimation of 
foreigners, upon the spirit of generalization so honorably characteristic 
of the French mind. The common-places of politics, in France, are 
large and sweeping practical maxims, from which as ultimate premisses 
men reason downwards to particular applications, and this they call 
being logical and consistent. For instance, they are perpetually ar- 
guing that such and such a measure ought to be adopted, because it is 
a consequence of the principle on which the form of government is 
founded ; of the principle of legitimacy, or the principle of the sove- 
reignty of the people. To which it may be answered, that if these be 
really practical principles, they must rest upon speculative grounds j 



LOGIC OF PRACTICE, OR ART. 591 

the sovereignty of the people (for example) must be a right foundation 
for government, because a government thus constituted tends to pro- 
duce certain beneficial effects. Inasmuch, however, as no government 
produces all possible beneficial effects, but all are attended w^ith more 
or fewer inconveniences; and since these cannot be combated by 
means drawn from the very causes which produce them ; it would be 
often a much stronger recommendation of some practical arrangement, 
that it does not follow from what is called the general principle of the 
government, than that it does. Under a government of legitimacy, the 
presumption is far rather in favor of institutions of popular origin ; and 
in a democracy, in favor of arrangements tending to check the impetus 
of popular will. The line of argumentation so commonly mistaken in 
France for political philosophy, tends to the practical conclusion that 
we should exert our utmost efforts to aggravate, instead of alleviating, 
whatever are the characteristic imperfections of the system of institu- 
tions which we prefer, or under which we happen to live. 

§ 5. The Logic of Art (it appears from all that has now been said) 
consists essentially of this one principle, that inquiry and discussion 
should take place on the field of science alone. The rules of art are 
required to conform to the conclusions of science, not to principles or 
premisses of its own. 

An Art, or a body of Art, consists of the rules, together with as 
much of the speculative propositions as comprises the justification of 
those rules. The complete art of any matter, includes a selection of 
such a portion from the science, as is necessary to show on what con- 
ditions the effects, which the art aims at producing, depend. And Art 
in general, consists of the truths of Science, arranged in the most con- 
venient order for practice, instead of the order which is the most con- 
venient for thought. Science groups and arranges its truths so as to 
enable us to take in at one view as much as possible of the general order 
of the universe. Art, though it must assume the same general laws, 
follows them only into such of their detailed consequences as have led 
to the formation of rules of conduct; and brings together from parts of 
the field of science most remote from one another, the truths relating 
to the production of the different and heterogeneous conditions neces- 
sary to each effect which the exigencies of practical life require to be 
produced. 

On this natural difference between the order of the propositions of 
Science and those of Art (science following one cause to its various 
effects, while art traces one effect to its multiplied and diversified 
causes and conditions), a principle may be grounded, which has been 
suggested with his usual sagacity, but not dwelt upon or accompanied 
with the necessary explanations, by M. Comte. It is, that there ought 
to be a set of intermediate scientific truths, derived from the higher 
generalities of science, and destined to serve as the generalia or first 
principles of the various arts. The scientific operation of fi'aming 
these intermediate principles, M. Comte considers as one of those re- 
sults of philosophy which are reserved for futurity. The only com- 
plete example which he can point out as actually realized, and which 
can be held up as a type to be imitated in more important matters, is 
the general theory of the art of Descriptive Geometiy, as conceived by 
M. Monge. It is not, however, difficult to understand what the nature 



69.2 LOGIC OF THE MORAL SCIENCES. 

of these intermediate general principles must be. After framing the 
most comprehensive possible conception of the end to be aimed at, that 
is, of the effect to be produced, and determining in the same compre- 
hensive manner the set of conditions on v^^hich that effect depends; 
there remains to be taken, a general survey of the resources which can 
be commanded for realizing this set of conditions ; and when the result 
of this survey has been embodied in the fewest and most extensive 
propositions possible, those propositions will express the general rela- 
tion between the available means and the end, and from them, there- 
fore, the practical methods of the art will follow as corollaries. But 
the further development of this idea may be left to those who have the 
means and on whom the special office devolves, of practically apply- 
ing it for the purpose of constructing, on scientific principles, the gen- 
eral theories of the different arts.* 

§ 6. After these observations on the Logic of Practice in general, 
little needs here be said of that department of Practice which 4ias 
received the name of Morality ; since it forms no part of the appro- 
priate object of this work to discuss how far morality depends, like 
other arts, upon the consideration of means and ends, and how far, if 
at all, upon anything else. 

This, however, may be said ; that questions of practical morality 
are partly similar to those which are to be decided by a judge, and 
partly to those which have to be solved by a legislator or adminis- 
trator. In some things our conduct ought to conform itself to a pre- 
scribed rule ; in others, it is to be guided by the best judgment which 
can be formed of the merits of the particular case. 

Without entering into the disputed questions respecting the founda- 
tion of morality, we may consider as a conclusion following alike from 
all systems of ethics, that, in a certain description of cases at least, 
morality consists in the simple observance of a rule. The cases in 
question are those in which, although any rule which can be formed is 
probably (as we remarked on maxims of policy) more or less imper- 
lectly adapted to a portion of the cases which it comprises, there is 
still a necessity that some rule, of a nature simple enough to be easily 
understood and remembered, should not only be laid down for 
guidance, but universally observed, in order that the various persons 
concerned may know what they have to expect : the inconvenience of 
uncertainty on their part being a gi'eater evil than that which may 
possibly arise, in a minority of cases, from the imperfect adaptation of 
the rule to those cases. 

Such, for example, is the rule of veracity; that of not infringing the 
legal rights of others ; and so forth : concerning which it is obvious 
that although many cases exist in which a deviation from the rule 
would in the particular case produce more good than evil, it is neces- 
sary for general security, either that the rules should be inflexibly 
observed, or that the license of deviating from them, if such be ever 
permitted, should be confined to definite classes of cases, and of a very 
peculiar and extreme nature. 

* A systematic treatise on the general means which man possesses of acting upon na- 
ture, is one of the works which M. Comte holds out the hope of his producing at some 
future time ; and no subject affords a larger scope for the faculties of so original and com- 
prehensive a mind. 



LOGIC OF PRACTICE, OR ART. 593 

With respect, therefore, to these cases, practical ethics must, like 
the administration of positive law, follow a method strictly and directly 
ratiocinative : whether the rules themselves are obtained, like those 
of other arts, from a scientific consideration of tendencies, or are 
referred to the authority of intuitive consciousness or express reve- 
lation. 

In cases, however, in which there does not exist a necessity for a 
common rule, to be acknowledged and relied upon as the basis of 
social life ; where we are at liberty to inquire what is the most moral 
course under the particular circumstances of the case, without refer- 
ence to the authorized expectations of other people ; there the Method 
of Ethics cannot differ materially from the method of every other 
department of practice. Like other arts, it sets out from a general 
principle, or original major premiss, enunciative of its particular end: 
whether that end be the greatest possible happiness, as is contended 
by some, or the conformity of our character to ideal perfection 
according to some particular standard, as others hold. But on this as 
on other subjects, when the end has been laid dovm, it belongs to 
Science to inquire what are the kinds of actions by which this end, 
this happiness or this perfection of character, is capable of being 
realized. When Science has framed propositions, which are the com- 
pleted expression of the whole of the conditions necessary to the 
desired end, these are handed over to Art, which has nothing further 
to do but to transform them into coiTosponding rules of conduct. 

§ 7. With these remarks we must close this summary view of the 
application of the general logic of scientific inquiry to the moral and 
social departments of science. Notwithstanding the extreme gener- 
ality of the principles of method which I have laid down (a generality 
which I trust is not, in this instance, synonymous with vagueness), I 
have indulged the hope that to some of those on whom the task will 
devolve of bringing those most important of all sciences into a more 
satisfactory state, these observations may be useful, both in removing 
erroneous and in clearing up the true conceptions of the means by 
which, on subjects of so high a degree of complication, truth can be 
attained. Should this have been accomplished, something not unim- 
portant will have been contributed towards what is probably destined 
to be the great intellectual achievement of the next two or three gen- 
erations of European thinkers : although, for the realization of thr 
important results, of which it has been thus indirectly attempted io 
facilitate the attainment, mankind must ever be principally indebted 
to the genius and industry of ethical and sociological philosophers, 
whether of the present or of future times. 



INDEX, 



A. 

Abstract names, page 18 ; may be changed 
to concrete, 71. 

Abstraction, 389. 

Accidens, 81, 84, 90. 

Accidental propositions, 7i. 

Actions, 36, 522. 

Adjectives, real names, 16. 

/Equipollency of assertions, 108. 

^Equivocal terms, 30. 

Agent and patient, 201. 

Agreement, method of, 224, 238 ; its im- 
perfection, 2.'31, 308, 313. 

Algebra, 164, 177, n., 429. 

Ambiguity, 25, 53. 

Analogy, 30, 47, 332 ; its value, 335 ; false 
analogy, 491. 

Analysis, 7, 92 ; chemical, 255. 

Antecedent, 310; distinct from cause, 304. 

Approximate generalizations, 351, 529, 
541. 

A priori and a postci-iori, 259, 490, 546. 

A priori truths, the argument for them an- 
swered, 154. 

Archimedes, 466. 

Aristotelian logic, 2. 

Aristotle, his categories, 31 ; predicables, 
81 ; doctrine of motion, 394, 467 ; of 
the lever, 395, n. 

Arithmetic, 164. 

Arnott, Dr., his treatment of inflamma- 
tion, 284, 71. 

Art and Science, 2, 588, 591. 

Assertions, 107, 360. 

Association, laws of, 159, 285, 419, 532; 
as affecting the meaning of words, 104, 
407, 417. 

Assumptions, at the foundation of deduct- 
ive reasoning, 169. 

Astronomy, 575 ; ilhistrates the process of 
induction, 173 ; its progress, 528. 

Attributes, 19, 37, 43, 49, 67, 93; connot- 
ed, 21, 80; quality, 42; of mind, 50. 

Axioms of reasoning, 120, 170; arc exper- 
imental truths, 1.52, 163; of geometry, 
151, 370; of mechanics, 160, 162, n.; 
of arithmetic, 168. 

Axiomata media, their value, 544, 584. 



Bacon, his description of logic, 6; his serv- 
ices to science, 187, 544; his method 
now reversed, 286; of induction, 468; 
false metaphor, AdQ ; on axiomata me- 
dia, 544. 



Being, 32, 53. 

BelleJ, object of, 67 ; superstitions, 457. 

Bentham, on classification of laws, 447 ; 
his school of politics, 558. 

Berkeley, theory of vision, 4 ; argument 
for universal mind, 507 ; his opponents, 
517. 

Bias in forming opinions, 450. 

Body, 38, 41. 

Botany, its descriptive terms, 423, 442. 

Brown, T., theory of ratiocination, 135; 
on the " sufficient reason," 465 ; muscu- 
lar sense; 533. 

C. 

Calculus, 368. 

Carlyle, his nletaphor concerning strength, 
495. 

Carpenter, W. B., his Physiology, 213, n. 

Categorematic terms, 16. 

Categories, 31, 52. 

Causation, law of, 196, 271 ; derived from 
experience, 197; its evidence, 337, 339; 
its limit, 342 ; applied to human will, 
522. 

Cause, 38, 44, 194; how far the object of 
human study, 196, 209; according to 
the schoolmen, 199 ; is the sum of con- 
ditions, 200 ; permanent, 206 ; the word 
should not be discarded, 210 ; plurality, 
250 ; proximate or remote, 300. 

Certainty of mathematical reasoning, 148, 
169. 

Chance, 312, 340; not the negation of 
law, 313 ; its elimination, 317 ; calcula- 
tion, 319, 322 ; applies not to ignorance, 
but to partial knowledge, 320, 325. 

Character, 525 ; laws of its formation, 540 ; 
national, 541. 

Chemistry , xX.?, present condition, 145; its 
combinations, 161 ; aim, 214, 255; no- 
menclature, 441 ; method, applied to 
social science, 550. 

Church, 504. 

Cicero, on the Epicureans, 474, 513; 
Stoics, 494, 505. 

Circumstances, selection of, 217,260: in- 
fluence, 525, 581. 

Civilization, 402, 425. 

Class defined, 18, 63, 69, «0, 117. 

Classification, 432 ; loose, 25 ; nature of, 
80 ; natural and artificial, 83, 434 ; on 
various principles, 88, 435 ; groups and 
series, 443. 

Coincidence, 314, 326. 



596 



INDEX. 



Coleridge on the value of language, 413; 
distinction between inconceivable and 
unimaginable, 462 ; on causality, 474 ; 
" finding level," 501 ; extract from, 476 ; 

Collective names, distinct from general, 18. 

Colligation of facts, 178, 182, 388. 

Colonization, 500. 

Comparison, 392. 

Composition of causes, 210, 234, 271, 302, 
307, 316; of two sorts, 212, 254, 257; 
in social science, 550. 

Comte, A., his positive philosophy, 172, 
587 ; on imperfect generalization, 181 ; 
doctrine of cause, 209, 341; physiology, 
266 ; color, 289 ; hypotheses, 295, 336 ; 
verification of the nebular hypothesis, 
298 ; mathematics, 369 ; classification, 
433 ; zoological systems, 435, 447 ; 
groups and series, 443 ; confusion of 
mental science with physiology, 531; 
sociology, 561, 578; political economy, 
567; signs of progress, 576; three stages 
of speculation, 586 ; principles for prac- 
tice, 591. 

Conception, 389 ; a step in induction, 178, 
388, 396; even when imperfect, 181. 

Conceptualist doctrine, 60, 389. 

Concomitant variations, 233, 241. 267 ; ap- 
plied to social science, 554. 

Concrete names, 18; are connotative, 20. 

Condillac, 19, 362. 

Conditions, as distinct from cause, 197. 

Connotation, 20, 68 ; gives the significa- 
tion, 23, 62, 92, 403, 428; false mean- 
ing of, 26, n. ; not regarded in some dis- 
cussions, 410 ; changes of, 25, 407, 416. 

Connotative names, 20, 24 ; many-word- 
ed, 22. 

Consciousness, 4, 34, 42, 107. 

Consensus, 564, 583. 

Consilience, 546, 585. 

Conversion of propositions, 109 ; of prem- 
isses, 114. 

Convertible, 95. 

Copernicus, arguments of his opponents, 
478, 483 ; in his favor, 494. 

Copula, 12 ; does not imply existence, 53, 
76. 

Correlative names, 28. 

Cousin, doctrine of substance, 40, n. ; of 
cause and effect, 473 ; of punishment, 
481. 

Cum hoc, ergo propter hoc, 490. 

Cumulative effects, 329. 

Cuvier, his classification, 80. 

D. 

Darwin en Ideas, 473. 

Deduction, 1.37, 141, 144; its especial 
value, 254, 270, 286, 555; its method, 
induction, 264; ratiocination, 267; ver- 
ification, 269, 545 ; applied to mental 
science, 540; to social, 555, 561. 

Definition, 77 ; how possible, 1 ; theory 
of, 91, 95; imperfect, 94; essential or 
accidental, 94; scientific, 96, 99, 101; 



(in geometry, 148, 164, 370 ;) of names 
and things, 98, 103 ; importance, 105, 
404. 

Demonstration, 148. 

Demonstrative truths, 101. 

Denominative, a term for connotative, 21. 

Derivative laws, 286, 327. 

Descartes, doctrine of co-ordinates, 147 ; 
vortices, 157; method, 191, 460; argu- 
ment against Newton, 472 ; cause and 
effect, 474; for the being of God, 505. 

Description, 94, 95. 

Dew, Wells's theory of, 242. 

Diamond, properties of, 344. 

Dictum de omni et de nullo, 64, 117. 

Difference, method of, 225, 238, 241 ; ap- 
plied to social science, 552. 

Differentia, 81, 86. 

Disbelief, gi'ounds of, 374. 

Distributed terms, 58. 

Disturbing force, 259. 

E. 

Education, 581. 

Effects, how far proportional to causes, 
214; complicated, 254 ; progressive, 
300 ; cumulative, 329. 

Egyptian science, 379. 

Electricity, 219, 240, 283, 425; induced, 
240. 

Emotion, 37 ; fallacious appeal to, 516. 

Empirical laws, 236, 305, 537, 545, 576; 
degree of certainty. 349, 488; statistics, 
571. 

Empirical method, 261 ; still used in chem- 
istry, 145; applied to social science, 550. 

Entity, 32. 

Enumeration, simple, as ground of induc- 
tion, 186, 235,347, 478, 487.; of law of 
causation, 339 ; of mathematical axioms, 
364. 

Epicureans, 474, 513. 

Error, its sources, 450. 

Essence, 32, 75, 82, 86, 95, 512. 

Essential propositions, 74, 77, 78. 

Ethics, its method is that of art, not of 
science, 588, 593. 

Ethology, 537, 543; (political, 569.) 

Etymology, a source of fallacy, 503. 

Euler, multiplication of negative quanti- 
ties, 514. 

Existence, 32, 53, 360. 

Experience, the ground of mathematical 
evidence, 152, 161 ; maxims of, 411. 

Experiment, compared with observation, 
218; four methods, 222; agreement, 224, 
238, 251, 308, 313 ; difference, 225, 238, 
241 ; (joint or indirect, 229, 239, 253 ;) 
residues, 230, 248;- concomitant varia 
lions, 233, 241 ; in some cases impossible, 
219, 263, 265; in mental science, 219, 
540; in social, 551. 

Expetimenta fructifera et lucifera, 547. 

Experimental stage of science, 144. 

Explanation of laws, 271 ; (by separate 
laws, 271; intermediate laws, 272 ; sub- 



INDEX. 



597 



sumption, 274 ;) not accounting for them, 
277 ; limits, 286. 



Fallacies, 448; classification, 451, 454; 
of simple inspection (or k prioi-i), 456 ; 
of observation, 475 ; of generalization, 
485 ; of ratiocination, 498 ; of confu- 
sion, 502 ; of composition, 510; ignora- 
tio elenchi, 516. 

Faraday, experiments in electricity, 240, 
283. 

Fatalism, not involved in docti'ine of ne- 
cessity, 524 ; result of circumstances, 
581. 

Feeling, includes sensation, einotion, and 
thought, 34; (and volition, 36 ;) bodily 
or mental, 35. 

Felony, 25, n. 

" Fortune favors fools,'''' 476. 

Free-trade, 482, 572. 

Free-will, 522, 525. 

Fundamentum relationis, 45, 332. 

Functions, 368. 

G. 

General names, 17, 399, 401; constitute 
classes, 63, 80, 83. 

General propositions, not ordinarily used 
in reasoning, 126 ; their value, 132. 

Generalization, 273, 341, 416, 489, 538; 
a process of inference, 124; imperfect, 
it3 use in science, 181 ; approximate, 
351 ; scientific value, 358. 

Gentleman, growth of meaning of the 
word, 414. 

Genus, 81, 84. 

Geology, method of proof, 298. 

Geometry, its postulates, 102, 466 ; reason- 
ing, 142, 148, 158, 370 ; its axioms de 
rived from observation, 152 ; universal 
application, 194; simple processes, 372; 
method, applied to social science, 555. 

Graham, Prof., law of the permeation of 
gases, 283. 

Gravity, 157, 461, 472; (specific, 511.) 

Greeks, 53, 217, 431, 466, 497. 

H. 

Harlley, 533. 

Heat, definition of, 97. 

Herschel, Sir J., doctrine of axioms, 163, 
n. ; his Discourse on Natural Philoso- 
phy, 172, 242, 248. 

Heteropathic laws, 213, 256. 

Historical method, applied to sociology, 
574. 

History, science and philosophy of, 586, 
587. 

Hohbes, doctrine of names, 15 ; of propo- 
sitions, 61, 119"; makes tnith arbitrary, 
65, 99 ; compared with Locke, 75, n. ; 
on the social compact, 515, 557. 

Human nature, may be a subject of sci- 
ence, 527, 543 ; society included in it, 
548. 



Hypotheses, necessary in mathematical 
reasoning, 150, 168 ; in induction, 180, 
290, 294; different classes, 291; from 
analogy, 336 ; involved in scientific pi'op- 
ositions, 431 ; in narration, 483. 



Idealism, 40. 

Ideas, 13, 60, 560. 

Identity, 47. 

Ignoratio elenchi, 516. 

Imaginary objects, 34; remedies, 480. 

Imaginary laws, 479. 

Imagination, its connection with associa- 
tion, 285. 

Impossibility , its limits, 379. 

Imposture, 476. 

Inconceivableness, no proof of falsehood, 
156, 161, 338, 461 ; is violation of an ax- 
iom, 163, n. 

Individual names, 17, 21, 400 ; sometimes 
connotative, 22. 

Induction, 111, 137, 171, 183; complica- 
ted, 138 ; belongs to every science, 164; 
importance, 171; defined, 172; improp- 
er, 175 ; incorrect, 187 ; mathematical, 
176 ; by simple enumeration, 186 ; its 
true type, 192; four methods, 222 (see 
Experiment)', of particulars, 398. 

Inertia, reasons given for it, 464. 

Inference, 4, 7, 108; apparent, 108; real, 
111,398. 

Infima species, 82, 85, 350, 427, 436. 

Infinite, ambiguity of the word, 508. 

Intellect, its relative prominence and pow- 
er, 585. 

Interest, not the only motive, 559, 570. 

Intermixture of effects, 254; of laws, 564. 

Intuition, 3, 4; its truths, 4; not subjects 
of logic, 5, 485. 

.1. 
Judgment, implied in propositions, 59 ; 
mistaken for sensation, 483, n. 

K. 

Kant, doctrine of substance, 40. 

Kepler, induction of the motions of the 

planets, 177, 180; of their number, 494; 

hypotheses, 293, 391 ; laws, 545. 



Landed proprietor in England and Ben- 
gal, 417. 

Language, an instrument of thinking, 11 ; 
changes of meaning, 25, 407, 416 ; 
source of ambiguity, 53, 104, 420; its 
preservative value, 409, 413 ; philosoph- 
ical, 421; technical, 422; (its value, 
424 ; its perfection, 429 ;) symbolical, 
429; Greek and German, 431. 

Laplace, his nebular hypothesis, 298 ; doc- 
trine of chance, 319 ; of probabilities, 
380. 

Latos of 'Nature, 189 ; their explanation, 
271, 286 ; deinvative or ultimate, 286. 



598 



INTDEX. 



Leibnitz, 460, 463 ; view of Newton's the- 
ory, 157, n., 472; pre-established har- 
mony, 474. 

Liberty and necessity, 207, 521, 525. 

Liebig, theory of poisons, 237 ; conta- 
giousness of chemical action, 277 ; res- 
piration, 280; putrefaction, 282. 

Likeness, 46. 

Linnceus, his terminology, 423 ; system, 
433. 

Locke, his philosophical character, 75, n. ; 
doctrine of essences, 77 ; use of the word 
idea, 78, n. 

Logic, definitions of, 2 ; a science as well 
as art, 2; what it includes, 3, 7, 107,389; 
the science of proof or evidence, 5, 7 ; 
utility, 6, 172; (as to language, 421;) 
distinct from metaphysics, 5, 8, 36, 41, 
360, 456, 484 ; of Names and Proposi- 
tions, 11; o-^ Reasoning, 107; oi Induc- 
tion, 171 ; of Operations Subsidiary , 383; 
oi Fallacies, 448; o^ Moral Science, 519; 
of Morality, 588. 

Loyalty, change of meaning, 415 ; an ele- 
ment in national character, 582. 

M. 

Magnetism, 240, 283, 295, n. 
Malthus, doctrine of population, 517. 
Man, what the name connotes, 20, 24, 1 ^, 

87, 88, 92 ; species, 85 ; definitions, 95. 
Marks, 121, 140, 147, 170, 344. 
Mechanics, 160, 162, 556. 
Medical Science, 547. 
Mercantile theory, 500. 
Metaphor, 495. 
Metaphysics, 87 ; distinct from logic, 5, 8, 

36, 41, 360, 456, 484. (See Mind.) 
Meteorology, 527. 
Method, not to be deteraiined k priori, 

519. (See Experiment.) 

Mill, his analysis of mind, 26, 42, 54, 532. 
Mind, 41, 50; difficulty of its study, 219, 

520, 529 ; its laws, 532, 539. 
Mineralogy, its nomenclature, 442. 
Miracles, according to Brown, 376. 
Money, its two meanings, 503. 
Morality, ground of, 412, 525; logic of, 

588, 592. 
Motion, first law of, 335, 465 ; referred to 

causes, 300, 464; Aristotle's doctrine, 

394. 
Motives, 522, 526. 
Mysticism,AQA. 

N. 

Names, of things, not of ideas, 13, 15; ob- 
jects of study, 14; definition by Hobbes, 
15 ; general and singular, 17, 399 ; 
(proper, 21, 23; many-worded, 22;) 
concrete and abstract, 18 ; connotative 
and non-connotative, 20 ; (changes of 
connotation, 25, 407, 416;) positive and 
negative, 27, 54 ; (privative, 28;) rela- 
tive, 28; univocal and aoquivocal, 30; 
distributed, 58; general, 80; of feelings. 



undefinable, 94 ; instrument of thought, 
397 ; as subsidiary to induction, 398. 

National character, 541, 582. 

Nationality, 583. 

Natural history, 437. 

Nature, 189, 512; its uniformity, the ax- 
iom of induction, 184; course of, 189, 
216; laws, 189,271. 

Necessary truths, 148, 162, 170. 

Necessity, 203, 521, 525 ; statement of the 
doctrine, 207, 522; the name, 523. 

Netoton, his theory, 157, 461, 472; meth- 
od, 292, 545. 

Nomenclature, 426, 441. 

Nominalism, 61, 98, 99, 118. 

Number, 365 ; agency in science, 141, 165, 
367 ; Pythagorean speculations, 493. 

O. 

Objective facts, 52. 

Observation, 383 ; passive or active, 187 ; 

talent of, 216 ; logic of, 385. 
Omens, 458. 

Opposition of propositions, 110. 
Optimism, 475. 

Order of nature, 189, 216; in place, 364. 
Organization, 211, 213, 265, 406, 520; 

laws, 311, 444. 



Pagan, meaning of the word, 415. 

Paronymous terms, 513. 

Particles, parts of names, 16 ; of proposi- 
tions, 55. 

Particulars, used in reasoning, 126, 398. 

Paternal government, 493. 

Pathology, experimental method, 266. 

Perception, 35 ; confounded with judg- 
ment, 483, n. 

Petitio principii, 510. 

Philosophical language, 421. 

Phlogistic theory, 479. 

Phrenology, 295, n., 535. 

Physical method in social science, 561. 

Physiology, 311, 444, 531. 

Plato, investigation of the meaning of 
words, 407 ; of good and evil, 504 ; ar- 
gument for incorporeal substances, 514. 

Plurality of causes, 250, 313. 

Polarity, 391. 

Political economy, 481, 500, 566. 

Political ethology, 569. 

Politico, 263, 547, 590. 

Postulates, 102, 149, 169. 

Practice, distinct from science, 591. 

Predicables, express relations, not facts. 
81. 

Predicate, 12. 

Predication. See Proposition. 

Prediction, an aim of science, 182, 189. 
573. 

Premisses, change of, 499. 

Probability, 380. 

Progress, 575, 587. 

Progressive effects, 300. 

Proof 108. ' 



INDEX. 



599 



Proper names, 21, 23; sometimes conno- 
tative, 22 ; cannot be defined, 91. 

Properties, 83, 344. 

Proposition, 52, 107 ; defined, 12 ; in- 
cludes two objects, 13, &7 ; affirmative 
and negative, 54; simple and complex, 
55 ; categorical and hypothetical, 56 ; 
universal, particular, indefinite, and sin- 
gular, 57 ; import of, 59, 68, 70 ; relates to 
things, not ideas, 60 ; Hobbes's defini- 
tion, 61 ; verbal, 73 ; essential, 78 ; real, 
79, 119. 

Proprktm, 81, 90. 

Proximate kind, 84. 

Psychology, 532; distinct from ethology, 
544. 

Public opinion, influence on rulers, 559. 



Quality, 42. 
Quantity, 48. 



Q. 



R. 



Ratiocination, 111, 117. 

Real propositions, ''9. 

Realism, 99. 

Reason, 87. 

Reasoning, 2, 108, 130; propositions not 
used as ultimate, 79 ; scientific, ground- 
ed on facts, not on definitions, 102; 
fi-om particulars to particulars, 125, 398; 
type of, 136 ; train of, 137. 

Reductio ad absurdum, 169, 498. 

RedMCtion of Syllogisms, 114. 

Reid, on sensation, 473. 

Relation, 28, 44. 

Religion, its evidence, 376; influence, 585. 

Resemblance, 46, 3-61 ; ground of loose 
generalization, 401. 

Residues, method of, 230, 248 ; applied to 
calculation of chance, 318; to social sci- 
ence, 554. 

Resolution of laws, 271. 

Respiration, 280. 

Rhetoric, 3. 

Right, ambiguity of the word, 508. 

Romans, their avoidance of ill omens, 458 ; 
feeling of nationality, 583. 



Sameness and likeness, 47 ; according to 
Whately, 48, n., 506. 

Science, its tendency to become deduct- 
ive, 144 ; how, 146 ; exact or imperfect, 
528, 538, 548 ; its history, 579 ; of hu- 
m"an nature, 520, 527, 543 ; its prospect- 
ive completeness, 587. 

Sensation, 34, 43, 272, 384, 473, 486, 530, 
536. 

Signatures, doctrine of, 471. 

Singular names, 17 ; propositions, 57. 

Social science, its complexity, 547 ; imper- 
fection, 584. (See Sociology.) 

Society, state of, 574. 

Sociology, 561, 570 ; a deductive science, 
563. 



Specialization in meaning of words, 418. 

Species, 81, 84, 88 ; {injima, 82, 85, 350, 
427, 436.) 

Species sensibiles, 472. 

Speculation, its influence and its three 
stages, 586 ; must be the ground of true 
principles of practice, 590. 

Spinosa, 474. 

SpiHtual truths, oscillations of, 411. 

Statistics, 571. 

Stewart, D., on changes of meaning, 104, 
407 ; on mathematical reasoning, 127, 
150 ; on hypothesis in narration, 483. 

Subject, 12, 42. 

Subjective facts, 52, 464. 

Submission, how inculcated, 581. 

Substance, 37, 39, 456 ; body and mind, 
38 ; idealist doctrine, 40 ; general, 75, 
80. 

Substantive secundce, 74, 464. 

SubsJimption of laws, 274. 

Succession, order of, sought by science, 
195. 

Sufficient reason, 465. 

Superstition, 457, 479. 

Syllogism, 2, 64, 108, 112, 430; figures 
and modes, 113; their use, 116, n.; re- 
duction of, 114; is it a process of infer- 
ence? 122; its use, 129; as a process of 
interpretation, 130 ; and a test, 133. 

Symbols, 429. 

Sympathetic powder, 480. 

Syncate gorematic terms, 16. 

Synonyms, why so few, 414. 



Temperament, 535. 

Tendency, a way of stating the action of 

causes, 258. 
Terminology, 426. 
Terms, 7, 11 ; use of, 33. 
Theory, ambiguity of the w^ord, 504; its 

employment, 589. 
Things, 30, 118; summaiy, 51. 
Tidology, 527. 

Transition o^ vaeomngs, 104, 407. 
Truth, known in two ways, 3. 
Type, of reasoning, 136 ; in classification, 

436, 439. 

U. 

Ultimate laws, cannot be fewer than the 
distinguishable feelings, 287. 

Uniformity of nature, the axiom of induc- 
tion, 184 ; what it means, 186 ; of coex- 
istence, 343, 377, 574. 

Universals, 117, 

Universal names, 30. 



Verbal propositions, 73, 78. 
Verification, 269, 293, 545, 562. 
Vico, Scienza Nuova, 575. 
Villain, signification of the word,^ 412. 
Virtue, its various significations, 412. 
Vis viva, 507. 



600 



rNDEX. 



Vision, theory of, 4. 
Volitions, 36, 522, 526. 

W. 

Water, composition of, 309. 

Wells, theory of dew, 242. 

Whately, definition of logic, 2 ; doctrine 
of definition examined, 98 ; of the syllo- 
gism, 123, 131; of induction, 185, 7i.; 
of analogy, 332 ; on fallacies, 455 ; on 
ambiguous middle, 502 ; iiTelevant con- 
clusion, 516. 

Whewdl, his meta.physics, 36 ; view of de- 



monstrative reasoning, 102, 150 ; argu- 
ment for a priori truths, 154; his posi- 
tions reviewed, 153-161 ; doctrine of in- 
duction, 178, 297, 388, 390: of defini- 
tion, 404; technical terms, 422; classi- 
fication, 433, 442 ; type and definition, 
436 ; Greek science, 465 ; imaginary 
laws, 479. 
Will, whether included in law, 207, n., 
521 ; its education, 526. 



Zoology, its classification, 435, 445. 



THE END. 



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